Question 1 (at least 200 words)Collins(p. 490) asserts the fo

Question 1: (at least 200 words)
Collins(p. 490) asserts the following: "Some of the fundamental
social philosophical assumptions about human nature and social
organization made by political and economic theorists, and
embodied in some of our most significant political and
economic institutions, are diametrically opposed to some of the
assumptions about human nature and social organization made
by organization theorists and embodied in a large number of
organizational structures."
What is your reaction to this assertion? What evidence does
Collins present to defend his assessment? For much of the
remainder of the paper, Collins advances the idea that what is
true about government should be true about business--if we like
democratic governments, we have no reason to prefer autocratic
workplaces. To what extent do you agree with Collins'
argument? If you agree, can you offer more support to his
argument (perhaps from personal experience)? If you disagree,
what questions do you have for Collins?
Question 2: (at least 200 words)
On p. 501, Collins mentions many participatory management
practices proposed by communitarians and alludes to the few
proposed by libertarians. Which set of practices appeal to you
more? What specific practices would you like to see in an ideal
world? Do you think it is possible to see widespread workplace
democratization in the United States? Why or why not?
3/31/20
1
Chapter 11

Properties of Stock Options
1
Properties of Stock Options - Goals
• Discuss the factors affecting option prices
• Include the current stock price, strike price, time to maturity,
volatility of the stock price, risk-free interest rate, and paid-out
dividends
• Identify the upper and lower bounds for European- and
American-style option prices
• Introduce the put-call parity
• The optimal early exercise decision
• Consider the effect of dividend payments on
• Upper and lower bounds of option prices, the put-call parity,
and
the early exercise decision
2
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2
Factors Affecting Option Prices - Notation
�: European call option price �: American call option price

�: European put option price �: American put option price
�!: Current stock price �": Stock price at option maturity
�: Strike price �: Dividends that are expected to be paid
during option’s life
�: Life of option �: Risk-free rate for maturity T with
continuously compounding
�: Volatility of the stock price
3
Sensitivity Analysis on Option Prices
※Note that the European call (put) value can be derived as
• � = �!"#�[max(�# − �,0)] (� = �!"#�[max(� − �#,0)])
※The American call (put) value can be derived as
• � = �[�!"$max(�$ − �,0)] (� = �[�!"$max(� − �$,0)]),
• where � is the time point to exercise American options
Factors � � � �
�! + – + –
� – + – +
� ? ? + +
� + + + +
� + – + –
� – + – +
4

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3
Effect of Factors on Option Pricing
• Current stock price �4 ↑
• For both European and American calls, prob. of being ITM
(in-the-money) ↑ and thus call
values ↑
• For both European and American puts, prob. of being ITM ↓(
or probability of being
OTM out-of-money ↑) and thus put values ↓
*� = 50,� = 5%,� = 30%,� = 0,and � = 1
5
• Strike price � ↑
• For both European and American calls, prob. of being ITM ↓
and thus call values ↓
• For both European and American puts, prob. of being ITM ↑
and thus put values ↑
*�% = 50,� = 5%,� = 30%,� = 0,and � = 1
6
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4

• Time to maturity � ↑
• For American options, the holder of the long-life option has
all the exercise
opportunities open to the holder of the short-life option–and
more Þ The long-
life American option must be worth as least as the short-life
American option
• European calls and puts generally (not always) become more
valuable as the time
to expiration increases
*�% = 50,� = 50,� = 5%,� = 30%,and � = 0
7
• For European calls,
• Suppose two European call options, �& and �', on a stock
with the same � and with
different maturity �& and �' (> �&)
• If there is a cash dividends paid in [�&,�'], the stock price
declines on the dividend
payment date so that the short-life call �& could be worth more
than the long-life
call �'
• For deeply ITM European put options, short-life put �! (with
�! time to maturity)

could be worth more than the long-life put �" (with �" time to
maturity)
• Note that the put value can be derived as �!"#�[max(� −
�#,0)]
• Consider an extreme case in which the stock price is close to 0
so that �# can be
almost ignored when calculating payoffs of puts
• The option values of the above two put options are �& =
�!"#!� � − 0 = �!"#!�
and �' = �!"#"� � − 0 = �!"#"� ⇒ �& > �' (inverse
relationship between put
values and �)
8
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5
• Volatility � ↑ (the chance that the stock will perform better or
poorer increases)
• Recall: call options have limited downside risk (the most he
can lose is the price of the
option)à an increase in the volatility (� ↑) increases the
probability of a price increase
à option value ↑
• Recall: put options have limited downside risk risk (the most
he can lose is the price of
the option) à an increase in the volatility (� ↑) increases the

probability of a price
decrease à option value ↑
*�% = 50,� = 50,� = 5%,� = 0,and � = 1
9
• Risk-free rate � ↑
• The expected return of the underlying asset ↑, and the discount
rate ↑ such that the PV
of future CFs ↓
• For calls, the option value ↑ because the higher expected �#
and the higher prob. to be
ITM dominate the effect of lower PVs
• For puts, option value ↓ due to the higher expected �#, the
lower prob. to be ITM, and
the effect of lower PVs
*�% = 50,� = 50,� = 30%,� = 0,and � = 1
10
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6
• Dividend payment ↑
• Dividends have the effect of reducing the stock price on the

ex-dividend date
• For calls, prob. of being ITM ↓ and thus call values ↓
• For puts, prob. of being ITM ↑ and thus put values ↑
0
2
4
6
8
10
0 2 4 6 8 10
Call
option
price, c
Dividends, D
0
2
4
6
8
10
0 2 4 6 8 10

Put
option
price, p
Dividends, D
*�% = 50,� = 50,� = 5%,� = 30%,and � = 1
12
Upper and Lower Bounds for Option Prices
• Some assumptions
• There are no transactions costs
• The tax rate issue is ignored in this chapter
• However, all results in this chapter hold when all trading
profits (net of trading
losses) are subject to the same tax rate
• Borrowing and lending are always possible at the risk-free
interest rate
• There is no dividends payment during the option life
• In the last section of this chapter, this constraint will be
released
13
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7
• Upper bounds for the European and American call and put
• Since both American and European calls grant the holders the
right to buy one share
of a stock for a certain price, the option can never be worth
more than the value of
the stock share today
• An American put grants the holder the right to sell one share
of a stock for � at any
time point, so the option value today can never be worth more
than �
• For a European put, since its payoff at maturity cannot be
worth more than �, it
cannot be worth more than the PV of � today
• An American option is worth at least as much as the
corresponding European option,
so � ≤ � and � ≤ �
Upper bound for call Upper bound for put
American � ≤ �% � ≤ �
European � ≤ �% (� ≤ �) � ≤ ��!"# (� ≤ �)
14
• Lower bounds for European calls and puts
• The lower bound for European calls

• Portfolio A: one European call option plus a zero-coupon bond
that provides a payoff of � at
time �
• If �# > � at �, the call is exercised, and one stock share is
purchased with the principal of the
bond Þ Portfolio A is worth �#
• If �# ≤ � at �, the portfolio holder receives the repayment of
the principal of the bond Þ
Portfolio A is worth �
ÞPortfolio A is worth max(�#,�) at �
• Portfolio B: one share of the stock Þ worth �# at �
※Portfolio A is worth more than Portfolio B Þ this should also
be true in PV terms Þ
� + ��!"# ≥ �% Þ � ≥ �% − ��!"# �� ≥ 0 à � ≥
max(�% − ��!"#, 0)
Lower bound for call Lower bound for put
European � ≥ max(�% − ��!"#,0) � ≥ max(��!"# − �%,0)
15
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8
Proof that c> Max[0,S0 -PV(K)]
• Obviously, c > 0
• Proof that c > S-PV(K)

• What if c < S0 - PV(K)?
• Then c – S0 + PV(K) < 0
• Then -c + S0 - PV(K) > 0 permits arbitrage, because cash is
received today, and
there are no cash outflows at expiration.
______At Expiration______
• Today: ST > K ST < K
• Buy call -c +(ST – K) 0
• Sell stock + S0 - ST - ST
• Lend -PV(K) + K + K
>0 0 -ST+K>0
16
• Is there any an arbitrage opportunity if � = 3, �! = 20, � =
18, � = 10%,
� = 0, and � = 1?
17
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9
• Is there any an arbitrage opportunity if � = 3, �! = 20, � =
18, � = 10%,

� = 0, and � = 1?
• Since the call price violates the lower bound constraint ($20 −
$18�!%.&)& = $3.71) , the
following strategy can arbitrage from this distortion (c is too
low)
• Buy the underestimated call and short one share of stock Þ
Generate a cash inflow of
$20 – $3 = $17
• Deposit $17 at � = 10% for one year Þ Generate an income of
$17�&%%)& = $18.79 at
the end of the year
• If �# > $18, exercise the call to purchase one share of stock at
$18 and close out the
short position Þ The net income is $18.79 – $18 = $0.79
• If �# < $18, give up the right of the call, purchase 1 share at
�# in the market, and close
out the short position Þ The net income is $18.79 – �#, which
must be higher than
$0.79
18
• The lower bound for European puts
• Portfolio C: one European put option plus one share
• If �# ≤ � at �, the put is exercised and sell the one share of
stock owned for � Þ
Portfolio C is worth �

• If �# > � at �, the put expires worthless Þ Portfolio C is
worth �#
ÞPortfolio C is worth max(�#,�) at �
• Portfolio D: an amount of cash equal to ��@A" (or
equivalently a zero-
coupon bond with the payoff � at time �)
• Portfolio C is more valuable than Portfolio D Þ � + �! ≥
��@A" Þ � ≥
��@A" − �! à � ≥ max(��@A" − �! , 0)
20
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10
Proof of the European Put Lower Bound
What if: p < Ke-rT - S0 ?
Then, p- Ke-rT + S0 < 0
Or, -p+ Ke-rT - S0 >0
At expiration:
Today ST>K ST<K
Buy put -p 0 +(K-ST)
Borrow + Ke-rT -K -K
Buy stock -S +ST +ST
>0 >0 0

So, if Pp< Ke-rT - S, an arbitrage is possible, because the trader
can receive a cash in-flow today, and
not have to pay money in the future (in fact, in some cases, the
trader receives money in the
future, too.
21
• Is there any arbitrage opportunity if � = 1, �I = 37, � = 40, �
= 5%,
� = 0, and � = 0.5?
22
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11
• Is there any arbitrage opportunity if � = 1, �I = 37, � = 40, �
= 5%,
� = 0, and � = 0.5?
• Since the put price violates the lower bound constraint
($40�@!.!CD!.C − $37 =
$2.01) , the following strategy can arbitrage from this distortion
(p too low)
• Borrow $38 at � = 5% for 6 months Þ Need to pay off
$38�+%)%.+ = $38.96 after half a

year
• Use the borrowing fund to buy the underestimated put and one
share of stock
• If �# > $40, discard the put, sell the stock for �#, and repay
the loan Þ The net income is
�# – $38.96 > 0
• If �# < $40, exercise the right of the put to sell the share of
stock at $40 and repay the
loan Þ The net income is $40 – $38.96 = $1.04
23
Summary
At expiration:
Today ST>K ST<K
Buy put -1 0 +(40-ST)
Borrow $39.01 = 40�MI.INOI.N -40 -40
Buy stock -37 +ST +ST
>0 >0 0
24
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12
• Lower bounds for American calls and puts

• The lower bounds for American calls and puts are their
exercise value
because the holders of them always can exercise them to obtain
the
current exercise value
• The American option is worth at least as much as zero because
the option
holder has only the right but no obligation to exercise the
option
Lower bound for call Lower bound for put
American � ≥ max(�% − �,0) � ≥ max(� − �%,0)
25
Put-Call Parity
• Consider Portfolios A and :
• Portfolio A: 1 European call option plus a zero-coupon bond
that provides
a payoff of � at time �
• Portfolio C: 1 European put plus 1 share of the stock
Portfolio A �� > � �� ≤ �
Call option �$ − � 0
Zero-coupon bond � �
Total �$ �
Portfolio C �� > � �� ≤ �
Put option 0 � − �$
1 share of stock �$ �$
Total �$ �

27
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13
Put-Call Parity
• Due to the law of one price, Portfolios A and C must therefore
be worth the
same today
� + ��@A" = � + �!
• The above equation is known as the put-call parity
• The put-call parity defines a relationship between the prices of
a European call and put
option, both of which are with the identical � and �
• Is there any arbitrage opportunity if � = 1 or � = 2.25 given
� = 3, �! = 31,
� = 30, � = 10%, � = 0, and � = 0.25?
• Write down the strategies.
28
Put-Call Parity
• Is there any arbitrage opportunity if � = 1 or � = 2.25 given
� = 3, �! = 31,
� = 30, � = 10%, � = 0, and � = 0.25?
• The theoretical price of the put option is 1.26 by solving 3 +

30�!%.&)%.'+ = � + 31
• The arbitrage strategies for � = 2.25 and � = 1 are shown in
the following table
29
3/31/20
14
Put-Call Parity
• Rewrite the put-call parity: � + ��MPQ = � + �I ⇒ � +
��MPQ − �I = �,
based on which it is simpler to identify the arbitrage
opportunity
Three-month put price = $2.25 (p overvalued)
(Long � + ��!�� − �� and short �)
Three-month put price = $1
(Short � + ��!�� − �� and long �)
Buy the call at $3, short the stock to realize $31,
and short the put to realize $2.25 Þ Deposit the
net cash flow $30.25 at 10% for 3 months
Short the call to realize $3, buy the stock at $31,
buy put at $1, and borrow $29 at 10% for 3
months Þ The net cash flow is 0
If �# > 30 after 3 months:
Receive $31.02 from the deposit, exercise the call
to buy the stock at $30 Þ Net profit = $1.02

If �# > 30 after 3 months:
The call is exercised and thus need to sell the
stock for $30, and use $29.73 to repay loan Þ
Net profit = $0.27
If �# < 30 after 3 months:
Receive $31.02 from the deposit, the put is
exercised and thus need to buy the stock at $30
Þ Net profit = $1.02
If �# < 30 after 3 months:
Exercise the put to sell the stock for $30, and use
$29.73 to repay loan Þ Net profit = $0.27
30
Put-Call Parity
• Extension of the put-call parity for the American call and put
(exercise 18)
�% − � ≤ � − � ≤ �% − ��&'(
• Identify the upper and lower bounds of � given � = 1.5, �! =
19, � =
20, � = 10%, � = 0, and � = 5/12
19 − 20 ≤ 1.5 − � ≤ 19 − 20�@!.LDC/LN
⇒ 1.68 ≤ � ≤ 2.50
31
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15
Optimal Early Exercise Decision
• Usually there is some chance that an American option will be
exercised early
• The early exercise occurs when � < exercise value, where �
reflects the PV of holding
all future exercise opportunities
• An exception is an American call on a non-dividend paying
stock, which
should never be exercised early
∵ � ≥ �, − ��-.# and � ≥ � (bounds)
∴ � ≥ � ≥ �% − ��!"# > �% − � if r>0 � > �% − �
(�� )
• This means that C is always greater than the option’s intrinsic
value prior to
maturity. If it were optimal to exercise at a particular time prior
to maturity,
C would equal the option’s intrinsic value at that time.
Þ It is not optimal to exercise American call option if there is
no
dividend payments
32
Early Exercise
• For a deeply ITM American call option: � = 42, �I = 100, �
=

60, � = 0.25, and � = 0
• Should you exercise the call immediately if
1. You intend to hold the stock (after exercising the option) for
the next 3 months?
• No, it is better to delay paying the strike price 3 months later
2. You still want to hold the stock, but you do not feel that the
stock is worth
holding for the next 3 months?
• No, it is possible to purchase the stock at a price lower than �
= 60 after 3 months
3. You decide to sell the stock share immediately after the
exercise?
• No, selling the American call for $42 is better than
undertaking the above strategy,
which is with the payoff of $100 – $60 = $40
34
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16
Early Exercise
• A summary of reasons for not exercising an American call
early if
there are no dividends
• Due to no dividends, no income is sacrificed if you hold the

American call
instead of holding the underlying stock shares
• Payment of the strike price can be delayed (Q1 on previous
slide)
• Holding the call provides the possibility that the purchasing
price could be
lower than but never higher than the strike price (Q2 on
previous slide)
• The payoff from exercising the American call is lower than the
payoff from
selling the American call directly (Q3 on previous slide)
35
Early Exercise – American call options
• For an American option only the dividend value can
negatively affect the value of the call
option.
• Call Value = Intrinsic Value + Interest Rate Value + Volatility
Value - Dividend Value
• If the underlying stock pays no dividend (or no dividend is to
be paid prior to expiration of the option), a
call option can never be less than parity (intrinsic value).
• However, if the negative effects of the dividend are greater
than the positive effects of the other
components, it might be possible for the call, if it is European,
to be less than parity (intrinsic value).
• When a stock pays a dividend, the value of the stock is
diminished by the amount of that

dividend.
• Since the stockholder receives the value of the dividend, the
two changes offset, such that there is no
net change of value for the stockholder.
• On the other hand, when a stock pays a dividend, the option
holder owns no right to the paid dividend.
• The option value will decrease to represent the new intrinsic
value as a result of the stock value decrease,
and the option holder will lose value on the option with no
offsetting gain from the paid dividend.
• Then the only reason a trader would ever consider to exercise
a call stock option early is to
receive the dividend.
• If the stock pays a dividend, the time a trader should consider
early exercise is the day before the stock
goes ex-dividend.
36
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17
Early Exercise
• For a European put option the upper and lower bounds are:
• max(�, − ��-.#) ≤ � ≤ ��-.#
• The lower bounds for American puts are their exercise value P
≥ max(� − �!)

and P ≤ �
max(� − �!) ≤ � ≤ �
• It can be optimal to exercise an American put option on a non-
dividend-paying
stock early
∵ � ≥ ��@A" − �! and � ≥ �
∴ � ≥ � ≥ ��@A" − �!,
Þ For American puts, as long as their values are lower than
max(� − �,,0), they are
early exercised and the option value rises to become max(� −
�,,0)
37
Early Exercise – American put options
• For a put option the only component that can negatively affect
its price is
the interest rate value.
• Put Value = Intrinsic Value - Interest Rate Value + Volatility
Value + Dividend Value
• Unlike the call option, the time a put option is a candidate for
early
exercise is anytime the interest which can be earned through the
sale of
the stock at the exercise price is considerably large.
• Determining the exact time at which this occurs is quite
difficult. If the
underlying stock pays a significant dividend it is most likely to
occur on the

day after the stock goes ex-dividend.
38
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18
Effects of Dividend Payments
• The no dividends assumption is unrealistic
• The underlying stocks of most exchange-traded stock options
are issued
by large firms
• Large firms usually pay dividends periodically (quarterly or
annually)
• Denote � to be the amount of dividend payment at time � (�
< �) and
�! = ��@AO to be the PV of the dividend payment
• If there are multiple dividend payments during the life of the
option, �% is the sum
of the PV of these dividend payments
39
• Similar to determining the forward (or future) price, �I should
be
deducted from the current stock price to derive the lower

bounds
and the put-call parity of options
• The lower bounds for European calls and puts
� ≥ �! − �! − ��@A" = �! − �! − ��@A"
� ≥ ��@A" − �! − �! = �! + ��@A" − �!
• The put-call parity for European options
� + ��@A" = � + �! − �! ⇒ � + �! + ��@A" = � + �!
• The put-call parity for American options
(�! − �!) − � ≤ � − � ≤ �! − ��@A"
(The only exception for the rule of replacing �, with �, −�, is
the upper bounds
of the put-call parity for American options)
40
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19
• When dividends are expected, we can no longer assert that an
American call option will not be exercised early
∵ � ≥ �! − �! − ��@A" and � ≥ �
∴ � ≥ � ≥ �! − �! − ��@A",
which is not necessarily larger than the exercise value, �! − �
• It is inclined to exercise an American call immediately prior
to an

ex-dividend date
• In fact, it is never optimal to exercise a call at any other time
points
(discussed in Appendix of Ch. 13)
41
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1
Chapter 7
Swaps
1
Swaps
• A swap is an over-the-counter derivatives agreement between
two
companies to exchange cash flows in the future.
• The agreement defines the dates when the cash flows are to be
paid and the
way in which they are to be calculated.
• Usually the calculation of the cash flows involves the future
value of an
interest rate, an exchange rate, or other market variable.
• A forward contract can be viewed as a simple swap.

• Whereas a forward contract is equivalent to the exchange of
cash flows on just on future
date, swaps typically lead to cash-flow exchanges taking place
on several future dates.
2
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2
Swaps - Fundamentals
• So the basic idea of a swap:
• agree to exchange interest payments of different kinds
• different interest computations
• different currencies
• during a given time period (settlement period) on certain dates
(settlement dates)
• with interest payments computed on notional amount
• with a predetermined termination date
• Notional amount
• never exchanges hands in single-currency interest rate swaps à
parties agree to exchange
only the net amount (netting)
• Reference interest rate
• LIBOR = reference floating rate in most cases
3

Mechanism of interest rate swaps
• By far the most common over-the-counter derivative is a
‘‘plain vanilla’’
interest rate swap.
• In this a company agrees to pay cash flows equal to interest at
a predetermined fixed
rate on a notional principal for a number of years.
• In return, it receives interest at a floating rate on the same
notional principal for the
same period of time.
• LIBOR
• The floating rate in most interest rate swap agreements is the
London Interbank Offered
Rate (LIBOR)
4
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3
5
Swap structure
• Without intermediary
• With Intermediary

Firm A Firm B
Firm A
Bank
Firm B
5
Example
• Consider a hypothetical three-year swap initiated on March 8,
2016, between
Apple and Citigroup. We suppose Apple agrees to pay to
Citigroup an interest
rate of 3% per annum on a notional principal of $100 million,
and in return
Citigroup agrees to pay Apple the six-month LIBOR rate on the
same notional
principal.
• Apple is the fixed-rate payer ; Citigroup is the floating-rate
payer .
• Assume the agreement specifies that payments are to be
exchanged every six
months and that the 3% interest rate is quoted with semiannual
compounding.
6
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4
Example
• The first exchange would take place on September 8, 2016, six
months after
the initiation of the agreement.
• Citigroup would pay Apple interest on the $100 million
principal at the six-
month LIBOR rate prevailing six months prior to September 8,
2016—that is,
on March 8, 2016. Suppose that the six-month LIBOR rate on
March 8, 2016,
is 2.2% ($1.1 million)
• Apple would pay Citigroup $1.5 million. This is the interest
on the $100
million principal for six months at a rate of 3% per year ($1.5
million)
• Note that there is no uncertainty about this first exchange of
payments
because it is determined by the LIBOR rate at the time the
contract is agreed
to.
7
Example
• The second exchange of payments would take place on March
8, 2017, one
year after the initiation of the agreement. Apple would pay $1.5
million to
Citigroup.

• Suppose that the six-month LIBOR rate on September 8, 2016,
proves to be
2.8%. Citigroup pays $1.4 million to Apple.
• Suppose there are 6 exchanges:
8
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5
Interest rate swaps
• Plain-vanilla Interest Rate Swap
• Contract by which
• Buyer (long) is committed to pay fixed rate R (similar to FRA:
buyer locks in
borrowing rate)
• Seller (short) is committed to pay variable r (e.g., LIBOR)
• on notional
• no exchange of principal
• at future dates set in advance
• t + Dt, t + 2 Dt, t + 3Dt , t+ 4 Dt, ...
• most common swap : 6-month LIBOR (Dt=6 months)
9

10
Why swaps?
Evolution of Swaps—A brief History
• Increase in exchange rate volatility (1972)
• increase in earnings volatility
• fluctuation in asset value due to exchange rate volatility
• The
Solution
--parallel loans
• two firms simultaneously make financial loans to each other
• increasing use in the 1970’s
• but difficult to find partners
• ~1981 swaps written by banks to help firms conduct parall el
loan transactions
10
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6
11
Economic Benefits of Swaps
1. Financial Arbitrage
• Differential currency borrowing rates
• Differing fixed/floating borrowing rates
2. Tax and Regulatory Arbitrage
3. Managing interest rate or currency risk
• May be cheaper than alternatives (futures, for instance)
4. Completing markets
• No available alternatives
• e.g. originally no interest rate futures, just swaps
11
Using the Swap to Transform a Liability
• As shown the previous example, for Apple, the swap could be
used to transform a

floating-rate loan into a fixed-rate loan.
• Suppose that Apple has arranged to borrow $100 million for
three years at LIBOR
plus 10 basis points ( LIBOR plus 0.1%.)
• After Apple has entered into the swap with the following three
sets of cash flows:
1. It pays LIBOR plus 0.1% to its outside lenders.
2. It receives LIBOR under the terms of the swap.
3. It pays 3% under the terms of the swap.
• These three sets of cash flows net out to an interest rate
payment of 3.1%
• Thus, for Apple the swap could have the effect of
transforming borrowings at a
floating rate of LIBOR plus 10 basis points into borrowings at a
fixed rate of 3.1%.
12
2/26/20

7
13
Using the Swap to Transform a Liability
• A company wishing to transform a fixed-rate loan into a
floating-rate loan would
enter into the opposite swap.
• Suppose that Intel has borrowed $100 million at 3.2% for
three years and wishes to
switch to a floating rate linked to LIBOR.
• Like Apple it contacts Citigroup. We assume that it agrees to
enter into the following
swap to convert to a floating rate:
1. It pays 3.2% to its outside lenders.
2. It pays LIBOR under the terms of the swap.
3. It receives 2.97% under the terms of the swap.
14

2/26/20
8
Using the Swap to Transform an Asset
• Swaps can also be used to transform the nature of an asset.
Consider Apple in our example.
• The swap in could have the effect of transforming an asset
earning a fixed rate of interest
into an asset earning a floating rate of interest.
• Suppose that Apple owns $100 million in bonds that will
provide interest at 2.7% per annum
over the next three years.
• After Apple has entered into the swap, it is in the position .It
has three sets of cash flows:
1. It receives 2.7% on the bonds.
2. It receives LIBOR under the terms of the swap.

• These three sets of cash flows net out to an interest rate inflow
of LIBOR minus 30 basis
points.
15
Changing the nature of an asset – one more example
• Suppose that Microsoft owns $100
million in bonds that will provide
interest at 4.7% per annum over the
next 3 years. Microsoft could use a
swap to transform an asset earning
4.7% into an asset earning LIBOR
minus 30 basis points.
• Microsoft can enter into a swap, it
with the following three sets of cash
flows:
1. It receives 4.7% on the bonds.
2. It receives LIBOR under the terms of the
swap.

• Suppose that Intel has an investment of
$100 million that yields LIBOR minus 20
basis points. Intel wants to transform an
asset earning LIBOR minus 20 basis
points into an asset earning 4.8%.
• Intel can enter into a swap, it with the
following three sets of cash flows:
1. It receives LIBOR minus 20 basis points on
its investment.
2. It pays LIBOR under the terms of the swap.
3. It receives 5% under the terms of the swap.
16
2/26/20
9
Role of Financial Intermediary
• Firm usually do not enter into swaps with each other but use

intermediaries.
• A market maker such as Citigroup provides the full set of
quotes for plain
vanilla U.S. dollar swaps.
• ‘‘Plain vanilla’’ LIBOR-for-fixed swaps on US interest rates
are usually
structured so that the financial institution earns about 3 or 4
basis points
(0.03% or 0.04%) on a pair of off setting transactions.
17
Organization of Trading
• A market maker such as Citigroup provides the full set of
quotes for plain
vanilla U.S. dollar swaps.
• A Swap Rate is the average of bid and offer
18

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10
Day count issues (briefly cover)
• The day count conventions affect payments on a swap, and
some of the numbers calculated in the
examples we have given do not exactly reflect these day count
conventions.
• In general, a LIBOR-based floating-rate cash flow on a swap
payment date is calculated as
LRn/360, where L is the principal, R is the relevant LIBOR
rate, and n is the number of days since
the last payment date.
• The fixed rate that is paid in a swap transaction is similarly
quoted with a particular day count
basis being specified. As a result, the fixed payments may not
be exactly equal on each payment
date.
• The fixed rate is usually quoted as actual/365 or 30/360. It is

not therefore directly comparable
with LIBOR because it applies to a full year.
• To make the rates approximately comparable, either the 6-
month LIBOR rate must be multiplied
by 365/360 or the fixed rate must be multiplied by 360/365.
19
The comparative advantage argument
• An explanation commonly put forward to explain the
popularity of swaps concerns
comparative advantage.
• Some companies, it is argued, have a comparative advantage
when borrowing in
fixed-rate markets, whereas other companies have a comparative
advantage when
borrowing in floating-rate markets.
• To obtain a new loan, it makes sense for a company to go to
the market where it has a
comparative advantage.

• As a result, the company may borrow fixed when it wants
floating, or borrow floating when it
wants fixed.
• The swap is used to transform a fixed-rate loan into a floating-
rate loan, and vice
versa.
Difference between
the two fixed rates
and floating rates are
not the same
20
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11
Critique
• Should the spreads between the rates offered to AAACorp and
BBBCorp be

different in fixed and floating markets?
• Now that the interest rate swap market has been in existence
for a long time,
we might reasonably expect these types of differences to have
been
arbitraged away.
• The reason that spread differentials appear to exist is due to
the nature of
the contracts available to companies in fixed and floating
markets
• In the floating-rate market, the lender usually has the
opportunity to
review the floating rates every 6 months à if the
creditworthiness of
AAACorp or BBBCorp has declined, the lender has the option
of increasing
the spread over LIBOR that is charged.
• The providers of fixed-rate financing do not have the option to
change the
terms of the loan in this way

21
ST vs LT
• The spreads between the rates offered to AAACorp and
BBBCorp are a
reflection of the extent to which BBBCorp is more likely than
AAACorp to
default.
• During the next 6 months, there is very little chance that
either AAACorp or
BBBCorp will default.
• As we look further ahead, the probability of a default by a
company with a
relatively low credit rating (such as BBBCorp) is liable to
increase faster than
the probability of a default by a company with a relatively high
credit rating
(such as AAACorp).
• This is why the spread between the 5-year rates is greater than
the spread
between the 6-month rates.

22
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12
The nature of swap rates
• Let’s examine the nature of swap rates and the relationship
between swap
and LIBOR markets.
• LIBOR is the rate of interest at which AA-rated banks borrow
for periods up to
12 months from other banks.
• A swap rate is the average of
• (a) the fixed rate that a swap market maker is prepared to pay
in exchange for receiving
LIBOR (its bid rate) and
• (b) the fixed rate that it is prepared to receive in return for

paying LIBOR (its offer rate).
• Like LIBOR rates, swap rates are not risk-free lending rates.
However, they are
reasonably close to risk-free in normal market conditions
23
The nature of swap rates
• A financial institution can earn the 5-year swap rate on a
certain principal by doing
the following:
1. Lend the principal for the first 6 months to an AA borrower
and then relend it for successive
6-month periods to other AA borrowers; and
2. Enter into a swap to exchange the LIBOR income for the 5-
year swap rate
• This shows that the 5-year swap rate is an interest rate with a
credit risk
corresponding to the situation where 10 consecutive 6-month
LIBOR loans to AA

companies are made.
• Note that 5-year swap rates are less than 5-year AA borrowing
rates.
• It is much more attractive to lend money for successive 6-
month periods to borrowers who
are always AA at the beginning of the periods than to lend it to
one borrower for the whole 5
years when all we can be sure of is that the borrower is AA at
the beginning of the 5 years à
swap rates are continuously “refreshed” LIBOR rates.
24
2/26/20
13
Valuation of interest rate swaps
• An interest rate swap is worth close to zero when it is first
initiated. After it has been

in existence for some time, its value may be positive or
negative.
• Each exchange of payments in an interest rate swap is a
forward rate agreement (FRA)
where interest at a predetermined fixed rate is exchanged for
interest at the LIBOR
floating rate.
• FRA can be valued by assuming that forward rates are
realized. Because it is nothing
more than a portfolio of FRAs, an interest rate swap can also be
valued by assuming
that forward rates are realized. The procedure is:
1. Calculate forward rates for each of the LIBOR rates that will
determine swap cash
flows.
2. Calculate the swap cash flows on the assumption that LIBOR
rates will equal forward rates.
3. Discount these swap cash flows (using the LIBOR/swap zero
curve) to obtain the swap value.
25

Example – valuing interest rate swap
• Suppose corporations A and B enter into the following swap
agreement:
• Notional amount: $10,000,000
• A makes semiannual payments to B of 3% of the notional
• B makes semiannual payment to A of LIBOR+0.5% (this is a
6-month LIBOR).
• This contract is equivalent to 4 forward contracts
• Suppose that the forward rates are:
– Current LIBOR rate = 2.0%
– 6 to 12 month rate = 2.5%
– 12 to 18 month rate = 3.0%
– 18 to 24 month rate = 3.5%
– 24 to 30 month rate = 4.0%
Pay-
ments
6 months 1 year 18 months 2 years
A to B $0.3m $0.3m $0.3m $0.3m
B to A $10m at

LIBOR0+0.5%
$10m at
LIBOR6+0.5%
$10m at
LIBOR12+0.5%
$10m at
LIBOR18+0.5%
26
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14
Interest Rate Swap Pricing
• Sum all discounted cash flows A to B (similarly to bond
valuation we use the corresponding ”spot” rate for each
future period – here forward LIBOR rate):

• CF1 = -10m*0.03/(1.025) = -0.2927m
• CF2 = -10m*0.03/[(1.025)(1.03)] = -0.2842m
• CF3 = -10m*0.03/[(1.025)(1.03)(1.035)] = -0.2745m
• CF4 = -10m*0.03/[(1.025)(1.03)(1.035)(1.04)] = -0.2640m
Sum -1.1154m
• Similarly, B’s floating rate payments to A
• CF1 = -10m*0.025/(1.025) = 0.2439
• CF2 = -10m*0.030/[(1.025)(1.03)] = 0.2842
• CF3 = -10m*0.035/[(1.025)(1.03)(1.035)] = 0.3203
• CF4 = -10m*0.040/[(1.025)(1.03)(1.035)(1.04)] = 0.3520
Sum -1.2004
27
Interest Rate Swap Pricing
• Value to A is net flow to A:
$1.2004m - $1.1154m = $0.085m
• What happens if LIBOR rates increase more than expected?
• B’s payments increase
• Good for A, Bad for B

28
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15
How the value changes through time
• The fixed rate in an interest rate swap is chosen so that the
swap is worth
zero initially. This means that the sum of the values of the
FRAs underlying
the swap is initially zero.
• It does not mean that the value of each individual FRA is zero.
In general,
some FRAs will have positive values while others will have
negative values.
• Recall,
29

Fixed-for-fixed Currency Swaps
• Involves exchanging principal and interest payments at a fixed
rate in one
currency for principal and interest payments at a fixed rate in
another
currency.
• A currency swap agreement requires the principal to be
specified in each of
the two currencies.
• The principal amounts in each currency are usually exchanged
at the
beginning and at the end of the life of the swap.
• Usually the principal amounts are chosen to be approximately
equivalent
using the exchange rate at the swap’s initiation.
• But when they are exchanged at the end of the life of the
swap, their values
may be quite different.

30
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16
Example – flat term structure and continuous compounding
• The term structure of risk-free interest rates is flat in both
Japan and the
United States. The Japanese rate is 1.5% per annum and the
U.S. rate is 2.5%
per annum (both with continuous compounding).
• A financial institution has entered into a currency swap in
which it receives
3% per annum in yen and pays 4% per annum in dollars once a
year. The
principals in the two currencies are $10 million and 1,200
million yen. The
swap will last for another three years, and the current exchange
rate is 110
yen = $1.

Continuous discounting
at 2.5% and 1.5%
31
Example – flat term structure and continuous compounding
• Vswap = S0 x BF - BD
• value of a swap where the foreign currency is received, and
dollars are paid
• where BF is the value, measured in the foreign currency, of
the bond defined by the foreign
cash flows on the swap and BD is the value of the bond defined
by the domestic cash flows
on the swap, and S0 is the spot exchange rate (expressed as
number of dollars per unit of
foreign currency)
• The value of the swap in dollars is therefore (1252/110) -
10.491= 0.9629 million
32

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17
Currency Swaps – more rigorous approach
• Company A
• Wants to borrow ¥1 billion
• Company J
• Wants to borrow $10 million
• Same time frame (2 years)
• Assume (for simplicity) that ¥1 = $0.01
• Swap contract
• Semi-annual payments (USD forward rates: 2.5%, 3%, 3.5% &
4%)
• fixed-for-fixed swap
• A pays 2.5% on yen
• J pays 3.0% on dollars

33
Currency Swap Cash Flows
Swap Value
1. Forward prices
– This contract is equivalent to 4 forward contracts
2. Transaction costs
– Bank gets paid, lessens the value of a swap
3. Default risk
– Counterparty risk reduces swap value
Payments 6 months 1 year 18 months 2 years
A to J ¥25m ¥25m ¥25m ¥1025m
J to A $0.3m $0.3m $0.3m $10.3m
34

2/26/20
18
Currency Swap Value
• Vswap = BD – S0 x BF
• where BF is the value, measured in the foreign currency, of
the bond defined by
the foreign cash flows on the swap and BD is the value of the
bond defined by
the domestic cash flows on the swap, and S0 is the spot
exchange rate
(expressed as number of dollars per unit of foreign currency)
• Value of A payments to J
• Sum of discounted cash flows
• Assume forward prices for yen are
• $0.0105
• $0.0110
• $0.0115
• $0.0120

• Here we use forward price equivalents for cash flows to
discount
35
Currency Swap Pricing
• Sum all discounted cash flows (in $):
• CF1 = -25*0.0105/(1.025) = -0.2561
• CF2 = -25*0.0110/[(1.025)(1.03)] = -0.2605
• CF3 = -25*0.0115/[(1.025)(1.03)(1.035)] = -0.2631
• CF4 = -1025*0.0120/[(1.025)(1.03)(1.035)(1.04)] = -10.8236
Sum -11.6033
• Similarly for J’s payments to A (in $):
• CF1 = 0.3/(1.025) = 0.2927
• CF2 = 0.3/[(1.025)(1.03)] = 0.2842
• CF3 = 0.3/[(1.025)(1.03)(1.035)] = 0.2745
• CF4 = 10.3/[(1.025)(1.03)(1.035)(1.04)] = 9.0636
Sum 9.9150
36

2/26/20
19
Currency Swap Pricing
• All CFs from Company A’s perspective, so the value of swap
for
Company A is
$9.915m – $11.6033m = -$1.6883m
• Require payment up front for entering the swap!
• Value of yen expected to rise relative to dollar over the next 2
years
• Note:
• Some examples in the book use net cash flows--combines all
CFs in each
period after converting to $ equivalents

37
Currency Swaps (cont.)
• If yen rises more than expected, what happens?
• A has locked in forward rates
• Gets payment up front
• Rising yen makes $ less valuable
38
2/26/20
20
Credit/Default Risk
• The credit risk arises from the possibility of a default by the
counterparty when
the value of the contract to the financial institution is positive.
• Not the same thing as market risk
• arises from the possibility that market variables such as

interest rates and
exchange rates will move in such a way that the value of a
contract to the
financial institution becomes negative.
• Market risks can be hedged by entering into off setting
contracts; credit risks are
less easy to hedge.
• Can use a CDS - like an insurance contract that pays off if a
particular
company or country defaults
• Priced into the discount rates above
39
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1

Week10
MechanicsofOptionsMarket
Mechanicsofoptionsmarkets
• Someofthetopicscoveredinthischapter
• Typesofoptions
• Organizationofoptionsmarkets
• Terminologyused
• Howthecontractsaretraded,
• Howmarginrequirementsareset,
• Wewillmostlydiscussaboutstockoptions
4/21/18
2
Typesofoptions
• Acall isanoptiontoBUY acertainasset byacertaindate fora

certainpricethatis fixedtoday
• Aput isanoptiontoSELL acertainasset byacertaindate fora
certainpricethatis fixedtoday
• Thedatespecifiedinthecontractisknownastheexpiration
date orthematuritydate.
• Thepricespecifiedinthecontractisknownastheexercise
price orthestrikeprice.
Typesofoptions
• Americanoptions canbeexercisedatanytimeuptothe
expirationdate,
• Europeanoptions canbeexercisedonlyontheexpirationdate
itself.
• MostoftheoptionsthataretradedonexchangesareAmerican.
• EuropeanoptionsaregenerallyeasiertoanalyzethanAmerican
options,andsomeofthepropertiesofanAmericanoptionare
frequentlydeducedfromthoseofitsEuropeancounterpart.

4/21/18
3
Calloption
• AninvestorbuysaEuropeancalloptionwithastrikepriceof$100
topurchase100sharesofacertainstock(thebuyerofaput
optionhopesthatthepriceofthestockwillincrease).
• Supposethatthecurrentstockpriceis$98,theexpirationdateof
theoptionisinfourmonths,andthepriceofanoptionto
purchaseoneshareis$5.
• Theinitialinvestmentis$500. Supposethatatexpirationthestock
priceis$115.
• Willtheoptionbeexercised?Ifyes,whatwilltheprofitbe?
• Yes,itwillbeexercisedsincethepriceisgreaterthanthestrike
price.
• Theprofitwillbe(115-105)x100=$1000.
4/21/18

4
Putoption
• An
investorbuysaEuropeanputoptionwithastrikepriceof$70tosell
100sharesofacertainstock(hopingthatthepriceofthestockwill
decrease).
• Supposethatthecurrentstockpriceis$65,theexpirationdateofthe
optionisinthreemonths,andthepriceofanoptiontoselloneshareis
$7.
•
Theinitialinvestmentis$700.BecausetheoptionisEuropean,itwillb
e
exercisedonlyifthestockpriceisbelow$70onthee xpirationdate.
• Supposethatthestockpriceis$55onthisdate.Theinvestorcanbuy
100sharesfor$55pershareand,underthetermsoftheputoption,
sellthesamesharesfor$70torealizeagainof$15pershare,or$1,500
oranetof$800ifwetakeintoaccountthetransactioncosts.
4/21/18
5

Optionspositions
• Therearetwosidestoeveryoptioncontract.
• Ononesideistheinvestorwhohastakenthelongposition(i.e.,has
boughttheoption).
• Ontheothersideistheinvestorwhohastakenashortposition(i.e.,
hassoldorwrittentheoption).
•
Thewriterofanoptionreceivescashupfront,buthaspotentialliabiliti
eslater.
•
Thewriter’sprofitorlossisthereverseofthatforthepurchaseroftheop
tion
4/21/18
6

Optionspositions
• Therearefourtypesofoptionposition:
1. Alongpositioninacalloption
2. Alongpositioninaputoption
3. Ashortpositioninacalloption
4. Ashortpositioninaputoption.
PayoffsofEuropeanCallOptions
• Payofflongposition=!
�$ − �, ��$ > �
0, ��$ ≤ �
= �� $ − �,0
• Thepayofftotheshortpositionwillbe−�� $ − �,0 or
• Payoffshortposition=!
� − �$, ��$ > �
0, ��$ ≤ �
= �� − �$,0

4/21/18
7
PayoffsofEuropeanPutOptions
• Payofflongposition=!
� − �$, ��$ ≤ �
0, ��$ > �
= �� − �$,0
• Thepayofftotheshortpositionwillbe−�� − �$,0 or
�� $ − �,0
4/21/18
8
Underlyingassets

• ETPOptions
• TheCBOEtradesoptionsonmanyexchange-
tradedproducts(ETPs).
•
ETPsarelistedonanexchangeandtradedlikeashareofacompany’ssto
ck.
•
Theyaredesignedtoreplicatetheperformanceofaparticularmarket,o
ftenby
trackinganunderlyingbenchmarkindex.
•
SPDRS&P500ETFtrustisdesignedtoprovideinvestorswiththeretur
nthey
wouldearniftheyinvestedinthe500stocksthatconstitutetheS&P500
index
• StockOptions
•
ExchangesintheUS:ChicagoBoardOptionsExchange,NYSEEuron
ext,
InternationalSecurityExchange,BostonOpticsExchange.
•
Optionstradeonseveralthousanddifferentstocks.Onecontractgives
theholderthe

righttobuyorsell100sharesatthespecifiedstrikeprice.Thiscontracts
izeis
convenientbecausethesharesthemselvesarenormallytradedinlotso
f100.
Underlyingassets
• ForeignCurrencyOptions
• Mostcurrencyoptionstradingisnowintheover-the-
countermarket,butthereis
some exchangetrading
• ItoffersEuropean-
stylecontractsonavarietyofdifferentcurrencies.Onecontractisto
buyorsell10,000unitsofaforeigncurrency(1,000,000uni tsinthecas
eofthe
Japaneseyen)forU.S.dollarsexchangetrading
• IndexOptions
•
ThemostpopularexchangetradedcontractsintheUnitedStatesaretho
seontheS&P
500Index(SPX),theS&P100Index(OEX),theNASDAQ-
100Index(NDX),andtheDow
JonesIndustrialIndex(DJX).

• FuturesOptions
•
Whenanexchangetradesaparticularfuturescontract,itoftenalsotrad
esAmerican
optionsonthatfuturescontract.
•
Thelifeofafuturesoptionnormallyendsashortperiodoftimebeforeth
eexpirationof
tradingintheunderlyingfuturescontract.
4/21/18
9
SpecificationsofStockOptions
• Expiration Dates
• One of the items used to describe a stock option is the month
in which the expiration date
occurs.

• In 1973, in the U.S.: January ( January, April, July, and
October) , February ( February, May,
August, and November) , or March ( March, June, September,
and December) cycles
•
Forexample,atthebeginningofJanuary,optionsaretradedwithexpir
ationdatesinJanuary,
February,April,andJuly;attheendofJanuary,theyaretradedwithexp
irationdatesin
February,March,April,andJuly;
•
Forexample,expirationmonthsavailablefromSeptember2008forthr
eedifferent
stocks:
•
Microsoft:Sept2008,Oct2008,Jan2009,April2009,Jan2010andJan
2011.
• Progressive:Sept2008,Oct2008,Nov2008andFeb2009.
•
CitiGroup:Sept2008,Oct2008,Dec2008,Jan2009,Mar2009,Jan201

0andJan2011.
Expirationdates
• Unlike purchasing shares of stock, purchasing an option
contract is generally
used as a shorter-mid term investment.
• When you buy or sell an option contract (controlling 100
shares of stock), you
must agree to an expiration date, as part of that contract.
• It is not vital to learn why expiration cycles occur in the
weeks/months that they
do, but rather what is more important is understanding what
expiration is and
how to choose an expiration date because it becomes pivotal in
determining
whether or not a trade was a success or failure.
• Expiration is important because it sets a timeframe for your
trade.
• Whether or not a trade is going in the right direction and how
much time left until that
option expires define what profit or loss you will incur as an

investor.
4/21/18
10
Expirationdates
• Most stock options have weekly, monthly, and quarterly
cycles.
• Something to keep in mind when choosing an expiration date
is
what cycle the option is in, as this can have an impact on how
liquid the underlying is.
• Weekly cycles tend to be less liquid than monthly/quarterly,
so
you may have a little trouble getting out of a trade in a weekly
expiration cycle.
• Weekly expiration cycles are commonly used for earnings
trades.

• Strike Prices
• The exchange normally chooses the strike prices at which
options can be written
so that they are spaced $2.50, $5, or $10 apart.
• Typically the spacing is $2.50 when the stock price is between
$5 and $25, $5
when the stock price is between $25 and $200, and $10 for
stock prices above
$200.
• When a new expiration date is introduced, the two or three
strike
prices closest to the current stock price are usually selected by
the
exchange.
• If the stock price moves outside the range defined by the
highest and
lowest strike price, trading is usually introduced in an option
with a
new strike price

4/21/18
11
Example
• Suppose that the stock price is $84 when trading begins in the
October options. Call and put options would probably first be
offered with strike prices of $80, $85, and $90.
• What if the stock price rose above $90? Or if it fell below
$80?
• In the first case it is likely that a strike price of $95 would be
offered; in the second case it is likely that a price of $75 would
be
offered; and so on.
• Terminology
• For any given asset at any given time, many different option
contracts may

be trading.
• Suppose there are four expiration dates and five strike prices
for options on
a particular stock. If call and put options trade with every
expiration date
and every strike price, there are a total of 40 different contracts.
• All options of the same type (calls or puts) on a stock are
referred to as an
option class.
• An option series consists of all the options of a given class
with the
same expiration date and strike price.
• Options are referred to as in the money , at the money , or out
of the
money .
• A call option is in the money when S > K , at the money when
S=K , and out
of the money when S < K .
• The intrinsic value of an option is defined as the maximum of

zero and the
payoff from the option if it were exercised immediately. For a
call option,
the intrinsic value is max{S-K; 0}.
4/21/18
12
DividendsandStockSplits
• The early over-the-counter options were dividend protected
• If a company declared a cash dividend, the strike price for
options on the company’s
stock was reduced on the ex-dividend day by the amount of the
dividend.
• Exchange-traded options are not usually adjusted for cash
dividends.
• In other words, when a cash dividend occurs, there are no
adjustments to the terms of
the option contract. An exception is sometimes made for large
cash dividends

• Exchange-traded options are adjusted for stock splits.
• For example, in a 3-for-1 stock split, three new shares are
issued to replace each existing
share and should cause the stock price to go down to one-third
of its previous value.
• After an 3-for-1 stock split, the strike price is reduced to 1/3
of its previous value, and
the number of shares covered by one contract is increased to 3/1
of its previous value.
4/21/18
13
PositionLimitsandExerciseLimits
• Position limit for option contracts defines the maximum
number
of option contracts that an investor can hold on one side of the
market.
• For this purpose, long calls and short puts are considered to be

on the
same side of the market
• Also, short calls and long puts are considered to be on the
same side of
the market
• The exercise limit usually equals the position limit.
• It defines the maximum number of contracts that can be
exercised by any
individual (or group of individuals acting together) in any
period of five
consecutive business days.
Trading
• Over95%oftheordersattheChicagoBoardOptionsExchange
arehandledelectronically.
• MarketMakers
•
Mostoptionsexchangesusemarketmakerstofacilitatetrading.Amar
ket
makerforacertainoptionisanindividualwho,whenaskedtodoso,will
quotebothabidandanofferpriceontheoption.

• Theexchangesetsupperlimitsforthebid–offerspread
• OffsettingOrders
• Aninvestorwhohaspurchasedanoptioncancloseoutthepositionby
issuinganoffsettingordertosellthesameoptionandviceversa
4/21/18
14
Commissions
• Foraretailinvestor,commissionsvarysignificantlyfrombroker to
broker.
• Discountbrokersgenerallychargelowercommissionsthanfull -
servicebrokers.
• Thepurchaseofeightcontractswhentheoptionpriceis$3would
cost$20+(0.02x$2,400)=$68incommissions.
MarginRequirements
• Whencallorputoptionswithmaturitieslessthanninemonths

arepurchased,theoptionpricemustbepaidinfull.
• Foroptionswithmaturitiesgreaterthanninemonths,investors
canbuyonmargin,borrowingupto25%oftheoptionvalue.
• Atraderwhowritesoptionsisrequiredtomaintainfundsinamargin
account.
• Boththetrader’sbrokerandtheexchangewanttobesatisfiedthatthe
traderwillnotdefaultiftheoptionisexercised.
• Theamountofmarginrequireddependsonthetrader’sposition.
4/21/18
15
WritingNakedOptions
• Anakedoption isanoptionthatisnotcombinedwithanoffsetting
positionintheunderlyingstock.
• Theinitialandmaintenancemarginforawrittennakedcalloptionis
thegreaterofthefollowingtwocalculations(forbrokers):

1.Atotalof100%oftheproceedsofthesaleplus20%oftheunderlyings
hare
pricelesstheamountifanybywhichtheoptionisoutofthemoney
2.Atotalof100%oftheoptionproceedsplus10%oftheunderlyingshar
eprice.
4/21/18
16
OptionsClearingCorporation
• The Options Clearing Corporation (OCC) performs much the
same function for
options markets as the clearinghouse does for futures markets
• It guarantees that options writers will fulfill their obligations
under the terms of
options contracts and keeps a record of all long and short
positions
• The OCC has a number of members (brokers), and all options

trades must be
cleared through a member
• The OCC member in turn maintains a margin account with the
OCC.
• When an investor notifies a broker to exercise an option, the
broker in turn
notifies the OCC member that clears its trades.
• This member then places an exercise order with the OCC.
• The OCC randomly selects a member with an outstanding
short position in the same
option.
Regulation
• Exchange-traded options markets are regulated in a number of
different ways.
• Both the exchange and its Options Clearing Corporation have
rules
governing the behavior of traders.
• In addition, there are both federal and state regulatory
authorities.

• In general, options markets have demonstrated a willingness to
regulate themselves.
4/21/18
17
Taxation
• Determining the tax implications of option trading strategies
can
be tricky, and an investor who is in doubt about this should
consult a tax specialist.
• In the United States, the general rule is that (unless the
taxpayer is
a professional trader) gains and losses from the trading of stock
options are taxed as capital gains or losses.
• For both the holder and the writer of a stock option, a gain or
loss
is recognized when

(a) the option expires unexercised, or
(b) the option position is closed out.
W16695
HAS LIBOR LOST ITS STATURE IN DERIVATIVES
MARKETS?1
Ken Mark wrote this case under the supervision of Professor
Walid Busaba solely to provide material for class discussion.
The
authors do not intend to illustrate either effective or ineffective
handling of a managerial situation. The authors may have
disguised
certain names and other identifying information to protect
confidentiality.
This publication may not be transmitted, photocopied, digitized

or otherwise reproduced in any form or by any means without
the
permission of the copyright holder. Reproduction of this
material is not covered under authorization by any reproduction
rights
organization. To order copies or request permission to
reproduce materials, contact Ivey Publishing, Ivey Business
School, Western
University, London, Ontario, Canada, N6G 0N1; (t)
519.661.3208; (e) [email protected]; www.iveycases.com.
Copyright © 2016, Richard Ivey School of Business Foundation
Version: 2016-10-31
It was April 5, 2016, in New York, and the management of a
large U.S. proprietary trading group was
debating what discount rate to use to value the group’s interest-
rate swap portfolio. The group had a
substantial interest-rate swap portfolio laid over its fixed-
income fund. The counterparties to the swaps
were major U.S. banks, and the deals were collateralized. The
question was which of the two reference
rates—the London interbank offered rate (LIBOR) or overnight

indexed swap (OIS) rate—was a more
appropriate discount rate. Members of the management team
needed to consider that derivative pricing
practices had evolved in recent years as market participants
refined their pricing approaches to capture the
elements underlying the pricing of derivative transactions in a
changing market.
The increased use of collateral (in derivative transactions) was
driven by an increased focus in the over-
the-counter market on credit risk and funding risk management,
as well as by the migration of derivative
activity to clearing houses where transactions were typically
fully collateralized. As a result, certain
collateralized derivatives may be presumed to require valuation
based on discounting at the OIS rate.
The head of the management team noted that there was talk
from the Bank of England about an
alternative, nearly “risk-free” reference rate that could
potentially be launched during 2016. There was
also a rumour that OIS rates—whether in U.S. dollars, euros
(euro overnight index average), or pounds
sterling (sterling overnight index average)—were becoming
more popular reference rates in financial

transactions and securities, some of which might end up in the
group’s fixed-income fund. He wondered
whether it was time to substitute some of the maturing LIBOR-
based interest-rate swaps with OISs.
THE LONDON INTERBANK OFFERED RATE
The increasing use of futures contracts to hedge against
interest-rate risk sparked demand for a reference
rate on which these contracts could be based. In 1986, the
British Bankers’ Association (BBA) posted the
first LIBOR rates for three currencies: the U.S. dollar, the
Japanese yen, and the British pound.
1 This case has been written on the basis of published sources
only.
For the exclusive use of Y. Zhang, 2020.
This document is authorized for use only by Yue Zhang in
Derivatives 2020 taught by CATALIN STEFANESCU,
American University from Apr 2020 to May 2020.

mailto:[email protected]
http://www.iveycases.com/
Page 2 9B16N058
At its inception, LIBOR was actually three separate rates based
on average rates charged by panels of
banks for each currency. The BBA selected a minimum of eight
contributor banks per panel, and each
bank submitted its estimated cost to borrow a “reasonable”
amount of currency for a short period of time
from another bank. The BBA worked with a steering group
consisting of market practitioners on the
LIBOR rate fixing process. By 2008, LIBOR rates were posted
for 10 currencies in total and 15 maturities
per currency (see Exhibit 1).
A total of 15 different maturities—from an overnight rate to a
12-month rate—was collected for each
currency from each contributor by 11 a.m. each day.
Contributors—often treasurers at their banks—
assessed how much working capital their banks needed to meet

the maturing liabilities on their balance
sheets. In preparing their LIBOR submissions, the contributors
answered the question, “At what rate
could you borrow funds, were you to do so by asking for and
then accepting interbank offers in a
reasonable market size just prior to 11 a.m.?”2 BBA’s third-
party contractor, Thomson Reuters, managed
the process on its behalf, and contributors relied on a secure
online system to enter their submissions.
Only the middle two quartiles of rates were used in each LIBOR
calculation. To calculate the LIBOR rate
for a particular currency and maturity date, the arithmetic mean
of the middle two quartiles of
submissions was used. Although there were 150 rates in total,
these rates were collectively known as
“BBA LIBOR,” in reference to the organization that managed
the rate-setting process. Here is additional
information on LIBOR:
BBA LIBOR is not a compounded rate but is calculated on the
basis of actual days in funding period/360.
Therefore the formula is as follows: interest due = principal ×
(libor rate/100) × (actual no of days in
interest period/360). Please note that for GBP, the calculation

basis is 365 days. It is also important to
work out the exact/actual number of days in the funding period
which is not always 90 days for a 3 month
deposit but could e.g. be 89 or 91 days. If you have a funding
period of, for example, 45 days you could
extrapolate between the 1 and the 2 month rate to arrive at the
correct BBA LIBOR rate.
All currencies are fixed on a spot basis on each London
Business Day apart from Sterling, which is fixed
for same day value. EUR rates are fixed on each Target
Business Day regardless of whether it is a London
Business Day.3
One criticism of LIBOR was that banks did not need to use the
announced LIBOR rate when borrowing
from each other. Another was that most of the interbank
borrowing market was focused on money
borrowed for a week or less. Thus, panel representatives had to
make educated guesses when submitting
their interbank borrowing rates for the majority of the rates
requested.
Nevertheless, LIBOR was used as a benchmark for financial
contracts, including futures, mortgages, and

consumer loans. In 2012, it was used in financial instruments
with a total value of US$450 trillion.4 An
estimated 95 per cent of the contracts that referenced LIBOR
were for maturities of three months or
2 Jamie Dunkley and Harry Wilson, “Libor Explained: The Real
Cost of Money or Just a Fix?” The Telegraph, March 17,
2011, accessed September 9, 2016,
www.telegraph.co.uk/finance/newsbysector/banksandfinance/
8386513/Libor-explained-the-real-cost-of-money-or-just-a-
fix.html.
3 “BBA LIBOR: Definition and Conventions,” Treasury and
Finance Info, accessed September 9, 2016,
www.treasuryandfinance.info/TF/bba-libor-definition-and-
conventions.html.
4 “BoE Says Plans to Introduce Libor Alternative Next Year,”
The Irish Times, March 18, 2015, accessed September 9, 2016,
www.irishtimes.com/business/financial-services/boe-says-plans-
to-introduce-libor-alternative-next-year-1.2144052; All
currency amounts are in U.S. dollars except where otherwise
specified.

Page 3 9B16N058
longer. LIBOR accurately reflected what actual interbank
borrowing rates could be, according to the
International Monetary Fund.5
LIBORs had been found to be reasonably accurate, most of the
time tracking closely similar benchmarks
that were tied to actual unsecured bank funding rates, such as
those for commercial paper. The glaring
exception was the period immediately after the September 2008
failure of the New York investment
banking firm Lehman Brothers, which triggered a global
financial crisis. The three-month U.S. LIBOR
diverged from two similar publicly available short-term rates:
the Intercapital New York funding rate
(ICAP NYFR)6 and the three-month rate on eurodollar deposits,
which were U.S. dollar-denominated

deposits at banks located outside the United States.
It had been nearly four years since a number of criminal
settlements by Barclays Bank suggested
collusion and fraud in the setting of the LIBOR. Barclays was
accused of manipulating the rate up or
down depending on the positions held by its internal trading
desks. Furthermore, traders at Barclays had
allegedly colluded with rate setters at other banks to influence
rate submissions from these other banks.
After a lengthy investigation, the process by which LIBOR was
calculated was reviewed, and stewardship
of the rate was transferred from the BBA to Intercontinental
Exchange Benchmark Administration in
February 2014.
HOW—AND WHY—LIBOR WAS MANIPULATED
Starting around 2003, Barclays’s traders began trying to
manipulate the LIBOR rate by asking their
bank’s LIBOR rate contributor to influence the rate based on
their trading positions. Barclays’s traders
also worked with contacts in other banks to influence their
rates.

LIBOR was also manipulated during the global financial crisis
of 2007–2008, when banks such as
Barclays, not wishing to signal to the markets that they were in
trouble, submitted LIBOR estimates that
were artificially low. The International Monetary Fund provided
further information on this phenomenon:
In part, LIBOR may have been lower after the Lehman failure
because of an unintended consequence of a
British Bankers’ Association rule meant to ensure that banks
reported their borrowing costs truthfully:
immediate publication of individual banks’ reports. While
normally this would encourage honesty, in
2007–08 this safeguard may have backfired. Banks were
reportedly loath to suggest that they were having
trouble obtaining funds by reporting a rate higher than other
banks were being charged. So to mask its
liquidity problems, a bank with funding problems had an
incentive to report lower rates than it really
believed it would be offered. Indeed, a number of studies have
suggested that banks submitted lowball
rates after the collapse of the investment bank Bear Stearns in
March 2008 as well as after the Lehman
collapse six months later.7

5 John Kiff, “What Is LIBOR?” Finance & Development 49, no.
4 (December 2012), accessed September 9, 2016,
www.imf.org/external/pubs/ft/fandd/2012/12/basics.htm.
6 ICAP is an interdealer broker and a provider of global market
information and commentary for professionals in the
international financial markets. The ICAP NYFR is a survey-
based measure of one- and three-month unsecured bank
funding costs. A daily NYFR poll is taken during the morning
in New York, when the eurodollar market is most active. The
banks are asked to submit a rate where a representative
institution would likely be able to obtain funding in the market.
ICAP
NYFR is positioned by ICAP as a U.S. rate alternative to
LIBOR. Richard Leong, “ICAP to Launch U.S. Rate Alternative
to
LIBOR,” Reuters, May 1, 2008, accessed September 9, 2016,
www.reuters.com/article/ usa-rates-icap-
idUSN0139330120080501; “ICAP Launches NYFR Fixings,”
BusinessWire, June 10, 2008, accessed September 9, 2016,
www.businesswire.com/news/home/20080610006387/en/ICAP-
Launches-NYFR-Fixings-SM.
7 John Kiff, “What Is LIBOR?” Finance & Development 49, no.
4 (December 2012), accessed September 9, 2016,

Page 4 9B16N058
Barclays agreed in June 2012 to pay fines totalling about $450
million to regulators in the United
Kingdom and the United States. Other banks were also under
investigation for misreporting LIBOR rates,
and bank equity analysts estimated that fines and lawsuits could
total almost $50 billion.
The case of Thomas Hayes, a former trader for both UBS Group
AG (UBS) and Citigroup Inc., illustrated
how LIBOR rates were influenced. LIBOR rate contributors did
not estimate their rates with data only;
they also relied on the opinions of others in their network,

according to an article in Bloomberg
BusinessWeek about Hayes’s actions at UBS:
During his time as a junior trader in London, Hayes had gotten
to know several of the 16 individuals
responsible for making their bank’s daily submission for the
Japanese yen. His stroke of genius was
realizing that these men mostly relied on interdealer brokers,
the fast-talking middlemen involved in
every trade, for guidance on what to submit each day.8
Via instant message, Hayes conveyed to these interdealer
brokers his target for yen LIBOR for that day.
In return, every time a contributor from a bank called to ask for
the dealer’s opinion on LIBOR’s
direction, the dealer would provide an answer that would work
to Hayes’s advantage. As for Hayes, his
profit and loss on the LIBOR-linked trades could move from a
$20 million loss to an $8 million profit
depending on the LIBOR rate. Each basis point movement in
LIBOR was worth hundreds of thousands of
dollars on Hayes’s 400 billion yen (US$3.3 billion) position. It
was so important to Hayes that he
formalized the relationship with the broker in question,
negotiating an additional £15,000 a month for the

broker’s LIBOR-related “services.” UBS, via a spokesperson,
denied the institution had any knowledge of
why the additional payments were being arranged.9
THE INVESTIGATION AND RESULT
U.S. and European regulatory authorities led a detailed
investigation into the LIBOR rigging scandal that
resulted in $9 billion in fines paid by banks such as Barclays,
Citigroup, Deutsche Bank, J.P. Morgan,
Rabobank, Royal Bank of Scotland, Société Générale, and UBS.
The investigation uncovered close cooperation between traders
and brokers in the various banks and over
2,000 instances of wrongdoing by UBS employees alone. Yet,
only one person received a prison sentence
for his involvement in the scandal to date. On August 3, 2015,
Hayes was sentenced to 14 years in prison
after he was found guilty of conspiring to manipulate LIBOR.
The prosecutor alleged that Hayes led a
group of 25 traders and brokers from 10 firms to influence
LIBOR.10 In his defence, Hayes’s lawyer
claimed that LIBOR manipulation was widespread throughout
the industry for at least five years prior to

Hayes’s employment at UBS, and that Hayes’s superiors were
aware of his efforts.
Hayes was the only participant found guilty of rigging LIBOR,
and a lawyer unconnected with the case
suggested that it was Hayes’s decision to testify in court,
combined with his contradictory statements, that
led to his conviction. “In this case, Hayes’ pivotal decision to
testify has proven disastrous. It would have
been better for Hayes to have remained silent,” said David
Corker, a partner at law firm Corker Binning
8 Liam Vaughan and Gavin Finch, “Was Tom Hayes Running
the Biggest Financial Conspiracy in History? Or Just Taking
the Fall for One?” Bloomberg BusinessWeek, September 13,
2015, accessed September 9, 2016,
www.bloomberg.com/news/articles/2015-09-14/was-tom-hayes-
running-the-biggest-financial-conspiracy-in-history-.
9 Ibid.
10 Gavin Finch and Liam Vaughan, “Former Libor ‘Ringmaster’
Hayes Gets 14 Years for Libor Rigging,” Bloomberg
BusinessWeek, August 3, 2015, accessed September 9, 2016,
www.bloomberg.com/news/articles/2015-08-03/former-libor-
ringmaster-hayes-guilty-of-manipulating-rates.

Page 5 9B16N058
in London.11 On January 28, 2016, the U.K. Serious Fraud
Office closed its investigation against six
brokers after finding them not guilty of the charge of helping
Hayes in his manipulation of LIBOR.12
LIBOR AFTER THE SCANDAL—REFORM OR REPLACE?
The calls for a replacement to LIBOR came as early as 2011,
when evidence of misconduct first came to
light. In Britain, Martin Wheatley, managing director of the
U.K. Financial Services Authority, was asked
by the Chancellor of the Exchequer to analyze the LIBOR

scandal to see if a wider policy response was
needed. He prepared a comprehensive list of recommendations
for reform in response (see Exhibit 2).
In summary, Wheatley proposed that LIBOR be retained as the
standard benchmark, but that the various
rate submissions be backed up by data to suggest they were a
true reflection of estimated borrowing costs.
The reported rate submissions would be released publicly only
after a three-month lag, to remove the
incentive for banks to influence their rate submissions to signal
financial strength. Criminal sanctions
were proposed for banks that had deliberately tried to
manipulate the rates submitted.13 A new firm—the
Intercontinental Exchange (ICE)—would administer LIBOR,
and the benchmark would switch from
being known as BBA LIBOR to be called ICE LIBOR.14
ICE LIBOR
ICE LIBOR fixed the rate in five currencies: the Swiss franc,
the euro, the pound sterling, the Japanese
yen and the U.S. dollar. (Rate fixing in the Danish krone,
Swedish krona, Canadian dollar, Australian

dollar, and New Zealand dollar was terminated due to the
absence of persistent trading activity to support
credible rate submissions.) ICE maintained a reference panel of
between 11 and 18 contributor banks for
each currency in question (see Exhibit 3). Submissions were
received and ranked in descending order,
with the highest and lowest quartiles of submissions excluded.
Thirty-five rates were produced each
business day: seven for each currency (see Exhibit 4).
In March 2015, the Bank of England indicated it would create a
working group to identify an alternative to
LIBOR. It intended specifically to base the new rate on actual
transactions between banks, not on bankers’
estimates. As of April 5, 2016, the working group had not
released any information about this alternative.
Other alternative benchmarks were being suggested, including
OISs.
U.S. OVERNIGHT INDEX SWAPS
An OIS was an interest rate swap where two parties exchanged a
floating rate for a fixed interest rate on a
notional amount. The term of the contract ranged from one week

to two years or more. In the United
States, the floating rate was based on an overnight rate index:
the effective federal funds rate, as issued
daily by the U.S. Federal Reserve (see Exhibit 5). At settlement
dates, both parties agreed to exchange the
difference between interest accrued at the fixed rate and interest
accrued at the floating rate (see Exhibit
11 Ibid.
12 Graham Ruddick, “Brokers Found Not Guilty of Libor Fraud
Label Trial a Farce,” The Guardian, January 28, 2016,
accessed September 9, 2016, www.theguardian.com/uk-
news/2016/jan/28/sixth-broker-found-not-guilty-in-libor-trial.
13 John Kiff, “What Is LIBOR?” Finance & Development 49,
no. 4 (December 2012), accessed September 9, 2016,
14 “ICE Benchmark Administration (IBA): ICE LIBOR,”
Intercontinental Exchange, Inc., accessed September 9, 2016,
www.theice.com/iba/libor.

Page 6 9B16N058
6). John Hull and Alana White provided more information about
OIS in an article that contrasted these
with LIBOR:
Overnight indexed swaps are interest rate swaps in which a
fixed rate of interest is exchanged for a
floating rate that is the geometric mean of a daily overnight
rate. The calculation of the payment on the
floating side is designed to replicate the aggregate interest that
would be earned from rolling over a
sequence of daily loans at the overnight rate. In U.S. dollars,
the overnight rate used is the effective
federal funds rate. In Euros, it is the Euro Overnight Index
Average (EONIA) and, in sterling, it is the
Sterling Overnight Index Average (SONIA). 15
OIS swaps tend to have relatively short lives (often three
months or less). However, transactions that last

as long as five to ten years are becoming more common. For
swaps of one-year or less there is only a
single payment at the maturity of the swap equal to the
difference between the fixed swap rate and the
compounded floating rate multiplied by the notional and the
accrual fraction. If the fixed rate is greater
than the compounded floating rate, it is a payment from the
fixed rate payer to the floating rate payer;
otherwise it is a payment from the floating rate payer to the
fixed rate payer. Similarly to LIBOR swaps,
longer term OIS swaps are divided into 3-month sub-periods
and a payment is made at the end of each
sub-period.16
Market participants monitored the OIS market as an indicator of
the functioning of the interbank credit
market. In particular, they looked at the LIBOR-OIS spread,
which was the difference between LIBOR
and OIS rates of equal maturity. Three-month LIBOR-OIS
spreads were typically around 10 basis points.
If the spread became larger, this was usually taken as a sign that
banks were less willing to lend to each
other. A smaller spread typically indicated there was a higher
level of liquidity in the market. The three-
month LIBOR-OIS spread widened to a high of 364 basis points

in October 2008, only returning to
typical levels a year later, in September 2009 (see Exhibit 7).17
Observers suggested the large movements
in LIBOR meant it was neither the best benchmark reference
rate in the market nor a risk-free rate.
Derivative contracts were valued, or marked to market, by
discounting their payoffs at the risk-free rate,
and LIBOR was widely accepted as a proxy for this rate for the
respective maturities. LIBOR rates for
maturities up to one year were published daily and, for longer
maturities, could be derived from LIBOR-
based interest-rate swap rates. While LIBOR might continue to
underlie derivative contracts until and if a
replacement were found, were OIS rates a more suitable proxy
for the risk-free rate? Observers argued
that the three-month OIS rate reflected the credit risk associated
with a sequence of overnight federal
funds interbank loans, which was minimal compared to the risk
of a three-month interbank loan, as
evidenced by the wide spread between the two during the
financial crisis.
PricewaterhouseCoopers’ Dataline newsletter made this
observation:

Discounting derivative cash flows using OIS may represent a
change in practice for end-users.
Many valuation systems used by end-users continue to use
LIBOR-based discounting in their
15 On April 1, 2016, the EONIA rate was −0.335% per cent and
the SONIA was 0.4651 per cent. “Daily Sterling overnight
index average (SONIA) lending rate,” Quandl, accessed
September 9, 2016, www.quandl.com/data/BOE/IUDSOIA-
Daily-
Sterling-overnight-index-average-SONIA-lending-rate; “Eonia
interest rate,” global-rates.com, accessed September 9, 2016,
www.global-rates.com/interest-rates/eonia/eonia.aspx.
16 John Hull and Alana White, “LIBOR vs. OIS: The
Derivatives Discounting Dilemma,” Journal of Investment
Management
11, no. 3 (April 2013): 6–7, accessed September 9, 2016,
www.joim.com/libor-vs-ois-derivatives-discounting-dilemma/.
17 Keith Jenkins, “LIBOR-OIS Spread Increase Suggests
Collateral Concern,” Bloomberg, May 6, 2010, accessed April
5,
2016, www.bloomberg.com/news/articles/2010-05-06/libor-ois-
spread-widening-suggests-money-market-collateral-concern-

rising.
Page 7 9B16N058
derivative valuation models as a default setting. However, many
systems and service providers
are now supporting OIS discounting.
Based on the guidance in ASC 820 [updated FASB Codification
of Paragraph 5 of SFAS No.
157]18 . . . valuations derived using LIBOR-based discounting
for certain products transacted
under certain terms may no longer be representative of fair
value.19

VALUING THE INTEREST-RATE SWAP PORTFOLIO:
LIBOR OR OIS?
To inform the debate further, the head of the management team
referenced an outstanding $100 million
notional principal swap with nine months until maturity (from
April 1, 2016) and quarterly interest
settlements. In the swap, the group would receive a 2 per cent
fixed rate in return for paying the three-
month LIBOR rate. The team head projected detailed
calculations of how the swap could be valued using
the LIBOR and OIS rates prevailing on April 5, 2016 onto the
screen.
To price a derivative instrument, such as an interest-rate swap,
valuation models typically estimated the
future contractual cash flows the counterparties agreed to
exchange periodically over the life of the
contract. Historically, the mid-market value of the transaction
had been approximated by discounting
those cash flows based on the LIBOR discount rate to reflect the
time value of money.

What were the arguments for and against valuing the swap with
LIBOR versus OIS, and which one
should the financial institution use? Going forward, should OIS
replace LIBOR as the reference rate in
interest rate swaps?
18 ASC is the accounting standards codification section of the
Financial Accounting Standards Board (FASB). Deliotte’s
description of ASC 820—Fair Value Measurements and
Disclosures notes that it “applies to U.S. GAAP that require or
permit fair value measurements or disclosures and provides a
single framework for measuring fair value and requires
disclosures about fair value measurement. The Topic defines
fair value on the basis of an ‘exit price’ notion and uses a ‘fair
value hierarchy,’ which results in a market-based—rather than
entity-specific—measurement.” Deliotte, accessed
September 9, 2016, www.iasplus.com/en-
us/standards/fasb/broad-transactions/asc820. According to the
FASB’s “Summary
of Statement No. 157,” the fifth paragraph reads as follows:
This Statement emphasizes that fair value is a market-based
measurement, not an entity-specific measurement. Therefore, a

fair value measurement should be determined based on the
assumptions that market participants would use in pricing the
asset or liability. As a basis for considering market partici pant
assumptions in fair value measurements, this Statement
establishes a fair value hierarchy that distinguishes between (1)
market participant assumptions developed based on market data
obtained from sources independent of the reporting entity
(observable inputs) and (2) the reporting entity’s own
assumptions about market participant assumptions developed
based
on the best information available in the circumstances
(unobservable inputs). The notion of unobservable inputs is
intended
to allow for situations in which there is little, if any, market
activity for the asset or liability at the measurement date. In
those
situations, the reporting entity need not undertake all possible
efforts to obtain information about market participant
assumptions. However, the reporting entity must not ignore
information about market participant assumptions that is
reasonably available without undue cost and effort. “Summary
of Statement No. 157,” Financial Accounting Standards
Board, accessed September 9, 2016,
www.fasb.org/summary/stsum157.shtml.
19 PricewaterhouseCoopers, “Derivative Valuation: The

Transition to OIS Discounting,” Dataline—A Look at Current
Financial Reporting Issues no. 2013-25 (December 10, 2013): 4,
accessed April 5, 2016,
www.pwc.com/us/en/cfodirect/assets/pdf/dataline/dl-2013-25-
ois-discounting.pdf.
Page 8 9B16N058
EXHIBIT 1: INFORMATION ON THE BBA LIBOR RATE
FIXING PROCESS BY CURRENCY
…

FIN-465
Individual project - SWAPS
PLEASE SUBMIT AN ELECTRONIC (you can also upload
excel files to support with your work).
Remember that NO collaboration is allowed with anyone. If you
have any doubts about the honor code that governs the
completion of this assignment, please consult the course
syllabus or ask me!
Case (100 points) Has Libor lost its stature in derivatives
markets?
1. (30 points) What is the difference between LIBOR and OIS as
benchmarks in valuing interest-rate swaps? Is LIBOR a risk-free
rate? How was LIBOR manipulated? (MAXIMUM 250 words)
2. (40 points) Value the interest rate swap (with a notional
amount of $100m) by relying on the data provided at the end of
the case study. The swap still has 9 months until maturity, and
interest rate settlements are quarterly. The fund is receiving 2%
in return for paying the 3-month LIBOR. All rates are quoted

with compounding frequency that corresponds to the term.
Your analysis has to be done in 3 steps:
a. Compare LIBOR rates to OIS rates at similar maturities
· To compute the 9-month LIBOR rate use a simple linear
interpolation (here’s an example
https://ncalculators.com/geometry/linear-interpolation-
calculator.htm
b. Compute the 3-month forward LIBOR rates on July 5, 2016
and on October 5, 2016 (read carefully the explanations under
Exhibit 4)
c. Value the swap. Which one has a higher value?
3. (30 points) Does the valuation of an interest-rate swap in
particular, and derivatives in general, depend on who the
counterparty is and whether the contract is collateralized?
(MAXIMUM 250 words)

The Ethical Superiority and Inevitabihty
of Participatory Management
as an Organizational System
Denis Collins
School of Business, Uniuersity of Wisconsin-Madison,
Madison, Wisconsin 53706
This article asks us to consider, on ethical grounds, the
superiority of participative managementover more autocratic
alternatives. The author questions the predominance of the
autocratic
choice in both management practice and theory. Applying the
examples of both political and
economic history, the author challenges why management seems
to be the last bastion of the
autocratic choice. Also based on these examples, the author
questions how long the autocratic
tradition in management can last.

Bart Victor
Abstract
During the heady revolutionary days of the 1960s, Slater and
Bennis (1964) declared the inevitability of democracy at the
workplace. Twenty-five years later, in a retrospection of that
article, the authors claimed that they were right (Slater and
Bennis 1990). Unfortunately, the data do not support their
claim (Lawler et al. 1992). Nonetheless, workplace democracy
is inevitable.
This article argues in favor of the inevitability of participa-
tory management, one form of workplace democracy, on the
basis of its coherence to the social philosophical assumptions
about human nature that underlie the forms of political
arrangements (democracy) and economic arrangements
(mixed economy) in the United States. These communitarian
philosophical assumptions have been thoroughly argued in
the political science and economic literature to be ethically
superior to other sets of social philosophical assumptions
that underlie authoritarianism and libertarianism. Currently,
organization theory is approximately 200 years behind this
literature. Persons who experience significant benefits as a
result of the central position of "liberty" in the social
philosophical assumptions of democracy and capitalism tend

to design organizational systems that significantly restrict the
liberty of their employees.
The current push for more democratic features is coming
from organization theorists doing work on corporate culture,
total quality management, gainsharing, and other systems of
management that encourage decentralization, and from busi -
ness ethics scholars doing work on the societal accountability
of organizations. The very slow rate of evolution to work-
place democracy is primarily attributed to the central role of
the power elite. Whereas the American political and eco-
nomic revolutionaries came from within the power elite of
their times that is not yet the case for workplace democracy
advocates.
{Participatory Management; Organization Theory, Busi-
ness Ethics; Political Theory)
In reflecting over the past 40 years of management
science, the renowned management scientist/philoso-
pher C. West Churchman (1994, p. 99) concluded:
As the first editor-in-chief of Management Science, I ex-
pressed my ambition for the society (TIMS) and its journal.
My notion was that a society and journal in the subject of a

science of management would investigate how humans can
manage their affairs well. For me, "well" means "ethically,"
or in the best interest of humanity in a world of filthy
oppression and murder (I'm a philosopher and therefore have
a philosophical bias, the same bias Plato had when he wrote
The Republic). I find that 40 years later management scientists
have been inventing all kinds of mathematical models and
novelties (management by objectives, game theory, artificial
intelligence, expert systems, TQM, chaos theory), and none of
these has contributed much to the ethical benefit of human
beings. Hence, in 1993, we are still waiting for a science of
management to emerge, although there are some lights at the
end of the tunnel.
A solution to the management science ethics prob-
lem raised by Churchman and the new organizational
paradigm shifts advocated by Daft and Lewin (1993)
can be found by uniting the social philosophical as-
1047-7039/97/0805/0489/$05.00
Copyright ® 1997. Institute for Operations Research
and the Management Sciences ORGANIZATION
SCIENCE/VOI. 8, No. 5, September-October 1997 489

DENIS COLLINS The Ethical Superiority and Inevitability of
Participatory Management
Table 1 Ethical Foundations of Poiiticai, Economic, and
Organization Theories
Authoritarianism Communitarianism Libertarianism
Poiiticai Theory
Example
Role of Sovereign
Role of Subjects
Economic Theory
Example
Role of Sovereign
Role of Subjects
Organization Theory
Example
Role of Sovereign

Role of Subjects
Dictatorship
Government commands in all
matters
Citizens obey commands for
peace
Planned economy
Government commands in all
matters
Managers obey commands for
GNP
Traditional management
Managers command in all
matters
Employees obey commands
for wages

Representative democracy
Government establishes goals and
monitors for harms and deviances
Interest groups pursue seif, group, and
national interests
Mixed economy
Government establishes goais and
monitors for harms and deviances •
Managers pursue self, group, and
national interests
Participatory management
Managers establish goals and monitor for
harms and deviances
Employees pursue self, group, and
company interests

Direct democracy
Government monitors for harms
Citizens pursue self-interests
Market economy
Government monitors for harms
Managers pursue self-interests
Self-management
Managers monitor for harms
Employees pursue self-interests
sumptions of organization theory with those of political
and economic theory. The United States has been an
international force in persuading other nations to adopt
a democratic political system and a mixed economy.
The worldwide trend during the 1980s and 1990s is
away from dictatorships and toward democracy and
mixed economies. As shown in Table 1, a range of
political arrangements parallels a range of economic
arrangements. These parallels are based on shared
social philosophies about the relationship between

sovereign and subjects in the political and economic
realms. Historically, the authoritarian model has been
dismissed from both political and economic discussions
in the United States. Currently, the framework for
both political and economic discussions is defined by
communitarians and libertarians.
Some of the fundamental social philosophical as-
sumptions about human nature and social organization
made by political and economic theorists, and embod-
ied in some of our most significant political and eco-
nomic institutions, are diametrically opposed to some
of the assumptions about human nature and social
organization made by organization theorists and em-
bodied in a large number of organizational structures.
A growing stream of political, economic, and organiza-
tion theorists have pointed out this contradiction, in-
cluding Adam Smith (1976b) in The Wealth of Nations.
Smith feared that business owners would be tempted
to apply division of labor to an unethical extreme,
where the worker "becomes as stupid and ignorant as
it is possible for a human creature to become" (1976b,
vol. ii, p. 303). In the 1800s, Alexis de Tocqueville
(1945) noted that democracy in America could be un-

dermined by the developing aristocracy being estab-
lished in industrial organizations. Karl Marx (1964) was
enraged by the meaningless lives of alienated workers.
These criticisms by conservative and liberal political
and economic theorists found a home in organization
theory among prominent human relations and human
resource management writers who maintained to vari-
ous degrees that nonmanagement employees should be
active participants in an organization's decision-making
process. Thus, significant progress toward the institu-
tionalization of participatory management—a system
of management whereby nonmanagement employees
significantly influence organizational decisions—has
been made over the past century.
Unfortunately, the original ethical foundation for
the superiority of participatory manageme nt over top-
down management has been discounted by organiza-
tion theorists and managers in favor of other argu-
ments, particularly the economic efficiency argument
that participatory management is superior to top-down
management because it increases employee productiv-
ity and firm profitability. However, the empirical re-
search on participatory management provides mixed
findings (Cotton et al. 1988, Wagner 1994). For in-

stance, managers often note that there is significant
management pressure to abandon participatory man-
agement mechanisms when it becomes apparent that
490 ORGANIZATION S C I E N C E / V O L 8, No. 5,
September-October 1997
DENIS COLLINS The Ethical Superiority and Inevitabitity of
Participatory Management
employee involvement is not increasing productivity or
profitability to the high degree anticipated (Collins
1995, Likert 1967). These managers conclude that the
economic justifications were highly exaggerated or sim-
ply false and revert back to top-down management
styles. Wagner (1994) is an example of an organization
theorist reaching such a conclusion. After conducting a
meta-analytical reassessment of research on participa-
tory management that revealed "average size" im-
provements, Wagner noted that "the conclusions of
this article give cause to question the practical signifi -
cance of participation as a means of influencing perfor -
mance or satisfaction at work" (p. 327; italics added).

Question 1 (at least 200 words)Collins(p. 490) asserts the fo

Question 1 (at least 200 words)Collins(p. 490) asserts the fo

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