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option basics
1. History of Options
• First use in Greece, 300 BC by olive speculator.
• Used in Netherlands in the Tulip bubble,1600s.
• England-18th century by corporate entities.
• Futures markets developed in US-19th century.
• Call options opened for trading, CBOE, 1973.
• Options based on Black-Scholes model
• Put options began trading in 1977.
• Nobel Prize for BS in 1997.
2. Option Basics-overview
• What is an option?
• Call and Put options.
• Long vs Short
• Premium
• Call option
• Selling an option
• Payoff vs Profit
• Call option payoff diagrams-long and short.
• Put option payoff diagrams-long and short.
• Break-even
• Assignment
• Value of an option (Intrinsic/Time)
• Money-ness of an option.
• Determinants of option price.
• Boundary Conditions.
3. What are options?
• The dictionary defines an option as a right to
choose or in other words a having a choice.
• In the world of finance this right to choose or
having a choice is called an OPTION.
• Like other derivatives, options are traded on an
underlying asset.(stocks, indices, commodities,
foreign exchange, interest rates)
4. What is this right to choose?
• The holder of a forward contract is obliged to trade at
maturity. He does not have a choice . He must take
possession of the asset, regardless of whether the
underlying asset has risen or fallen in price.
• An option provides the buyer/holder the right, but not
the obligation, to a future exchange at a price or rate
determined in the present. (Who has the obligation?)
• Does the option come free?
• The two most common ones are call options and put
options.
• Options are considered a low cost way to make an
investment without fully committing.
5. Call Vs Put Option
Call Option
• A call option gives the
buyer the right (not the
obligation)
• to buy an underlying
asset at an agreed
upon price (the strike
price) at a date in the
future (the expiration
date)
Put Option
• A Put Option gives the
buyer the right (but not
the obligation)
• to sell an underlying
asset at an
agreed‐upon‐price (the
strike price) at a date in
the future (the
expiration date ).
6. Buyer Seller Buyer Seller
1. Asset (Buy/Sell) Buy Sell Sell Buy
2.Right/Obligation Right Obligation Right Obligation
3.Premium (Pay/Receive) Pay Receive Pay Receive
4.Bullish/Bearish Bullish Bearish Bearish Bullish
5. Profits Unlimited Limited Unlimited Limited
to Premium to Premium
6.Losses Limited Unlimited Limited Unlimited
to Premium to Premium
7.Breakeven
8. Value on expiry Max(S-K,0) Max (K-S,0)
S = Market price of asset
K = Strike Price
Call Option(Right to buy) Put Option(Right to Sell)
Strike Price + Premium Strike Price - Premium
Call Option Vs. Put Option
7. Call + and Put -
Put
Buyer
Call
Option
Seller
Buyer
Seller
9. PCR
PCR means Put Call Ratio
Put Call Ratio means, the Volume of Put
Options to the Volume of Call of Options.
Put option expects, the Stock price to fall.
Call Option buyer expects the Stock price to
rise.
10. PCR
When calls are more than Puts, means the
anticipation of market is of a Bullish Sentiment.
When puts are more than calls, means it is a
sentiment of Bearish Market.
At the end of the day, when Put to call ratio is
taken, the overall market sentiment can be
captured.
11. PCR Analysis - Summary
PCR Higher
Puts Are More
Than Calls
Bearish
PCR Lower
Calls Are More
Than Puts
Bullish
12. Long Vs Short
Long
• Long-The position resulting from the purchase of a
contract or instrument, including an option.
• Long Position- ownership of a security, contract or
commodity that grants the owner the right to
transfer ownership by sale or gift.
Short
• Short- the sale of a contract or instrument that you
do not own (how?)
• Short option position-the position of an option
writer/seller that represents an obligation on the
part of the option writer to meet the terms of the
option if it is exercised by the owner.
13. OPTION
Seller
Premium Premium
Call Option PutOption
Itcan easily be seen fromthe above, thatboth acall option and aputoption have a
buyerand aseller. The buyerhas the right, and the sellerhas the obligation ,if the
buyerchooses to exercise the option. In return forthe option, the buyerpays the
sellerapremium.
CALL (Right, not
obligation to Buy)
PUT(Right, not
obligation to Sell)
BUYER SELLER BUYER
14. Option Terminology.
• Premium – the amount paid to the seller for buying an option
(call or Put) at the time of agreement. (Initial Investment)
• Strike price (K) – The price at which the option holder may buy or
sell the underlying as defined in the option contract. Also known
as exercise price.
• Exercise – Electing to buy or sell the underlier is known as
exercising the option.
• Time to expiration (T) – time units (a time unit has the length t)
until expiration
• European Option – the holder can exercise this option only at
expiry
• American Option – the holder can exercise this option at any time
during the life of the option
• (The right to exercise at any time is clearly valuable. Therefore
the value of an American option cannot be less than an
equivalent European option)
• Market Price, or Spot Price (S) – the current price you have to pay
in the market for the underlying.
15. Premium
• Why does the buyer of an option(call or put),
have to pay a premium?
• The buyer of an option has potential for profit
without the risk of a loss. For this situation the
buyer of an option has to pay a premium.
• What is the maximum loss ,that a buyer of an
option can incur?
16. Call option
• If the market price of the underlying is higher
than the strike price, it is profitable to exercise
the option.
• If market price is lower, the option holder
(buyer) is not obliged to exercise it since he
would incur a loss. The option would
automatically expire on its last date(expiry date)
17. Call option
• A call option gives the investor the right (not
the obligation!) to buy an underlying asset at an
agreed upon price (the strike price) at a date in
the future (the expiration date)
• The holder of a call option wants the underlying
asset to rise as much as possible so that he can
buy the asset for a relatively small amount, then
sell it and make money.
• The value of a purchased call option on expiry is
given by the expression max{S – K, 0} .The value
cannot be negative (also called payoff). Why?
18. Important-Selling an option.
• The seller of an option has a limited upside,
( is limited to the premium received), but an
unlimited downside depending on price
movement. Selling an option is risky.
19. Selling a call option
The call option we have discussed so far is a
purchased call option. But we can sell a call option
also. When we sell a call option we receive a
premium. Then we speak of a written call option.
The payoff and the profit of a written call option are
just the mirror images of the corresponding
purchased option.
20. Payoff Vs Profit
• Payoff is what we get when the option is
exercised, excluding the premium paid upfront.
Payoff minus premium = profit.
• Think of a lottery you won for Rs. 100000. This is
the payoff. If you bought the lottery ticket for Rs.
10, your profit is 99990. (100000-10).
• Payoff = Value of option = Vt.
• Profit = Payoff-premium.
25. Put Option
•A Put Option gives the holder the right (but not the
obligation!) to sell an underlying asset at an
agreed‐upon‐price (the strike price) at a date in the
future (the expiration date T).
•The holder of a put option wants the underlying asset
to fall as much as possible
•The payoff function of a Purchased Put Option on
expiry is max{ K – S, 0}, Cannot be negative.
26. Put Option
Strike Price(K)= 100
Premium= 5
Price(S)
80 20 15 -20 -15
85 15 10 -15 -10
90 10 5 -10 -5
95 5 0 -5 0
100 0 -5 0 5
105 0 -5 0 5
110 0 -5 0 5
115 0 -5 0 5
120 0 -5 0 5
Value/Payoff, of a put option-max{K-S, 0}
.The value cannot be negative
Long Put Short Put
Buyers
Payoff
Buyers
Profit
Sellers
Payoff
Sellers
Profit
31. Breakeven-Put
Strike Price(K)= 100
Premium= 5
Price(S)
80 20 15 -20 -15
85 15 10 -15 -10
90 10 5 -10 -5
95 5 0 -5 0
100 0 -5 0 5
105 0 -5 0 5
110 0 -5 0 5
115 0 -5 0 5
120 0 -5 0 5
What do you observe?
Long Put Short Put
Buyers
Payoff
Buyers
Profit
Sellers
Payoff
Sellers
Profit
32. Payoff Profile - Summary
Call
Buyer
• Profits unlimited
• Losses limited to the premium paid
Seller
• Profits limited to the premium received
• Losses unlimited
Put
Buyer
• Profits unlimited
• Losses limited to the premium paid
Seller
• Profits limited to the premium received
• Losses unlimited
33. What is assignment?
• Notification by the Options Clearing Corporation
to the seller or writer of an option that the
owner (who?) has exercised the option and the
terms of settlement must be met.
34. Naked Option (Uncovered option)
• A short option position that is not fully covered
if notification of assignment is received.
• A short call position is uncovered if the writer
does not have a long stock or long call position.
• A short put position is uncovered if the writer is
not short stock or long another put.
35. Value of an option
• Option Price (Premium) = Intrinsic Value + Time
Value.
• Intrinsic Value: For a call option, it is the greater
of,(a) Spot price (S) minus Strike Price (K) (b)
Zero. : For a put option, it is the greater of,(a)
Strike price(K) minus Spot Price (S)(b) Zero.
• Time Value is the value of an option arising from
time left to maturity/expiry.
• If premium is more than the intrinsic value, the
difference is time value.
36. Money-ness of an option ( from buyers point of view)
• In the case of a call option if the spot price is
greater than the strike price, it is In–the- Money.
If strike price is more than the spot price, it is
Out-of-the-Money .
• In the case of a put option if the strike price is
greater than the spot price it is In-the-Money .If
spot price is more than strike price, it is Out of
the Money.
• In the case of both Call and Put Options, if the
strike price equals the spot price, the option is
At the Money.
37. Intrinsic value, Time value & Moneyness
Call 57.00 52.50 7.00 ITM 4.50 2.50
Call 66.00 60.00 6.00 ITM 6.00 0.00
Call 75.00 72.00 3.50 ITM 3.00 0.50
Call 84.00 84.00 2.00 ATM 0.00 2.00
Call 89.00 90.00 1.00 OTM 0.00 1.00
Put 91.00 95.00 6.00 ITM 4.00 2.00
Put 102.00 108.00 8.50 ITM 6.00 2.50
Put 46.00 50.00 5.00 ITM 4.00 1.00
Put 35.00 35.00 1.50 ATM 0.00 1.50
Put 32.00 31.00 0.50 OTM 0.00 0.50
Time
Value
Type of
Option
Stock
Price
Exercise
Price
Option
Price
Money-
ness
Intrinsic
Value
38. Determinants of Option Price/Premium
1. Spot/Market Price. (S)
2. Strike Price. (K)
3. Time to expiry. (T)
4. Volatility (Standard Deviation σ)
5. Risk free Interest rate ( r )
We shall look at each of these from the holders/
buyers point of view.
39. Determinants of Option Price/Premium
Stock price (S) and Strike Price (K)
1. Call Option.
• Payoff = Stock Price – Strike Price.
• Therefore calls become more valuable when
stock price increases and less valuable when
strike price increases
2.Put option
• Payoff = Strike Price – Stock Price.
• Therefore puts become less valuable when stock
price increases and more valuable when strike
price increases.
40. Determinants of Option Price/Premium
Time to Expiry (T)
• Increasing time to expiry increases the value of
both calls and puts.
• The more time remains, the more favourable
values the underlier can potentially take. More
likely the option can expire ‘’ in the money’’.
• Extremes – tomorrow vs never
41. Determinants of Option Price/Premium
Volatility (σ )
• Like time to expiration, increasing volatility,
increases the value of both calls and puts.
• The more the stock price fluctuates the greater
the chance that it will expire ‘’ in the money’’.
• It is the most interesting price factor to option
traders. So much so that ‘’trading options’’ is
often called ‘’trading volatility’’
• Stock prices change continuously and
unpredictably, but options are all about
probability. Volatility (sd) is literally an indicator
of the probability of future stock prices.
42. Determinants of Option Price/Premium
Risk free Interest rate ( r )
• Increasing interest rates increases the value of a call
and decreases the value of a put.
• The intuition isn’t as obvious as with other factors
because it involves opportunity costs.
• Call- given a choice of buying a stock for Rs. 50 or
buying a call on the same stock (K=50) for Rs.5,
buying the call gives Rs. 45 additional on which
interest can be earned, till the call is exercised.
• Put-given a choice of selling a stock for Rs. 50 or
buying a put on the same stock (K=50) for Rs.5,
buying the put gives Rs. 55 less on which interest is
lost, till the put is exercised.
43. Effect of factor changes on option prices
Factor Effect on Call Effect on Put
Increase S + (-)
Increase K (-) +
Increase T + +
Increase σ + +
Increase r + (-)
44. Boundary conditions for options
• Option prices have upper and lower bounds.
• If an option price is above the upper bound or
below the lower bound, then there are profitable
opportunities for arbitrageurs.
45. Upper Bounds
Call (E & A)- a call option gives the holder the right to buy
one share of a stock for a certain price. No matter what
happens the option price can never be worth more than
the stock price. C ≤ S0. Why no time value?
If this relationship were not true an arbitrageur can easily
make a riskless profit by buying the stock and selling the
call.
Put (A) -a put option gives the holder the right to sell one
share of a stock for the strike price K. No matter how low
the stock price becomes the option can never be worth
more than K. P ≤ K. Why no time value?
47. • Remember interest rate ‘r’ is always
per annum unless specifically stated.
48. S0 - Ke-rT
where S0 is the current stock price.
A lower bound for the price of a call option on a non-dividend
paying stock is :
Lower Bound for calls on non-dividend paying stocks
49. S0-Ke-rt
= 20-18e-(0.1)(1)
= 3.71 (Theoretical minimum)
If the actual call price is 3.00, lesser than the theoretical
minimum, an arbitrageur can sell the stock and buy the call to
provide a cash inflow of 20- 3= 17. If invested for 1year at 10%
per annum 17grows to 17e0.1
=18.79.
At the end of the year, the option expires. If the stock price is
greater than 18.00,the arbitrageur exercises the option for 18.00
and makes a profit of 18.79- 18.00= 0.79.
If the stock price is less than 18.00, the stock is bought in the
market and the option expires. If the stock price is 17, the
arbitrageurs profit is 18.79- 17.00=1.79.
Lower Bound for calls- numerical example:
Suppose S0 =20,K =18, r = 10% and T = 1year. Then:
50. Ke-rt
- S0
where S0 is the current stock price.
Lower Bound for puts on non-dividend paying stocks
A lower bound for the price of a put option on a non-dividend
paying stock is :
51. Ke-rt
- S0 = 40e-0.05x0.5
- 37= 2.01 (Theoretical minimum)
At the end of 6 months, the option expires. If the stock price is
below 40.00 ,the arbitrageur exercises the option to sell the stock for $
40.00,repays the loan and makes a profit of 40.00-38.96 = 1.04.
If the stock price is more than 40.00, the option expires and the
arbitrageur sells the stock and repays the loan. If the stock price is 42,
the arbitrageurs profit is 42.00 - 38.96 = 3.04.
Lower Bound for puts- numerical example:
Suppose S0 =37,K =40 , r = 5% and T = 0.5 years. Then:
If the actual put price is 1.00, lesser than the theoretical minimum,
an arbitrageur can borrow 38.00 for 6 months and buy the stock and
the put . At the end of 6 months, the arbitrageur will be required to
repay 38e0.05 x 0.5
= 38.96.
53. Problems on lower boundaries
1.Consider a call option on a non-dividend-paying stock when the stock
price is 51, the strike price is 50,the time to maturity is 6 months and the
risk free interest rate is 12%. Calculate the lower bound for the call price.
2.Consider a put option on a non-dividend-paying stock when the stock
price is 38, the strike price is 40,the time to maturity is 3 months and the
risk free interest rate is 10%. Calculate the lower bound for the put price.
54. S0 - Ke-rT
= 3.91
Ke-rt
- S0 = 1.01
1.Consider a call option on a non-dividend-paying stock when the stock
price is 51, the strike price is 50,the time to maturity is 6 months and the
risk free interest rate is 12%. Calculate the lower bound for the call price.
2.Consider a put option on a non-dividend-paying stock when the stock
price is 38, the strike price is 40,the time to maturity is 3 months and the
risk free interest rate is 10%. Calculate the lower bound for the put price.
55. • When the strike price is lower than the spot price
of the underlying a call option will be :
a) At the money.
b) In the money.
c) Out of the money
d) American type.
56. An investor has Unitech shares in her portfolio. RBI
is increasing interest rates in the next 3 months
which is negative for the stock. What should the
investor do?
a) Buy 3 month call option of Unitech.
b) Buy 2 month put option of Unitech.
c) Sell 3 month put option of Unitech.
d) Buy 3 month put option of Unitech.
57. An investor bought a put option on a stock with a
strike price of Rs. 2000 for Rs. 200. The option will
be in the money when:
a) The stock price is less than 2000.
b) The stock price is greater than 2200.
c) The stock price is greater than 2000.
d) The stock price is less than 1800.
58. Which of the following positions has a limited
downside?
a) Sell futures.
b) Buy call option.
c) Sell stock.
d) Sell call option.
59. Nifty is trading at Rs. 3325 and an investor buys a
3400 call for Rs. 100. What should be the price of
Nifty on expiry, above which the investor starts to
make profits?
a) 3425
b) 3400
c) 3325
d) 3500
