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Option --Meaning
 A contract between two parties whereby one party obtains the
rights, but not the obligation, to buy or sell a particular asset, at a
specified price, on or before a specified date.
 Person who acquires the right is know as the option buyer or
option holder, while the other person is know as option seller or
option writer.
 The seller of the option for giving such option to the buyer
charges an amount which is known as the option premium.
 Example : one person buys an option contract to purchase 100 shares
of SBI at Rs. 300 per share for a period of three months. It mean
that the said person has the right to purchase the share of SBI at
Rs. 300 per share within three months from the date of contract. If the
price of SBI increase, he will exercise the option, and if price falls
below Rs. 300 then he will not exercise his option.

Options Terminology
 Parties of the option contract:
 Two parties to an option contract, the buyer (the holder) and
the writer (the seller).
 Writer grants the buyer a right to buy or sell a particular asset
in exchange for a certain sum of money for the obligation
taken by him in the option contract.
 Exercise price:
 The price at which the underlying asset may be sold or
purchased by option buyer from the option writer is called as
exercise or strike price.
 At this price buyer can exercise his option.
 Option premium:
 The price at which option holder buys the right from the
option writer is called option premium or option price.
Contd:
 Price or premium is paid by the holder to the writer of the option
against the obligation undertaken.
 This is fixed and paid at the time of the formation or writing an
option deal.
 Expiration date and exercise date:
 Date on which an option contract expires is called as expiration or
maturity date.
 Option holder has the right to exercise his option on any date
before the expiration date.
 Exercise date is the date upon which the option is actually
exercised.
 Expiration date is the last day upon which option may be
exercised.
 Option ‘In’, ‘Out’ and At-the-money:
 When the underlying future prices/ stock price is greater than the
strike price or exercise price, the call option will be in-the-money.
 When the underlying future prices/ stock price is lesser than the
strike price or exercise price, the call option will be out- of-the-
money.
 When the underlying future prices/ stock price is equal to the
strike price or exercise price, the call option will be at-the-money.
 Reverse is the position in case of put option.
 Pay off profile of option.
Call option Put option
In-the-money Future > Strike Future < Strike
Out-of-the-money Futures < Strike Futures > Strike
At-the-money Futures = Strike Futures = Strike
 Break- even- price:
 Gain on the option is just equal to the option premium.
 Break-even –price level is determined by adding the strike price
and the premium paid together.
 There is Zero-sum-game, the profit from selling a call is the
mirror image of profit from buying the call.
Types of options:
 Classified into –
(1) Call and Put options
(2) American and European options
(3) Exchange – traded and OTC–traded option
 Call options :
 When an option grants the buyer (holder) the right to purchase the
underlying asset/ stock from writer (seller) a particular quantity at a
specified price within a specified expiration date, it is called ‘ Call
option 'or simply a ‘Call’.
An investor buys a call option to purchase 100 SBI shares
Strike or exercise price Rs. 320 per share
Current stock price Rs. 310 per share
Price of an option to buy one share (premium) Rs. 20
Initial investment is Rs. 2000 (100x20)
At the expiration date, SBI share price is Rs. 350. A t this time,
the option is exercised for a gain of (Rs.350 – Rs. 320) x100
=3000. W hen the initial cost is taken into account , then the net
gain is Rs. 3000 – Rs. 2000 = Rs.1000.
 Put options :
 An option contract where the option buyer has the right to sell
the underlying asset to the writer, at a specified price at or
prior to the option maturity date , is called put option or
simply a ‘put’.
An investor purchases a put option to sell 100 SBI shares
Strike price Rs. 320 per share
Current share price Rs. 310 per share
Price of put option to sell one share Rs. 15
Initial investment on the option Rs. 1500 (100x15)
Expiration of the option, SBI share price is Rs. 300. At this
time, the investor buy 100 SBI shares at Rs. 300 and then sell
at Rs 320 to the option buyer to realize Rs. 20 per share, being
Rs. 2000 in total. When the initial cost is taken into account,
the net gain Rs.2000 – Rs1500 =Rs 500.
 American options :
 American option can be exercised at any time up to and
including the expiration date.
 Definition given above relating to ‘call’ and ‘put’ options
apply to American style options.
 Option traded in the world today are American style option.
 Nothing particularly geographical about the names, it is just a
convention.
 European options:
 European option can be exercised only at the expiration date.
 Exchange-traded:
 Exchange traded option contract, like future contract are
standardized and are traded on the recognized exchanges.
 OTC- traded options:
 Over-the-counter (OTC) options are customer-tailored
agreements sold directly by the dealer rather than through an
organized exchange.
 Terms and conditions of the contract are negotiated by the
parties to the contract.
Option Valuation
 Value of an option comprises two components – (1) Intrinsic
value and (2) Time value.
 Intrinsic (basic) value of the option:
 Gain to the holder of an option on immediate exercise.
 Investor can not exercise the option before maturity in
European option , hence, intrinsic (basic) value will be just
notional (imaginary, estimated)and not actual.
 In American option where the investor can exercise his right at
any time before the expiration date.
 It is also called as fundamental value or underlying value.
 Difference between market price and strike price of the
underlying asset.
 Call option :--- is determined as:
Max[(S –X),0]
Where S is current price of the underlying asset and X is strike
price of the underlying asset.
If S > X, It is positive intrinsic value and if S = X, intrinsic
value is Zero. It can not be negative because buyer will not
exercise the option. So it cannot fall below Zero.
 Put option :--- is determined as:
Max[(X – S),0]
If X > S it is positive intrinsic value, X = S intrinsic value is
Zero, but cannot be negative.
 Time value of the option:
 Value of American option at any time prior to expiration must
be at least to its intrinsic value.
 There is some possibility (option) or probability (chance) that
the current price will move in favor of the option holder.
 Difference between the value of the option at the particular time
T and its intrinsic value at the time is called the time value of
the option.
 In European option , this argument does not hold, determination
of time value is more complex.
 Major factor are expected volatility (instability) of the stock
price, the length of the period remaining to expiry date, extent to
which the option is in or out of the money.
Difference between option and future contracts
Option contract Future contract
In option contract, buyer is not
obligated to transact the
contract at a later date, only
seller is under obligation to
perform the contract ,only if
buyer desires so.
In future contract, both the
parties, buyer and seller are
under obligation to perform the
contract.
Buyer has to pay in cash the
option price ( premium) to the
seller and this is not returned to
the buyer he insists for actual
performance of contract or not.
No cash is transferred to either
party at time of the formation
of the contract.
Contd:
In case of option contract ,
buyer of an option can lose is
the option price against which
he possesses all the potential
benefits. Maximum profit that
the seller of the option
contract may realize is the
options price.
In case of future contract,
buyer realize the gains in cash
when the price of the future
contract increase and incurs
losses in case of fall in the
prices. Position is opposite in
case of the seller of the future
contract
In case of option contract, they
are brought into existence by
being traded; if none is trade,
none exists.
In case of future contract, there
is process of closing out position
which cause contracts to cease
to exit.
Underlying Assets in Exchange-traded
options Stock options:
 Trading on standardized call options on equity shares started in
1973 on CBOE (Chicago Board Options Exchange), whereas on
put options begun in 1977.
 Stock options on a number of over-the counter stocks are also
available.
 Foreign currency options:
 Foreign currency is another important asset, which is traded in
various exchanges.
 The Philadelphia stock exchange offers both European as well as
American option contracts.
 Major currencies which are traded in the option markets are US
dollar, Australian dollar, British pound, Canadian dollar, German
mark, etc.
 Index Options:
 Like stock option, index option’s strike price is the index value at
which the buyer of the option can buy or sell the underlying stock
index.
 The strike index is converted into dollar (rupee) value by multiplying
the strike index by the multiple for the contract.
 For example, the contract multiple for the S&P 100 is $100. assume
the cash index value for the S&P100 is 750 then the dollar value of
the S&P 100 is 750 x100 = $75000
 Futures options:
 An option contract on futures contract gives the rights to buy from or
sell to the writer a specified future contract at a designated price at a
time during the life of the options.
 If the futures option is a call option, the buyer has the right to acquire
a long futures position. A put option on a futures contact grants the
buyer the right to sell one particular futures contracts to the writer at
the expiration of the option.
 Interest rate options:
 Interest rate options can be written on cash instruments or futures.
 Various debt instruments, which are used as underlying
instruments for interest rate options on different exchanges.
 Government , large banking firms and mortgage-backed-securities
dealers who make a market in such option on specific securities.
 LEAPS options ( Long Term Equity Anticipated Securities)
 These options contracts are created for a longer period.
 The longest time before expiration for a standard exchange traded
option is six-month.
 Leaps option contract designed to offer with longer period
maturities even up to 39 months.
 Leaps option are available on individual stocks and some indexes.
 FLEX options:
 It is a specific type of option contract where some terms of the
option have been customized.
 Objective of customization of some terms to meet the wide range
of portfolio strategy needs of the institutional investors that can
not be satisfied through the standard exchange-traded options.
 FLEX options can be created for individual stock, stock indexes,
treasury securities, etc.
 Traded on an option exchange and cleared and guaranteed by the
clearing house of that exchange.
 The value of FLEX option depends up on the ability to customize
the terms on four dimensions, such as underlying asset, strike
price, expiration date and settlement style.
Determinants of option prices
 Current price of the underlying assets:
 Factor influence the option price is the current price of the
asset/ stock.
 Option price will change as the stock price changes.
 Example for a call option, option price increase as the stock
price increase and vice versa. Opposite in case of put option.
 Strike price of the option:
 Strike or exercise price of the option is fixed for the life of the
option.
 In case of call option, the lower the strike price , the higher
will be the option price and vice versa, reverse in case of put
option.
 Time to expiration of the option:
 Option is a wasting asset, option has a fixed maturity, there is
no value of option.
 Longer the time to expiration of the option, higher will be the
option price.
 Time to maturity decreases, lesser time remains an option for
stock price to rise or fall , and the probability (possibility) of a
favorable price movement decreases.
 Expected stock price volatility:
 Fluctuations in stock prices in future is a major factor to
influence the option price.
 Greater the expected volatility of the price of the stock.
 Investor would be (wishing to be) willing to pay more for the
option, more premium an option writer would demand for it
due to increase risk in the option contract.
 Risk free interest rate:
 Interest rate is an important factor which creates impact on the
option price.
 Buying option contract involves investment which bears cost
for the investor.
 Higher (top, elevated) the interest rate , the greater (better,
superior) the cost of buying the underlying and carrying it to
the expiration date of the call option.
 Anticipated cash payment on the stock:
 Anticipated (estimated, expected) cash payment on the stock
tend (be likely) to decrease the price of a call option, because
cash payment make it more attractive to hold stock than to
hold the option.
 Log normal assumption:
 Stock option pricing model must make certain assumptions
about how stock prices behave over time.
 Example, if the price of SBI share is Rs. 300 today in the
market, what is the probability distribution for the price in one
week or one month or one year?
 Basic assumption in B-S option pricing model is termed as a
random walks.
 Proportional changes in the stock price in the short period are
normally distributed.
 Implies that the stock price at any future time has a log normal
distribution.
Parameters of log normal distribution
Two basic parameters, for the behavior of a stock price under log
normal distribution are as under –
(1) The expected return from the stock
(2) The volatility of the stock price
 Expected return from the stock:
 Annual average return earned by investor in a short period of time.
 Expected return desired by the investor from stock depends on
riskiness of the stock.
 Higher the risk, higher will be the expected return. Depends on the
market rate of interest in the economy.
 Expected return can be considered with the period of time, and in
time limit. Usually two estimates (1) expected return in a very
short period (2) expected return over longer period.
 Volatility of the stock:
 Volatility (instability) of stock , S.D is a measure of
uncertainty about the return provided by the stock.
 Volatilities are expressed in percentages per annum.
 Estimating the volatility on a particular stock is to analyze the
stock past price movement over period of time.
 Stock price is usually observed at fixed intervals of time ( e.g.
day, week, month, etc)
Black – Scholes option pricing model
 It is developed in 1973 by two academicians, Fisher Black and
Myron Scholes and designed to price European option.
 Modified the model to make it applicable to American option.
 Popularity of the model is that it allows for an analytical
solution. It has formula into which values are input and from
which an option price is obtained.
 Not explaining derivation of the model, rather state the B-S
model of pricing formula.
 Assumptions under B-S Model:
 There are no transaction costs or taxes.
 There are no dividend on the stock.
 Stock trading is continuous
 Call option can be exercised only on expiration.
 Investor can borrow or lend at the same risk free rate of interest.
Binomial option pricing model
 Model was advocated by Cox, Ross, Rubinstein in 1979 and
takes the form of binomial model.
 Model is like B-S model does not permit an analytical solution
rather solves the problem numerically.
 Assumptions under Binomial Pricing Model:
 There are no market frictions, i.e. no transaction cost, no bid,
no margin requirement, no restriction on short sales, no taxes.
 There is no risk of default by the other party in the contract.
 Markets are competitive. It mean market participants act as
price takers and not the makers.
 There are no arbitrage opportunities. Prices have adjusted in
such a way so that there are no arbitrage opportunities in the
market.
One-step binomial model
 Consider simple situation , a stock price is currently Rs. 20,
and it is known that after three month, it may be either Rs. 22
or Rs. 18. Considering in valuing a European call option to
buy the stock for Rs.21 in three months. In this option ,
estimating two values i.e. Rs.22 and Rs. 18, if the value turns
up to Rs. 22, the option value Rs. 1, and if Rs.18, the value
will be zero.
 S is the initial stock price Rs. 20, U is called the up factor with
U = (22-20 =2/20,1.10) and down factor D with
D = (20-18=2/20,.90) . These are also called prices relatives.
 Stock price can take place only one of the two possible values
at the end of each interval is referred as the binomial model.
Payoff of long and short call:
Buying a call:
 Buyer of a call will gain whenever the price of the asset exceeds
the strike price.
 Buyer has to pay premium the gain will arise only after the
premium amount has been recovered beyond the exercise price.
 Asset price ends up below the exercise price , the buyer will
incur a loss of the premium amount paid.
 Buyer of an American call can exercise this right at any time
during the tenure of the contract.
 Maximum loss that the buyer can incur is only premium amount,
the maximum profit can be infinite.
Consider the following input:
Asset price = Rs.120, Strike price = Rs.125, Call premium = Rs.4
We need to buy a call. The payoff from buying a call.
Asset price end Gain from
exercising call
Premium paid Net gain
120 0 -4 -4
121 0 -4 -4
122 0 -4 -4
123 0 -4 -4
124 0 -4 -4
125 0 -4 -4
126 1 -4 -3
127 2 -4 -2
128 3 -4 -1
129 4 -4 0
130 5 -4 1
131 6 -4 2
 Selling a call:
 Seller of a call will gain whenever the price of the asset ends up
below the strike price.
 Price of the asset exceeds the strike price , he will suffer losses.
 Premium initially received will offset the losses for a small extent,
but the price ends up higher, his losses are greater.
 Seller of an American call is exposed to this risk at any time
during the tenure of the contract.
 Maximum loss that the seller can incur is infinite, maximum
profit will be the premium received.
Consider the following input:
Stock price = Rs.120,Strike price = Rs.125, Call premium = Rs.4
We need to sell a call. The payoff from selling a call.
Asset price end Loss from
exercising call
Premium received Net gain
121 0 4 4
122 0 4 4
123 0 4 4
124 0 4 4
125 0 4 4
126 -1 4 3
127 -2 4 2
128 -3 4 1
129 -4 4 0
130 -5 4 -1
131 -6 4 -2
132 -7 4 -3
Payoff of long and short put:
Buying a put:
 Buyer of a put will gain whenever the price of the asset ends up
below the strike price.
 Buyer has to pay premium, the gain will arise only after the
premium amount has been recovered.
 Asset price ends up above the exercise price, buyer will incur a
loss of the premium amount paid.
 Buyer of an American put can exercise this right at any time
during the tenure of the contract.
 Maximum loss that the buyer can incur is the premium amount,
maximum gain that the buyer can get is the strike price.
Consider the following input:
Asset price = Rs.120, Strike price = Rs.125, Call premium = Rs.4
We need to buy a put. The payoff from buying a put.
Asset price end Gain from
exercising put
Premium paid Net gain
117 8 -4 4
118 7 -4 3
119 6 -4 3
120 5 -4 2
121 4 -4 1
122 3 -4 -1
123 2 -4 -2
124 1 -4 -3
125 0 -4 -4
126 0 -4 -4
127 0 -4 -4
128 0 -4 -4
Selling a put:
 Seller of a put will gain whenever the price of the asset ends
up above the strike price.
 Price of the asset falls below the strike price , he will suffer
losses.
 Premium initially received will offset the losses for a small
extent, but the price ends up lower, his losses are greater.
 Seller of an American call is exposed to this risk at any time
during the tenure of the contract.
 Maximum loss that the seller can incur is the strike price,
maximum profit will be the premium received.
Consider the following input:
Stock price = Rs.120,Strike price = Rs.125, Call premium = Rs.4
We need to sell a put. The payoff from selling a put.
Asset price end Loss from put
exercised
Premium paid Net gain
117 -8 4 -4
118 -7 4 -3
119 -6 4 -2
120 -5 4 -1
121 -4 4 0
122 -3 4 1
123 -2 4 2
124 -1 4 3
125 -0 4 4
126 -0 4 4
127 -0 4 4
128 -0 4 4

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Unit iii

  • 1. Option --Meaning  A contract between two parties whereby one party obtains the rights, but not the obligation, to buy or sell a particular asset, at a specified price, on or before a specified date.  Person who acquires the right is know as the option buyer or option holder, while the other person is know as option seller or option writer.  The seller of the option for giving such option to the buyer charges an amount which is known as the option premium.  Example : one person buys an option contract to purchase 100 shares of SBI at Rs. 300 per share for a period of three months. It mean that the said person has the right to purchase the share of SBI at Rs. 300 per share within three months from the date of contract. If the price of SBI increase, he will exercise the option, and if price falls below Rs. 300 then he will not exercise his option. 
  • 2. Options Terminology  Parties of the option contract:  Two parties to an option contract, the buyer (the holder) and the writer (the seller).  Writer grants the buyer a right to buy or sell a particular asset in exchange for a certain sum of money for the obligation taken by him in the option contract.  Exercise price:  The price at which the underlying asset may be sold or purchased by option buyer from the option writer is called as exercise or strike price.  At this price buyer can exercise his option.  Option premium:  The price at which option holder buys the right from the option writer is called option premium or option price.
  • 3. Contd:  Price or premium is paid by the holder to the writer of the option against the obligation undertaken.  This is fixed and paid at the time of the formation or writing an option deal.  Expiration date and exercise date:  Date on which an option contract expires is called as expiration or maturity date.  Option holder has the right to exercise his option on any date before the expiration date.  Exercise date is the date upon which the option is actually exercised.  Expiration date is the last day upon which option may be exercised.
  • 4.  Option ‘In’, ‘Out’ and At-the-money:  When the underlying future prices/ stock price is greater than the strike price or exercise price, the call option will be in-the-money.  When the underlying future prices/ stock price is lesser than the strike price or exercise price, the call option will be out- of-the- money.  When the underlying future prices/ stock price is equal to the strike price or exercise price, the call option will be at-the-money.  Reverse is the position in case of put option.  Pay off profile of option. Call option Put option In-the-money Future > Strike Future < Strike Out-of-the-money Futures < Strike Futures > Strike At-the-money Futures = Strike Futures = Strike
  • 5.  Break- even- price:  Gain on the option is just equal to the option premium.  Break-even –price level is determined by adding the strike price and the premium paid together.  There is Zero-sum-game, the profit from selling a call is the mirror image of profit from buying the call. Types of options:  Classified into – (1) Call and Put options (2) American and European options (3) Exchange – traded and OTC–traded option
  • 6.  Call options :  When an option grants the buyer (holder) the right to purchase the underlying asset/ stock from writer (seller) a particular quantity at a specified price within a specified expiration date, it is called ‘ Call option 'or simply a ‘Call’. An investor buys a call option to purchase 100 SBI shares Strike or exercise price Rs. 320 per share Current stock price Rs. 310 per share Price of an option to buy one share (premium) Rs. 20 Initial investment is Rs. 2000 (100x20) At the expiration date, SBI share price is Rs. 350. A t this time, the option is exercised for a gain of (Rs.350 – Rs. 320) x100 =3000. W hen the initial cost is taken into account , then the net gain is Rs. 3000 – Rs. 2000 = Rs.1000.
  • 7.  Put options :  An option contract where the option buyer has the right to sell the underlying asset to the writer, at a specified price at or prior to the option maturity date , is called put option or simply a ‘put’. An investor purchases a put option to sell 100 SBI shares Strike price Rs. 320 per share Current share price Rs. 310 per share Price of put option to sell one share Rs. 15 Initial investment on the option Rs. 1500 (100x15) Expiration of the option, SBI share price is Rs. 300. At this time, the investor buy 100 SBI shares at Rs. 300 and then sell at Rs 320 to the option buyer to realize Rs. 20 per share, being Rs. 2000 in total. When the initial cost is taken into account, the net gain Rs.2000 – Rs1500 =Rs 500.
  • 8.  American options :  American option can be exercised at any time up to and including the expiration date.  Definition given above relating to ‘call’ and ‘put’ options apply to American style options.  Option traded in the world today are American style option.  Nothing particularly geographical about the names, it is just a convention.  European options:  European option can be exercised only at the expiration date.  Exchange-traded:  Exchange traded option contract, like future contract are standardized and are traded on the recognized exchanges.
  • 9.  OTC- traded options:  Over-the-counter (OTC) options are customer-tailored agreements sold directly by the dealer rather than through an organized exchange.  Terms and conditions of the contract are negotiated by the parties to the contract.
  • 10. Option Valuation  Value of an option comprises two components – (1) Intrinsic value and (2) Time value.  Intrinsic (basic) value of the option:  Gain to the holder of an option on immediate exercise.  Investor can not exercise the option before maturity in European option , hence, intrinsic (basic) value will be just notional (imaginary, estimated)and not actual.  In American option where the investor can exercise his right at any time before the expiration date.  It is also called as fundamental value or underlying value.  Difference between market price and strike price of the underlying asset.
  • 11.  Call option :--- is determined as: Max[(S –X),0] Where S is current price of the underlying asset and X is strike price of the underlying asset. If S > X, It is positive intrinsic value and if S = X, intrinsic value is Zero. It can not be negative because buyer will not exercise the option. So it cannot fall below Zero.  Put option :--- is determined as: Max[(X – S),0] If X > S it is positive intrinsic value, X = S intrinsic value is Zero, but cannot be negative.
  • 12.  Time value of the option:  Value of American option at any time prior to expiration must be at least to its intrinsic value.  There is some possibility (option) or probability (chance) that the current price will move in favor of the option holder.  Difference between the value of the option at the particular time T and its intrinsic value at the time is called the time value of the option.  In European option , this argument does not hold, determination of time value is more complex.  Major factor are expected volatility (instability) of the stock price, the length of the period remaining to expiry date, extent to which the option is in or out of the money.
  • 13. Difference between option and future contracts Option contract Future contract In option contract, buyer is not obligated to transact the contract at a later date, only seller is under obligation to perform the contract ,only if buyer desires so. In future contract, both the parties, buyer and seller are under obligation to perform the contract. Buyer has to pay in cash the option price ( premium) to the seller and this is not returned to the buyer he insists for actual performance of contract or not. No cash is transferred to either party at time of the formation of the contract.
  • 14. Contd: In case of option contract , buyer of an option can lose is the option price against which he possesses all the potential benefits. Maximum profit that the seller of the option contract may realize is the options price. In case of future contract, buyer realize the gains in cash when the price of the future contract increase and incurs losses in case of fall in the prices. Position is opposite in case of the seller of the future contract In case of option contract, they are brought into existence by being traded; if none is trade, none exists. In case of future contract, there is process of closing out position which cause contracts to cease to exit.
  • 15. Underlying Assets in Exchange-traded options Stock options:  Trading on standardized call options on equity shares started in 1973 on CBOE (Chicago Board Options Exchange), whereas on put options begun in 1977.  Stock options on a number of over-the counter stocks are also available.  Foreign currency options:  Foreign currency is another important asset, which is traded in various exchanges.  The Philadelphia stock exchange offers both European as well as American option contracts.  Major currencies which are traded in the option markets are US dollar, Australian dollar, British pound, Canadian dollar, German mark, etc.
  • 16.  Index Options:  Like stock option, index option’s strike price is the index value at which the buyer of the option can buy or sell the underlying stock index.  The strike index is converted into dollar (rupee) value by multiplying the strike index by the multiple for the contract.  For example, the contract multiple for the S&P 100 is $100. assume the cash index value for the S&P100 is 750 then the dollar value of the S&P 100 is 750 x100 = $75000  Futures options:  An option contract on futures contract gives the rights to buy from or sell to the writer a specified future contract at a designated price at a time during the life of the options.  If the futures option is a call option, the buyer has the right to acquire a long futures position. A put option on a futures contact grants the buyer the right to sell one particular futures contracts to the writer at the expiration of the option.
  • 17.  Interest rate options:  Interest rate options can be written on cash instruments or futures.  Various debt instruments, which are used as underlying instruments for interest rate options on different exchanges.  Government , large banking firms and mortgage-backed-securities dealers who make a market in such option on specific securities.  LEAPS options ( Long Term Equity Anticipated Securities)  These options contracts are created for a longer period.  The longest time before expiration for a standard exchange traded option is six-month.  Leaps option contract designed to offer with longer period maturities even up to 39 months.  Leaps option are available on individual stocks and some indexes.
  • 18.  FLEX options:  It is a specific type of option contract where some terms of the option have been customized.  Objective of customization of some terms to meet the wide range of portfolio strategy needs of the institutional investors that can not be satisfied through the standard exchange-traded options.  FLEX options can be created for individual stock, stock indexes, treasury securities, etc.  Traded on an option exchange and cleared and guaranteed by the clearing house of that exchange.  The value of FLEX option depends up on the ability to customize the terms on four dimensions, such as underlying asset, strike price, expiration date and settlement style.
  • 19. Determinants of option prices  Current price of the underlying assets:  Factor influence the option price is the current price of the asset/ stock.  Option price will change as the stock price changes.  Example for a call option, option price increase as the stock price increase and vice versa. Opposite in case of put option.  Strike price of the option:  Strike or exercise price of the option is fixed for the life of the option.  In case of call option, the lower the strike price , the higher will be the option price and vice versa, reverse in case of put option.
  • 20.  Time to expiration of the option:  Option is a wasting asset, option has a fixed maturity, there is no value of option.  Longer the time to expiration of the option, higher will be the option price.  Time to maturity decreases, lesser time remains an option for stock price to rise or fall , and the probability (possibility) of a favorable price movement decreases.  Expected stock price volatility:  Fluctuations in stock prices in future is a major factor to influence the option price.  Greater the expected volatility of the price of the stock.  Investor would be (wishing to be) willing to pay more for the option, more premium an option writer would demand for it due to increase risk in the option contract.
  • 21.  Risk free interest rate:  Interest rate is an important factor which creates impact on the option price.  Buying option contract involves investment which bears cost for the investor.  Higher (top, elevated) the interest rate , the greater (better, superior) the cost of buying the underlying and carrying it to the expiration date of the call option.  Anticipated cash payment on the stock:  Anticipated (estimated, expected) cash payment on the stock tend (be likely) to decrease the price of a call option, because cash payment make it more attractive to hold stock than to hold the option.
  • 22.  Log normal assumption:  Stock option pricing model must make certain assumptions about how stock prices behave over time.  Example, if the price of SBI share is Rs. 300 today in the market, what is the probability distribution for the price in one week or one month or one year?  Basic assumption in B-S option pricing model is termed as a random walks.  Proportional changes in the stock price in the short period are normally distributed.  Implies that the stock price at any future time has a log normal distribution.
  • 23. Parameters of log normal distribution Two basic parameters, for the behavior of a stock price under log normal distribution are as under – (1) The expected return from the stock (2) The volatility of the stock price  Expected return from the stock:  Annual average return earned by investor in a short period of time.  Expected return desired by the investor from stock depends on riskiness of the stock.  Higher the risk, higher will be the expected return. Depends on the market rate of interest in the economy.  Expected return can be considered with the period of time, and in time limit. Usually two estimates (1) expected return in a very short period (2) expected return over longer period.
  • 24.  Volatility of the stock:  Volatility (instability) of stock , S.D is a measure of uncertainty about the return provided by the stock.  Volatilities are expressed in percentages per annum.  Estimating the volatility on a particular stock is to analyze the stock past price movement over period of time.  Stock price is usually observed at fixed intervals of time ( e.g. day, week, month, etc)
  • 25. Black – Scholes option pricing model  It is developed in 1973 by two academicians, Fisher Black and Myron Scholes and designed to price European option.  Modified the model to make it applicable to American option.  Popularity of the model is that it allows for an analytical solution. It has formula into which values are input and from which an option price is obtained.  Not explaining derivation of the model, rather state the B-S model of pricing formula.  Assumptions under B-S Model:  There are no transaction costs or taxes.  There are no dividend on the stock.  Stock trading is continuous  Call option can be exercised only on expiration.  Investor can borrow or lend at the same risk free rate of interest.
  • 26. Binomial option pricing model  Model was advocated by Cox, Ross, Rubinstein in 1979 and takes the form of binomial model.  Model is like B-S model does not permit an analytical solution rather solves the problem numerically.  Assumptions under Binomial Pricing Model:  There are no market frictions, i.e. no transaction cost, no bid, no margin requirement, no restriction on short sales, no taxes.  There is no risk of default by the other party in the contract.  Markets are competitive. It mean market participants act as price takers and not the makers.  There are no arbitrage opportunities. Prices have adjusted in such a way so that there are no arbitrage opportunities in the market.
  • 27. One-step binomial model  Consider simple situation , a stock price is currently Rs. 20, and it is known that after three month, it may be either Rs. 22 or Rs. 18. Considering in valuing a European call option to buy the stock for Rs.21 in three months. In this option , estimating two values i.e. Rs.22 and Rs. 18, if the value turns up to Rs. 22, the option value Rs. 1, and if Rs.18, the value will be zero.  S is the initial stock price Rs. 20, U is called the up factor with U = (22-20 =2/20,1.10) and down factor D with D = (20-18=2/20,.90) . These are also called prices relatives.  Stock price can take place only one of the two possible values at the end of each interval is referred as the binomial model.
  • 28. Payoff of long and short call: Buying a call:  Buyer of a call will gain whenever the price of the asset exceeds the strike price.  Buyer has to pay premium the gain will arise only after the premium amount has been recovered beyond the exercise price.  Asset price ends up below the exercise price , the buyer will incur a loss of the premium amount paid.  Buyer of an American call can exercise this right at any time during the tenure of the contract.  Maximum loss that the buyer can incur is only premium amount, the maximum profit can be infinite.
  • 29. Consider the following input: Asset price = Rs.120, Strike price = Rs.125, Call premium = Rs.4 We need to buy a call. The payoff from buying a call. Asset price end Gain from exercising call Premium paid Net gain 120 0 -4 -4 121 0 -4 -4 122 0 -4 -4 123 0 -4 -4 124 0 -4 -4 125 0 -4 -4 126 1 -4 -3 127 2 -4 -2 128 3 -4 -1 129 4 -4 0 130 5 -4 1 131 6 -4 2
  • 30.  Selling a call:  Seller of a call will gain whenever the price of the asset ends up below the strike price.  Price of the asset exceeds the strike price , he will suffer losses.  Premium initially received will offset the losses for a small extent, but the price ends up higher, his losses are greater.  Seller of an American call is exposed to this risk at any time during the tenure of the contract.  Maximum loss that the seller can incur is infinite, maximum profit will be the premium received.
  • 31. Consider the following input: Stock price = Rs.120,Strike price = Rs.125, Call premium = Rs.4 We need to sell a call. The payoff from selling a call. Asset price end Loss from exercising call Premium received Net gain 121 0 4 4 122 0 4 4 123 0 4 4 124 0 4 4 125 0 4 4 126 -1 4 3 127 -2 4 2 128 -3 4 1 129 -4 4 0 130 -5 4 -1 131 -6 4 -2 132 -7 4 -3
  • 32. Payoff of long and short put: Buying a put:  Buyer of a put will gain whenever the price of the asset ends up below the strike price.  Buyer has to pay premium, the gain will arise only after the premium amount has been recovered.  Asset price ends up above the exercise price, buyer will incur a loss of the premium amount paid.  Buyer of an American put can exercise this right at any time during the tenure of the contract.  Maximum loss that the buyer can incur is the premium amount, maximum gain that the buyer can get is the strike price.
  • 33. Consider the following input: Asset price = Rs.120, Strike price = Rs.125, Call premium = Rs.4 We need to buy a put. The payoff from buying a put. Asset price end Gain from exercising put Premium paid Net gain 117 8 -4 4 118 7 -4 3 119 6 -4 3 120 5 -4 2 121 4 -4 1 122 3 -4 -1 123 2 -4 -2 124 1 -4 -3 125 0 -4 -4 126 0 -4 -4 127 0 -4 -4 128 0 -4 -4
  • 34. Selling a put:  Seller of a put will gain whenever the price of the asset ends up above the strike price.  Price of the asset falls below the strike price , he will suffer losses.  Premium initially received will offset the losses for a small extent, but the price ends up lower, his losses are greater.  Seller of an American call is exposed to this risk at any time during the tenure of the contract.  Maximum loss that the seller can incur is the strike price, maximum profit will be the premium received.
  • 35. Consider the following input: Stock price = Rs.120,Strike price = Rs.125, Call premium = Rs.4 We need to sell a put. The payoff from selling a put. Asset price end Loss from put exercised Premium paid Net gain 117 -8 4 -4 118 -7 4 -3 119 -6 4 -2 120 -5 4 -1 121 -4 4 0 122 -3 4 1 123 -2 4 2 124 -1 4 3 125 -0 4 4 126 -0 4 4 127 -0 4 4 128 -0 4 4