Chapter 9- Parity and Other option relatinship.ppt

Chapter 9Parity and Other Option Relationships

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-*

Put-Call ParityFor European options with the same strike price and time to expiration the parity relationship isCall put = PV (forward price strike price)or

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-*

Parity for Options on StocksGiven the interest is continuously compounded, if underlying asset is a stock and PV0,T(Div) is the present value of the dividends payable over the life of the option, then PV( F0,T )= S0 PV0,T (Div), therefore: C(K,T) P(K,T) = S0 PV0,T(Div) PV0,T(K)C(K,T) P(K,T) = S0 PV0,T(Div + K)

With:S0 :Long stockPV0,T(Div + K): Long a zero-coupon Bond ( or lending )

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-*

Parity for Options on StocksIf underlying asset is an index, , therefore:

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-*

Parity for Options on Stocks (contd)Examples 9.1 & 9.2Price of a non-dividend-paying stock: $40, r=8%, option strike price: $40, time to expiration: 3 months, European call: $2.78, European put: $1.99. $2.78=$1.99+$40 $40e -0.08x0.25Additionally, if the stock pays $5 just before expiration, call: $0.74, and put: $4.85. $0.74-$4.85=($40 $5e-0.08x0.25) $40e-0.08x0.25Synthetic security creation using paritySynthetic stock: buy call, sell put, lend PV of strike and dividendsSynthetic T-bill: buy stock, sell call, buy putSynthetic call: buy stock, buy put, borrow PV of strike and dividends Synthetic put: sell stock, buy call, lend PV of strike and dividends

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-*

Properties of Option PricesEuropean versus American OptionsSince an American option can be exercised at anytime, whereas a European option can only be exercised at expiration, an American option must always be at least as valuable as an otherwise identical European optionCAmer(S, K, T) > CEur(S, K, T) PAmer(S, K, T) > PEur(S, K, T)

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-*

Properties of Option Prices (contd)Maximum and Minimum Option PricesCall price cannotbe negativeexceed stock price

Put price cannotBe negativebe more than the strike price

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-*

Option priceOption price = intrinsic value + time value

With call option: intrinsic value at any point in time is the difference between underlying stock price and strike price.With put option: intrinsic value at any point in time is the difference between strike price and underlying stock price. The longer the time to expiration, the higher the time value.

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-*

Properties of Option Prices (contd)Early exercise for American optionsAn American call option on a non-dividend-paying stock should not be exercised early, becauseCAmer Ceur > ST -KThat means, one would lose money be exercising early instead of selling the option

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-*

Properties of Option Prices (contd)Time to ExpirationAn American option (both put and call) with more time to expiration is at least as valuable as an American option with less time to expiration. A European call option on a non-dividend-paying stock will be more valuable than an otherwise identical option with less time to expiration.

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-*

Properties of Option Prices (contd)Different strike prices (K1 < K2 < K3), for both European and American optionsA call with a low strike price is at least as valuable as an otherwise identical call with higher strike price

A put with a high strike price is at least as valuable as an otherwise identical put with low strike price

The premium difference between otherwise identical calls with different strike prices cannot be greater than the difference in strike prices

2013 Pearson Education, Inc., publishing as Prentice Hall. All rights reserved.9-*

Properties of Option Prices (contd)Different strike prices (K1 < K2 < K3), for both European and American optionsThe premium difference between otherwise identical puts with different strike prices cannot be greater than the difference in strike prices P(K2) P(K1) K2 K1

*********