Chapter 7 - Option greeks. This chapter presents the following content: Introduction, the principal option pricing derivatives, other derivatives, delta neutrality, two markets: directional and speed, dynamic hedging. | © 2004 South-Western Publishing Chapter 7 Option Greeks Outline Introduction The principal option pricing derivatives Other derivatives Delta neutrality Two markets: directional and speed Dynamic hedging Introduction There are several partial derivatives of the BSOPM, each with respect to a different variable: Delta Gamma Theta Etc. The Principal Option Pricing Derivatives Delta Measure of option sensitivity Hedge ratio Likelihood of becoming in-the-money Theta Gamma Sign relationships Delta Delta is an important by-product of the Black-Scholes model There are three common uses of delta Delta is the change in option premium expected from a small change in the stock price Measure of Option Sensitivity For a call option: For a put option: Measure of Option Sensitivity (cont’d) Delta indicates the number of shares of stock required to mimic the returns of the option ., a call delta of means it will act like shares of stock If the stock price rises by $, the call option will advance by about 80 cents Measure of Option Sensitivity (cont’d) For a European option, the absolute values of the put and call deltas will sum to one In the BSOPM, the call delta is exactly equal to N(d1) Measure of Option Sensitivity (cont’d) The delta of an at-the-money option declines linearly over time and approaches at expiration The delta of an out-of-the-money option approaches zero as time passes The delta of an in-the-money option approaches as time passes Hedge Ratio Delta is the hedge ratio Assume a short option position has a delta of . If someone owns 100 shares of the stock, writing four calls results in a theoretically perfect hedge Likelihood of Becoming In-the-Money Delta is a crude measure of the likelihood that a particular option will be in the money at option expiration ., a delta of indicates approximately a 45 percent chance that the stock price will be above the option striking price at . | © 2004 South-Western Publishing Chapter 7 Option Greeks Outline Introduction The principal option pricing derivatives Other derivatives Delta neutrality Two markets: directional and speed Dynamic hedging Introduction There are several partial derivatives of the BSOPM, each with respect to a different variable: Delta Gamma Theta Etc. The Principal Option Pricing Derivatives Delta Measure of option sensitivity Hedge ratio Likelihood of becoming in-the-money Theta Gamma Sign relationships Delta Delta is an important by-product of the Black-Scholes model There are three common uses of delta Delta is the change in option premium expected from a small change in the stock price Measure of Option Sensitivity For a call option: For a put option: Measure of Option Sensitivity (cont’d) Delta indicates the number of shares of stock required to mimic the returns of the option ., a call delta of means it will act like shares of stock If the stock price .
