Chapter 6 - The black-scholes option pricing model. This chapter presents the following content: Introduction, the black-scholes option pricing model, calculating black-scholes prices from historical data, implied volatility, using black-scholes to solve for the put premium, problems using the black-scholes model. | © 2004 South-Western Publishing Chapter 6 The Black-Scholes Option Pricing Model Outline Introduction The Black-Scholes option pricing model Calculating Black-Scholes prices from historical data Implied volatility Using Black-Scholes to solve for the put premium Problems using the Black-Scholes model Introduction The Black-Scholes option pricing model (BSOPM) has been one of the most important developments in finance in the last 50 years Has provided a good understanding of what options should sell for Has made options more attractive to individual and institutional investors The Black-Scholes Option Pricing Model The model Development and assumptions of the model Determinants of the option premium Assumptions of the Black-Scholes model Intuition into the Black-Scholes model The Model The Model (cont’d) Variable definitions: S = current stock price K = option strike price e = base of natural logarithms R = riskless interest rate T = time until option expiration = standard deviation (sigma) of returns on the underlying security ln = natural logarithm N(d1) and N(d2) = cumulative standard normal distribution functions Development and Assumptions of the Model Derivation from: Physics Mathematical short cuts Arbitrage arguments Fischer Black and Myron Scholes utilized the physics heat transfer equation to develop the BSOPM Determinants of the Option Premium Striking price Time until expiration Stock price Volatility Dividends Risk-free interest rate Striking Price The lower the striking price for a given stock, the more the option should be worth Because a call option lets you buy at a predetermined striking price Time Until Expiration The longer the time until expiration, the more the option is worth The option premium increases for more distant expirations for puts and calls Stock Price The higher the stock price, the more a given call option is worth A call option holder benefits from a rise in the stock price . | © 2004 South-Western Publishing Chapter 6 The Black-Scholes Option Pricing Model Outline Introduction The Black-Scholes option pricing model Calculating Black-Scholes prices from historical data Implied volatility Using Black-Scholes to solve for the put premium Problems using the Black-Scholes model Introduction The Black-Scholes option pricing model (BSOPM) has been one of the most important developments in finance in the last 50 years Has provided a good understanding of what options should sell for Has made options more attractive to individual and institutional investors The Black-Scholes Option Pricing Model The model Development and assumptions of the model Determinants of the option premium Assumptions of the Black-Scholes model Intuition into the Black-Scholes model The Model The Model (cont’d) Variable definitions: S = current stock price K = option strike price e = base of natural logarithms R = riskless interest rate T = time until option .
