The Black-Scholes Option-Pricing Model

10 Pages Posted: 21 Oct 2008

See all articles by Robert S. Harris

Robert S. Harris

University of Virginia - Darden School of Business

Robert M. Conroy

University of Virginia - Darden School of Business

Abstract

This note discusses the Black-Scholes option-pricing model and then applies the model to call options. The underlying logic of the model is emphasized and illustrated through the use of simple examples. The model is then applied using real data. The note pays particular attention to procedures for estimating the potential for stock-price changes (volatility). It also provides the reader with an appreciation of the economic underpinnings of the model as well as the ability to apply the model to real data.

Excerpt

UVA-F-1522

The Black-Scholes Option-Pricing Model

Fischer Black and Myron Scholes had one of the last century's most revealing insights about pricing in financial markets. In 1973, they published an article outlining the first practical theoretical model to price options. Their Black-Scholes model harnessed arbitrage forces that ensure that two ways to create the same ultimate payoff will be priced the same in well-functioning financial markets. The model's novel assumption was that an investor who wrote a call option and simultaneously bought a certain number of shares in the underlying asset could create a riskless cash payoff. Because the investor could also create risk-free payoffs using risk-free bonds, arbitrage forces would ensure that the risk-free-rate bond return would also apply to the riskless payoff involving the shares and call option. Once this was established, Black and Scholes could derive a practical way to estimate the value of the option based on variables that could be observed or reasonably estimated.

This note discusses the economics underlying the Black-Scholes model and then applies the model to the pricing of call options. We pay particular attention to procedures for estimating the potential for stock-price changes, as these possible movements are the key driver of option value.

The Underlying Economics

To illustrate the underlying economics of the Black-Scholes model, consider a simple example. Suppose the shares of XYZ are currently trading at $ 105 a share. You are offered a European call option with an exercise price of $ 100 and time to maturity of one year. How much should you be willing to pay for this option? First, we need some assumption about how the stock price will move. Let's make the simplifying assumption that the stock price will be either $ 115 or $ 95 at the end of one year.

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Keywords: options, valuation, Black-Scholes option-pricing model, volatility

Suggested Citation

Harris, Robert S. and Conroy, Robert M., The Black-Scholes Option-Pricing Model. Darden Case No. UVA-F-1522, Available at SSRN: https://ssrn.com/abstract=1279958

Robert S. Harris (Contact Author)

University of Virginia - Darden School of Business ( email )

P.O. Box 6550
Charlottesville, VA 22906-6550
United States
434-924-4823 (Phone)
434-924-4859 (Fax)

HOME PAGE: http://www.darden.virginia.edu/faculty/harris.htm

Robert M. Conroy

University of Virginia - Darden School of Business ( email )

P.O. Box 6550
Charlottesville, VA 22906-6550
United States

HOME PAGE: http://www.darden.virginia.edu/faculty/conroy.htm

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