Black-Scholes model history

A formula for pricing stock options. Stock options are a type of derivative instrument that provides the holder the right, but not the requirement, to buy or sell stock at a future date. Options to buy are called “call” options, and those to sell are “put” options. The Black-Scholes model was developed in 1970–71 by Fischer Black and Myron Scholes, with collaboration from Robert C. Merton. The three were young economists at the time. The model at first received a hostile reception from mainstream economists and was immediately rejected from three academic journals before finally being published in a leading economics journal in 1973. All three researchers soon became leaders in the academic field of financial economics and before long became influential Wall Street advisers.

Their research eventually earned Scholes and Merton the 1997 Nobel Prize in economic sciences. (Black died in 1995 and could not be named a recipient, although he was cited in the announcement.) The Black-Scholes model itself is mathematically complicated, but in many cases the option price depends only on the volatility (or variability) of the underlying stock. In this sense, options are said to provide the price of volatility. Greater volatility translates into greater option prices because of the very nature of options— they do not have to be exercised in the “bad” outcomes, so the option holder receives potential benefits without any downside.

The Black-Scholes model works due to an underlying arbitrage argument. Since a stock and a bond can be combined to mimic exactly the payouts of an option, the price of the option must be the same as the price of that “replicating portfolio,” or there would have to be an arbitrage opportunity that investors could exploit. The results of the Black-Scholes model can also be derived from a decision-tree framework pioneered by John Cox, Stephen Ross, and Mark Rubinstein in the mid-1970s. This technique relies on computer power and Monte Carlo simulation to reproduce all the possible scenarios for the movement of a stock and made Black-Scholes more operational by allowing option pricing in more complex situations.

The Black-Scholes model quickly revolutionized the pricing of derivative securities and helped an active market develop in options. Few, if any, academic studies in economics have had a bigger impact on the “real world.” In 1973, the CHICAGO BOARD OF TRADE opened a stock options exchange—the Chicago Board Options Exchange. Other exchanges quickly followed suit, and the model became associated with their development from their earliest days. The OPTIONS MARKETS quickly spread to include interest rates, and now a variety of options trade beyond those on stocks—including such new instruments as swaps, caps, floors, and swaptions. Both the over-thecounter and exchange-traded derivatives markets are among the largest in the world and currently trade trillions of dollars each year. In addition, hidden options can be found and priced in a variety of business and finance applications.

The model has also been used to price stock options granted to executives as part of their compensation packages. The controversy arising in the late 1990s over executive compensation and the use of stock options gave the model additional life as one of the few ways in which such executive compensation tools could be adequately priced for accounting purposes.

See also FUTURES MARKETS.

Further reading

• Bernstein, Peter L. Capital Ideas: The Improbable Origins of Modern Wall Street. New York: Free Press, 1993. 
• Reynolds, Bob. Understanding Derivatives: What You Really Need to Know about the Wild Card of International Finance. New York: Financial Times, 1995. 

Paul Harrison