A Test of the Applicability of the Black-Scholes Call Option Pricing Model: Valuing S&P 100 Index Call Options

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A Test Of The Applicability Of The Black-Scholes Call Option Pricing Model: Valuing S&P 100 Index Call Options

Financial markets worldwide have experienced unprecedented volatility in the recent past. The cause of such volatility is of much debate. However, many observers contend that this increased volatility is a result of programmed trading by large institutions utilizing computerized techniques. Many of these programmed trading systems attempt to take advantage of arbitrage opportunities that momentarily exist in the equity and the ever expanding options market.

Institutional traders often use proven option pricing models to identify such arbitrage opportunities. To date there has been little empirical research into the applicability of such "proven" option pricing models on the new and innovative indexed based options. This article will test the applicability of the time-tested Black-Scholes' call option pricing model to index options and will perhaps provide some additional insights into the workings of the new, and extremely volatile, financial markets of the 1980's.

Fischer Black and Myron Scholes [4] developed the Black-Scholes (B-S) call option pricing model at a time when stock options were traded in a very illiquid over-the-counter market whose trading volume represented less than one-tenth of one percent of the dollar volume of shares traded on the New York Stock Exchange (NYSE). Since that time there has been a tremendous growth in the volume of option trading.

With the establishment of the Chicago Board Options Exchange (CBOE) and its subsidiary, the Options Clearing Corporation (OCC), in April, 1973, came standardized exercise prices, expiration cycles, and a resultant liquid market for the trading of stock options. The CBOE began operations by opening trading in call options on 16 widely held NYSE listed stocks. By 1977 option trading was available on over 100 stocks and trading had expanded to as many as 150,000 option contracts in a single day. (1)

However, this growth has been dwarfed in recent years with the introduction on March 11, 1983, of trading in options on stock indexes. Such options are now traded on a number of major stock indexes and sub-indexes, and by far the most active of these index options are those based on the Standard and Poors 100 (S&P 100) Index. For example, in 1985 there were over 79 million option contracts traded on the S&P 100, a year-end open interest of 1.7 million contracts, average daily volume in excess of 329,000 contracts, and a record one day volume of 906,726 contracts. (2) Trading in this index accounted for more than 50% of all options traded, both stock and index. The dollar volume of option contracts traded is now second only to the NYSE.

Since Black and Scholes first published their original work concerning the pricing of options on stocks, there has been extensive research conducted regarding the viability of their model as well as development of alternative models [1, 5, 6, 12, 13, 14, 16, 17]. However, the model with which all compare their results remains the B-S. To date there has been little research conducted that tests the applicability of traditional option pricing models to stock index options [5, 8]. Therefore, this paper will assess the B-S call option pricing model's accuracy in predicting market prices of options traded on the S&P Index. This research will also determine if the B-S model exhibits the same strike price and expiration date biases for S&P 100 Index options as those found by Black and Scholes for stock options.

Differences between S&P 100 Index options and traditional stock options will be discussed in the next section. These differences are thought to lead to possible pricing errors in using a traditional stock option pricing model, such as the B-S model, to value index options. A discussion of the Black-Scholes call option pricing model and the assumptions it makes concerning the pricing of options appears next, followed by a presentation of the data collected and the results obtained. …