The Effects of Leverage on the Pricing S&P 500 Index Call Options
Posted: 15 Jan 2007
Date Written: October 2006
The purpose of this paper is to examine whether leverage has a significant statistical and economic effect on the pricing of S&P 500 index options. This is the first paper to directly test for leverage effects in stock index options. To analyze these effects we use the Geske (1979) compound option model. The Geske model is closed form, implies stochastic equity volatility, is consistent with Modigliani and Miller, incorporates debt refinancing, and includes possibly differential default and bankruptcy. Black-Scholes (1973) is a special case of the Geske model. In this paper we show that during the years 1996-2004 the aggregate market based debt to equity (D/E) ratio of the firms comprising the S&P 500 equity index varies from about 40-120 percent. We believe this is the first presentation of a market D/E ratio derived from option theory. Next and more importantly we are the first to report the details of the statistically significant economic effects that market leverage has on pricing S&P 500 index call options. We measure that the Geske model improves the net option valuation of listed in the money (or out of the money) S&P 500 index call options on average by about 35% (28%) compared to Black-Scholes values. We demonstrate that the improvement is directly (and monotonically) related to both the time to expiration of the option and the amount of leverage in this market index. For options with longer expirations and/or periods of higher market leverage the improvement is greater, ranging from about 40% to 80%. We also demonstrate economic significance in basis points by showing that dealers making a book in index options can expect benefits of at least several 100 basis points using Geske instead of Black-Scholes.
Keywords: Derivatives, Stochastic Stock Volatility, Leverage
JEL Classification: G12
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