The Importance of Leverage in Asset Pricing: Evidence from SP 500 Index Put Option Prices

摘要

The primary purpose of this paper is to introduce a new method for measuring and analyzing market leverage and credit risk effects on asset prices in the economy. To our knowledge this is the first paper to attempt to isolate and analyze the time series leverage and subsequent credit effects in stock index option prices. To analyze these effects we use both the Merton (1973) stock as an option model taking the observed equity index prices as given, and the Geske (1979) compound option model to produce index option prices. We examine whether the time series dynamics of market leverage have significant statistical and economic effects on the pricing of S&P 500 index put options. We present what we believe is the first market debt to equity (D/E) ratio derived from option theory using only contemporaneous market price data for the index level and index option prices. We show that during the years 1996-2004 the aggregate market based D/E ratio of the firms comprising the S&P 500 equity index varies between 40-120 percent. We demonstrate that this time series variation in the market value of aggregate corporate leverage of these 500 companies has significant economic effects on the prices of index option on the S&P 500. We show that by including leverage as a variable, Geske's option model is superior to models which omit leverage, such as Black-Scholes (BS) and Bakshi, Cao, and Chen (BCC) (1997). BCC's model has three versions which include stochastic volatility (SV), stochastic volatility and stochastic interest rates (SVSI), and stochastic volatility and jumps (SVJ). It may only be a slightly surprising that Geske dominates Black-Scholes, as long the data quality is sufficient to accurately measure leverage. It is much more interesting to learn that by the inclusion of leverage Geske dominates all three version of Bakshi, Cao, and Chen's more advanced models which omit leverage. We establish this as evidence that when leverage is an omitted variable the parameters of the more complex models are misestimated. Furthermore, without the leverage component of the stochastic volatility process, it appears the more complex models of BCC, Bates (2000), and Pan (2002) have difficulty accurately characterizing the return distribution and pricing the options.