Studies in index option pricing provide strong evidence in support of a jump risk premiumand conclude that it plays an important role in explaining both the joint time series behavior of spot and index option prices. At the individual equity level, Dennis and Mayhew (2002) andBakshi, Kapadia and Madan (2003) (BKM, hereafter) uncovered properties of option prices that indicate structural differences between the risk neutral and physical return distributions of equity returns. In a recent study, Duan and Wei (2008) document that this observed structural difference is related to the systematic risk of the underlying asset. Although there is now a growing body of empirical studies on individual equity options, our understanding of the risk factors that are embedded in these individual equity option prices and their economic magnitude is still limited. In particular, the role of the market jump risk premium in individual equity option pricing has not been examined to date.
In this paper, we investigate the pricing of market risk factors in individual equity options. We proceed by developing a factor model for equity returns and option pricing that takes into account the market diffusive and jump risks. In addition to the market risk factors, we allow each firm to be affected by its own equity specific shock. We model these three risk factors as time varying and allow them to be priced. Our study uses a large panel data set of 32 individual equity options and returns from 1996 to 2005. We impose consistency between returns and option prices by simultaneously fitting the model to the time series of equity and index returns as well as to the cross section of options. The estimation results show that the market jump and diffusive risk factors represent a sizable premium in the individual equities. More importantly, we find that their magnitudes are consistent with those estimated using index options (see Pan (2002)), thus suggesting that the price structure of equity and index options can be explained in a unified framework.
There are several reasons why it is important to understand the impact of the market risk factors on the equity option market. First, given that stock returns have a significant market component, the existence of a market jump and diffusive risks have a direct implication on how individual equity options are priced in the marketplace. Second, it allows us to verify to what degree market diffusive and jump risks are compensated for in the cross section of individual equities. Third, it enables us to test whether the differential price structure across individual equity options can be explained through a risk based model, instead of relying on demand based arguments as in Bollen and Whaley (2004).
There exists some empirical evidence that market jump risk is priced in the cross section of returns, albeit from using indirect measures. However, it is still an open question whether the market jump risk is priced in individual equity options. Duan and Wei (2008) show that the level and the slope of option implied volatilities are related to the proportion of the firms systematic risk. Although the finding of Duan and Wei (2008) can be interpreted as indirect evidence that the market risk factors are priced in individual equity options, the relative magnitude of these risk factors and how they impact individual equity options are still unknown. Our objective is to fill this gap in the literature by showing that market diffusive and jump risk factors are priced in individual equity options as well as in the underlying returns. In addition, we also estimate the magnitudes.
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Market jump risk and the price structure of individual equity options
