Measuring Systematic Risk Using Implied Beta in Option Prices

This paper provides a novel method to estimate β thoroughly based on option prices. Through combining the market model and the multivariate risk-neutral valuation relationship in Stapleton and Subrahmanyam (1984) and Câmara (2003), we develop a pricing model for individual stock options involving the volatility of the market index level and the levels of the β and the idiosyncratic risk of the underlying stock asset. Based on this option pricing model, it is possible to estimate β implicitly from the current prices of index options and individual stock options rather than from the historical stock prices in the traditional method. The proposed option pricing model can explain some aspects of volatility smiles and term structures. The empirical studies for the component stocks in Dow Jones Industrial Average (DJIA) show that the option-implied β from this novel method can provide reasonable estimates of β and perform better than historical β in predicting the realized value of β in future periods of time. Furthermore, the results of the competitive regression suggest that the option-implied β contains the information different from that in the historical β.