Volatility Risk Premiums Embedded in Individual Equity Options

Abstract

The accumulation of trading experience and empirical evidence since the original Black-Scholes (BS) model was developed, have made it increasingly evident that volatility is not a constant parameter, as BS assumed, but stochastic. With a second random factor associated with volatility affecting security returns, it would not be surprising if investors cared about bearing risk related to that factor. And there is considerable evidence from analysis of real world options that volatility risk is indeed a priced factor, with a negative price. That is, investors will pay extra for (accept lower returns on) securities like options whose values increase when volatility goes up. In that case, Black-Scholes implied volatilities will tend to be higher than actual volatilities, which provides one measure of the market price of volatility risk. Research on stochastic volatility has focused largely on stock index options, but modern portfolio theory makes a strong distinction between stochastic factors that are correlated with the market portfolio and those that are not, whose risk can be diversified. In this article, Bakshi and Kapadia look at the pricing of individual stock options to explore the effects of market volatility risk versus firm-specific volatility risk. They find that volatility risk is priced, negatively as expected, and that market volatility risk is more important than firm-specific risk.