The Factor Structure of Realized Volatility and its Implications for Option Pricing

The cross-section of realized return volatilities of US equities between 1965-2004 is well described by a linear factor structure. We show that the identified factor structure has important cross-sectional pricing implications for variance swap contracts. The principal volatility factor accounts for almost 40% of the cross-sectional variation in realized stock volatilities and earns a significant negative risk premium. Importantly, more than one volatility factor is priced in the market and a total of 3-5 factors are needed to explain the cross-section of observed volatility swap rates. Moreover, we find strong evidence for the existence of an aggregate jump risk factor being priced by the market. Our findings are robust to the exclusion of stock index contracts and confirm that index options are expensive relative to individual stock options. ∗We would like to thank Torben Andersen, Mikhail Chernov, Robert Korajczyk, Paul Gao, seminar participants at the Risk Management Conference (Mont Tremblant) and especially Ravi Jagannathan for his numerous suggestions and insights. † [email protected], University of Notre Dame. ‡ [email protected], Kellogg School of Management, Northwestern University.