Model Specification and Risk Premia: Evidence from Futures Options

Abstract

This paper examines specification issues and estimates diffusive and jump risk premia using S&P futures option prices from 1987 to 2003. We first develop a test to detect the presence of jumps in volatility, and find strong evidence supporting their presence. Based on the cross-sectional fit of option prices, we find strong evidence for jumps in prices and modest evidence for jumps in volatility. We are not able to identify a statistically significant diffusive volatility risk premium. We do find modest but statistically and economically significant jump risk premia.

Volatility-of-volatility and tail risk hedging returns

“…The insignificance of JV appears to be at odds with the literature showing that return jumps are priced in the index options (e.g., Bates, 2000;Pan, 2002;Broadie et al, 2007).…”

Computing the market price of volatility risk in the energy commodity markets

“…Several authors, such as Pan (2002) and more recently, Broadie et al (2007), disagree with the marginal impact of this risk parameter, noting that empirically disentangling multiple risk premiums is problematic. Our intuition regarding the sign of the market price of volatility risk is informed in part by the notion that options are purchased as hedges against significant declines in the equity market, and buyers of the options are willing to pay a premium for such downside protection.…”

“…By comparison, the work in energy markets incorporating options is mostly unexplored. As Broadie et al (2007) point out, it is very difficult to arrive at precise parameter estimates for multiple risk premia, especially when one is the volatility risk premium. Noting this issue, we attempt to estimate the volatility risk premium in energy markets by combining both implied and realized volatility in two-step estimation procedure.…”

Tractable hedging with additional hedge instruments

“…In general, the solution has to be determined 1 Models with stochastic volatility are discussed by Hull and White (1987) and Heston (1993), while Merton (1976) considers a jump-diffusion models. Bakshi et al (1997), Duffie et al (2000), Eraker et al (2003) and Broadie et al (2007), among others, analyze models with stochastic volatility and jumps. 2 Discretely adjusted option hedges are analyzed in Boyle and Emanuel (1980) and Bertsimas et al (2000).…”