On the market price of volatility risk

This work examines the extent of the bias between Black-Scholes (1973)/Black (1976) implied volatility and realized term volatility, estimation of the market price of volatility risk, and option model fit in the natural gas market. To examine this bias I institute a stochastic volatility data generating process, and demonstrate the bias through Monte Carlo simulation of the underlying parameters. This provides a numerical justification for testing the importance of a risk premia for volatility. I implement empirical tests for the market price of volatility risk by analyzing at-the-money options on the S&P 500 and S&P 100. Further, I extend the study by considering options on natural gas contracts by examining option model fit for a variety of parametric candidates. Using risk-neutral parameter estimates I re-estimate the market price of volatility risk using the full cross-section of option prices. The findings demonstrate a negative market price of volatility risk, and show that this risk is a significant component of the bias between Black-Scholes/Black implied volatility and realized term volatility.