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

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black-Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. journal of Political Economy 81, 637-654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177-181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets. (C) 2008 Elsevier B.V. All rights reserved.