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Computing The Market Price Of Volatility Risk In The Energy Commodity Markets

机译：计算能源商品市场中波动风险的市场价格

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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.
机译：在本文中，我们证明了需要负的波动性市场价格来弥补Black-Scholes之间的差异[Black，F.，Scholes，M.，1973。期权和公司负债的定价。政治经济学杂志81，637-654] / Black [Black，F.，1976。股票价格波动性研究。在：《美国统计协会1976年商业和经济统计部门会议记录》，第177-181页中隐含了波动率和实际波动率。最初，使用准蒙特卡洛模拟，我们用数字证明波动率风险的负市场价格是解释股市和商品能源市场中风险中性和统计波动率之间差异的关键风险溢价。这对于还包含跳转的多个规范是可靠的。接下来，我们使用10年期间天然气，取暖油和原油合约的期货和期权数据，我们估计了波动风险溢价，并证明了这三种商品的溢价均为负值且很重要。此外，天然气和取暖油表现出明显的季节性模式，其中冬季/提款月份的波动性风险溢价较高。计算波动性风险的这种负市场价格突出了波动性风险在理解这些金融市场中的价格波动性中的重要性。

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