Implied roughness in the term structure of oil market volatility
使用粗糙布朗运动驱动的非仿射随机波动模型，分析石油市场波动率的粗糙特征，通过蒙特卡洛模拟和期权数据校准，发现引入赫斯特参数可将校准效率提升近10倍，且粗糙度随时间变化。
This paper analyses the attributes and the significance of the roughness of oil market volatility. We employ unspanned stochastic volatility models driven by rough Brownian motions that yield semi-analytical prices for future options entailing efficient calibration applications. By performing a Monte Carlo simulation study, we show that the semi-analytical pricing performs well thus establishing its efficiency for calibration applications. Thus we calibrate option prices written on oil futures and provide empirical evidence of the roughness in oil volatility. Introducing just one additional parameter, the Hurst parameter, indicating the roughness of the volatility improves the calibration by almost a factor of 10. The calibrated option-implied Hurst parameter varies over time, but the entire set of parameters becomes more stable than in the non-rough case corresponding to a fixed Hurst parameter 1/2. These results underscore the importance to model the time dependency of the roughness of oil market volatility.