标题： 用方差伽马驱动的奥恩斯坦-乌伦贝克动态定价能源价差期权 显示英文标题

标题： Pricing energy spread options with variance gamma-driven Ornstein-Uhlenbeck dynamics

摘要： 我们考虑现货价格遵循由独立多变量方差伽马过程之和驱动的指数奥恩斯坦-乌伦贝克过程的能量价差期权定价。 在这个均值回归、无限活动价格过程中，使用Esscher变换来获得等价鞅测度。 我们关注弱方差alpha-gamma过程，并证明它在Esscher变换下不封闭。 通过推导创新项的累积生成函数的解析表达式，我们随后得到了远期合约的定价公式，并应用Hurd和Zhou的FFT方法对价差期权进行定价。 最后，我们展示了如何在现实世界测度下对能源价格进行估计并基于远期或看涨期权价格进行校准，并提供了价差期权定价的数值结果。 显示英文摘要

摘要： We consider the pricing of energy spread options for spot prices following an exponential Ornstein-Uhlenbeck process driven by a sum of independent multivariate variance gamma processes. Within this class of mean-reverting, infinite activity price processes, the Esscher transform is used to obtain an equivalent martingale measure. We focus on the weak variance alpha-gamma process and show that it is not closed under the Esscher transform. By deriving an analytic expression for the cumulant generating function of the innovation term, we then obtain a pricing formula for forwards and apply the FFT method of Hurd and Zhou to price spread options. Lastly, we demonstrate how the model should be both estimated on energy prices under the real world measure and calibrated on forward or call prices, and provide numerical results for the pricing of spread options.