回火稳定过程和CGMY过程驱动的Ornstein-Uhlenbeck型市场中的能量衍生品定价
Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein-Uhlenbeck Type
摘要：
在这项研究中，我们考虑能源衍生品的定价时，现货价格的演变遵循回火稳定或CGMY驱动的奥恩斯坦-乌伦贝克过程。为此，我们首先计算的特征函数的过渡律的封闭形式的过程。这一结果有助于推导无套利条件，使现货动态与远期曲线一致。此外，基于Cufaro Petroni和Sabino（2020）的结果，我们还构思了精确模拟此类过程骨架的有效算法，并提出了一种新的方法，当它们与Ornstein-Uhlenbeck型复合Poisson过程重合时。我们说明了适用的理论研究结果和仿真算法的背景下，定价不同的合同，即带的每日看涨期权，亚式期权与欧洲风格和摆动期权。最后，我们提出了对未来市场的扩展。
英文摘要：
In this study we consider the pricing of energy derivatives when the evolution of spot prices follows a tempered stable or a CGMY driven Ornstein- Uhlenbeck process. To this end, we first calculate the characteristic function of the transition law of such processes in closed form. This result is instrumental for the derivation of non-arbitrage conditions such that the spot dynamics is consistent with the forward curve. Moreover, based on the results of Cufaro Petroni and Sabino (2020), we also conceive efficient algorithms for the exact simulation of the skeleton of such processes and propose a novel procedure when they coincide with compound Poisson processes of Ornstein-Uhlenbeck type. We illustrate the applicability of the theoretical findings and the simulation algorithms in the context of the pricing different contracts namely, strips of daily call options, Asian options with European style and swing options. Finally, we present an extension to future markets.
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