论文标题
交换选项定价在差异伽马状模型下
Exchange option pricing under variance gamma-like models
论文作者
论文摘要
在本文中，当logprices的动态遵循众所周知的差异伽玛或Gardini等人[19]中引入的近期方差伽马++过程时，我们关注交换选项的定价。特别是，对于以前的模型，我们可以得出Margrabe的类型公式，而对于后者，我们可以编写“积分免费”公式。此外，我们展示了如何构建方差伽马++过程的一般多维版本，以保留数学和数值障碍。最后，我们将派生模型应用于德国和法国能源电力市场：我们使用实际市场数据校准了它们的参数，因此我们通过衍生的封闭配方，基于傅立叶的方法和蒙特卡洛技术来评估交换选项。
In this article we focus on the pricing of exchange options when the dynamic of logprices follows either the well-known variance gamma or the recent variance gamma++ process introduced in Gardini et al [19]. In particular, for the former model we can derive a Margrabe's type formula whereas, for the latter one we can write an "integral free" formula. Furthermore, we show how to construct a general multidimensional versions of the variance gamma++ processes preserving both the mathematical and numerical tractability. Finally we apply the derived models to German and French energy power markets: we calibrate their parameters using real market data and we accordingly evaluate exchange options with the derived closed formulas, Fourier based methods and Monte Carlo techniques.
