Pricing Forward Start Options in Models Based on (Time-Changed) Levy Processes
Pricing Forward Start Options in Models Based on (Time-Changed) Levy Processes
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基于（随时间变化的）征收流程的模型中的远期启动选项定价
DOI：
10.2139/ssrn.1319703
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Joerg Kienitz
中科院分区：
文献类型：
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作者：
P. Beyer;Joerg Kienitz
取决于前向偏斜的选项非常受欢迎。一个这样的选择是远期开始看涨期权-一个集团期权的基本组成部分。广泛应用的模型，以考虑向前倾斜动态定价这样的选项包括赫斯顿模型，赫斯顿-赫尔-白色模型和贝茨模型。在这些模型中，包括向前启动功能的选项的解决方案可使用（半）分析公式。今天，指数（从属）利维模型越来越受欢迎的资产动态建模。虽然简单的指数列维模型意味着相同的前向波动率表面的所有未来的时间，从属模型没有。根据从属动态的远期波动率表面，因此随机波动率可以模拟。基于特征函数和傅立叶变换方法的解析定价公式可用于这类模型。我们扩展的适用性分析定价的选项，包括向前启动功能。为此，我们推导出可用于基于傅立叶变换的方法的前向特征函数。作为例子，我们考虑方差Gamma模型和NIG模型分别服从Gamma Ornstein Uhlenbeck过程和Cox-Ingersoll-Ross过程。我们检查我们的分析结果，应用蒙特卡罗方法。这些结果可以例如应用于校准的正向波动率表面。
Options depending on the forward skew are very popular. One such option is the forward starting call option - the basic building block of a cliquet option. Widely applied models to account for the forward skew dynamics to price such options include the Heston model, the Heston-Hull-White model and the Bates model. Within these models solutions for options including forward start features are available using (semi) analytical formulas. Today exponential (subordinated) Levy models being increasingly popular for modelling the asset dynamics. While the simple exponential Levy models imply the same forward volatily surface for all future times the subordinated models do not. Depending on the subordinator the dynamic of the forward volatility surface and therefore stochastic volatility can be modelled. Analytical pricing formulas based on the characteristic function and Fourier transform methods are available for the class of these models. We extend the applicability of analytical pricing to options including forward start features. To this end we derive the forward characteristic functions which can be used in Fourier transform based methods. As examples we consider the Variance Gamma model and the NIG model subordinated by a Gamma Ornstein Uhlenbeck process and respectively by an Cox-Ingersoll-Ross process. We check our analytical results by applying Monte Carlo methods. These results can for instance be applied to calibration of the forward volatility surface.