标的资产服从NIG-Levy过程的亚式期权数值定价分析

Numerical Pricing Asian Option on Stocks Driven by the NIG-Levy Process

考虑到金融时间序列的厚尾性即呈现尖峰厚尾分布,波动率具有聚集性和持续性等特点,也即标的资产的价格可能会出现间断的跳跃,我们展示了在标的资产价格对数收益服从NIG-Levy过程的条件下,如何构建和计算等价鞅测度,我们考虑通过Esscher转换得到Q等价鞅测度,并以此为基础寻找风险中性概率的条件,最后利用这些条件探讨亚式期权的数值定价问题,利用低差异序列中的Halton、Sobol、Faure序列对亚式期权进行了数值定价分析.

Mostly, the return series of financial assets are fat tails distribution and the volatility appears the characteristics of the congregating and durative, In this study, we show that how to construct and compute equivalent martingale measures on stocks driven by the NIG-Levy process, we can get equivalent martingale measures by Esscher transform methods, and find the risk-neutral probability measure＇ condition, Finally, we consider numerical pricing analysis of Asian options by uses low discrepancy Sequences （Halton, Sobol Sequences）.