具有时变指数尾的回火稳定过程
Tempered Stable Processes with Time Varying Exponential Tails
摘要：
本文提出了一种新的具有随机指数尾的时间序列模型。该模型是基于具有时变参数的正态回火稳定分布构造的。该模型捕捉到了随机指数尾，它产生了期权定价中的波动率微笑效应和波动率期限结构。此外，该模型描述了波动率的时变波动性。应用该模型对标准普尔500指数收益率数据进行实证分析，得到了随机偏度和随机峰度的分布特征。我们提出了Monte-Carlo模拟技术的参数校准模型的标准普尔500期权价格。通过对模型的标定可以看出，随机指数尾的存在使得模型更好地分析了市场期权的价格。
英文摘要：
In this paper, we introduce a new time series model having a stochastic exponential tail. This model is constructed based on the Normal Tempered Stable distribution with a time-varying parameter. The model captures the stochastic exponential tail, which generates the volatility smile effect and volatility term structure in option pricing. Moreover, the model describes the time-varying volatility of volatility. We empirically show the stochastic skewness and stochastic kurtosis by applying the model to analyze S&P 500 index return data. We present the Monte-Carlo simulation technique for the parameter calibration of the model for the S&P 500 option prices. We can see that the stochastic exponential tail makes the model better to analyze the market option prices by the calibration.
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