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arXiv · 2006.07669

Tempered Stable Processes with Time Varying Exponential Tails

Young Shin Kim·Kum-Hwan Roh·Raphael Douady
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Abstract

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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Young Shin Kim, Kum-Hwan Roh, Raphael Douady. 2020-06-13. Tempered Stable Processes with Time Varying Exponential Tails. https://doi.org/10.1080/14697688.2021.1962958

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