Tempered Stable Processes with Time Varying Exponential Tails

Young Shin Kim (), Kum-Hwan Roh () and Raphael Douady ()
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Young Shin Kim: SBU - Stony Brook University [SUNY] - SUNY - State University of New York
Kum-Hwan Roh: HNU - Hannam University

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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.

Keywords: Option Pricing; Stochastic exponential tail; Volatility of volatility; Normal tempered stable distribution; Levy Process (search for similar items in EconPapers)
Date: 2020-11-22
New Economics Papers: this item is included in nep-ore and nep-rmg
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Related works:
Working Paper: Tempered stable processes with time-varying exponential tails (2021)
Working Paper: Tempered stable processes with time-varying exponential tails (2021)
Working Paper: Tempered Stable Processes with Time Varying Exponential Tails (2020)
Working Paper: Tempered Stable Processes with Time Varying Exponential Tails (2020)
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