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Tempered Stable Processes with Time Varying Exponential Tails

Young Shin Kim (), Kum-Hwan Roh () and Raphaël 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
Raphaël Douady: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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: Levy Process; Normal tempered stable distribution; Volatility of volatility; Stochastic exponential tail; Option Pricing (search for similar items in EconPapers)
Date: 2020-11-22
New Economics Papers: this item is included in nep-ets, nep-ore and nep-rmg
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