Tempered stable processes with time-varying exponential tails

Young Shin Kim, Kum-Hwan Roh and Raphael Douady ()

Quantitative Finance, 2022, vol. 22, issue 3, 541-561

Abstract: In this paper, we introduce a new time series model with a stochastic exponential tail. This model is constructed based on the Normal Tempered Stable distribution with a time-varying parameter. It 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 and empirically indicates stochastic skewness and stochastic kurtosis in the S&P 500 index return data. We present a Monte-Carlo simulation technique for parameter calibration of the model for S&P 500 option prices and show that a stochastic exponential tail improves the calibration performance.

Date: 2022
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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)
Working Paper: Tempered Stable Processes with Time Varying Exponential Tails (2020)
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DOI: 10.1080/14697688.2021.1962958

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