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Tempered Stable Processes with Time Varying Exponential Tails

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Young Shin Aaron Kim
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  • PersonId : 1082284
Kum-Hwan Roh
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  • PersonId : 1082285
Raphaël Douady

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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Dates and versions

hal-03018495 , version 1 (22-11-2020)

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  • HAL Id : hal-03018495 , version 1

Cite

Young Shin Aaron Kim, Kum-Hwan Roh, Raphaël Douady. Tempered Stable Processes with Time Varying Exponential Tails. 2020. ⟨hal-03018495⟩
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