Tempered Stable Processes with Time Varying Exponential Tails

Young Shin Aaron Kim (1) , Kum-Hwan Roh (2) , Raphaël Douady (3)

1 SBU - Stony Brook University [SUNY]
2 HNU - Hannam University
3 CES - Centre d'économie de la Sorbonne

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

Domains: Quantitative Finance [q-fin]; Computational Finance [q-fin.CP]; Statistics [stat]; Applications [stat.AP]; Quantitative Finance [q-fin]; General Finance [q-fin.GN]; Quantitative Finance [q-fin]; Portfolio Management [q-fin.PM]; Quantitative Finance [q-fin]; Pricing of Securities [q-fin.PR]; Quantitative Finance [q-fin]; Risk Management [q-fin.RM]; Quantitative Finance [q-fin]; Statistical Finance [q-fin.ST]

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