Tempered Stable Processes with Time Varying Exponential Tails
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
Cite
@article{arxiv.2006.07669,
title = {Tempered Stable Processes with Time Varying Exponential Tails},
author = {Young Shin Kim and Kum-Hwan Roh and Raphael Douady},
journal= {arXiv preprint arXiv:2006.07669},
year = {2023}
}
Comments
Kum-Hwan Roh gratefully acknowledges the support of Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea government [Grant No. NRF-2017R1D1A3B03036548]