Regulated Tempered Stable Processes with Stochastic Volatility: A Crypto Option Pricing Perspective

We propose a model for the price dynamics of Bitcoin and Ethereum that combines tempered stable subordinators with Heston’s stochastic volatility model. By introducing the stochastic nature of volatility into the tempered stable model, we are able to capture the high variability of the BTC and ETH price process. We consider the use of Gaussian mixture with risk-neutral correction, resulting in a log-price process that consists of a risk-neutral Heston’s stochastic volatility price process and a Gaussian mixture of the tempered stable subordinator and standard Brownian motion. We show that this model is able to accurately capture the stylized facts of the BTC and ETH price dynamics, as evidenced by the good fit of the model to the empirical data. Our results suggest that the combination of tempered stable subordinators and Heston’s model is a promising approach for modeling the price dynamics of Bitcoin and Ethereum.