Time-Changed Fast Mean-Reverting Stochastic Volatility Models

TL;DR

This paper develops a novel class of stochastic volatility models with random time-changes, enabling better modeling of jumps, leverage effects, and multi-scale volatility, and provides analytical approximations for European option prices.

Contribution

It introduces a new framework combining random time-changes with fast mean-reverting stochastic volatility, enhancing modeling flexibility and analytical tractability.

Findings

Implied volatility surfaces vary with model parameters.

Incorporation of jumps and leverage effects is feasible.

Multiple volatility factors operate on different time-scales.

Abstract

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility surfaces induced by these time-changes are examined as a function of the model parameters. Three key features of our framework are that we are able to incorporate jumps into the price process of the underlying asset, allow for the leverage effect, and accommodate multiple factors of volatility, which operate on different time-scales.