Gatheral double stochastic volatility model with Skorokhod reflection

TL;DR

This paper examines the Gatheral double stochastic volatility model's tendency to approach zero and introduces a Skorokhod reflection modification to prevent this, ensuring more realistic volatility behavior.

Contribution

The paper proposes a Skorokhod reflection modification to the Gatheral model, preventing volatility from reaching zero while maintaining model flexibility.

Findings

Original model can produce near-zero volatility for extended periods.

Skorokhod reflection effectively prevents volatility from hitting zero.

Modified model retains mean-reverting properties with improved stability.

Abstract

We investigate the Gatheral model of double mean-reverting stochastic volatility, in which the drift term itself follows a mean-reverting process, and the overall model exhibits mean-reverting behavior. We demonstrate that such processes can attain values arbitrarily close to zero and remain near zero for extended periods, making them practically and statistically indistinguishable from zero. To address this issue, we propose a modified model incorporating Skorokhod reflection, which preserves the model's flexibility while preventing volatility from approaching zero.