Theory of Probability and Mathematical Statistics
Gatheral double stochastic volatility model with Skorokhod reflection
Yuliya Mishura, Andrey Pilipenko and Kostiantyn Ralchenko
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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.
Keywords: Stochastic volatility, Gatheral model, Cox–Ingersoll–Ross process, CKLS model, mean reversion, stochastic differential equation, strong solution, Skorokhod reflection
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