Bi-cubic B-spline fitting-based local volatility model with mean reversion process

Abstract

This paper studies the traditional local volatility model and proposes: A novel local volatility model with mean-reversion process. The larger is the gap between local volatility and its mean level, the higher will be the rate at which local volatility will revert to the mean. Then, a B-spline method with proper knot control is applied to interpolate the local volatility matrix. The bi-cubic B-spline is used to recover the local volatility surface from this local volatility matrix. Finally, empirical tests show that the proposed mean-reversion local volatility model offers better prediction performance than the traditional local volatility model.