From (Martingale) Schrodinger Bridges to a New Class of Stochastic Volatility Model

Abstract

Following closely the construction of the Schrodinger bridge, we build a new class of Stochastic Volatility Models exactly calibrated to market instruments such as for example Vanillas and options on realized variance. These models differ strongly from the well-known local stochastic volatility models, in particular the instantaneous volatility-of-volatility of the associated naked SVMs is not modified, once calibrated to market instruments. They can be interpreted as a martingale version of the Schrodinger bridge. The numerical calibration is performed using a dynamic-like version of the Sinkhorn algorithm. We finally highlight a striking relation with Dyson non-colliding Brownian motions.

Keywords: Schrodinger bridge, stochastic control, Sinkhorn algorithm, stochastic volatility model, conditioned SDEs