From (Martingale) Schrodinger bridges to a new class of Stochastic Volatility Models

Understand

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, options on realized variance or VIX options.

• 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.