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arXiv · 1904.04554

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

Pierre Henry-Labordere
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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, 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. We finally highlight a striking relation with Dyson non-colliding Brownian motions.

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Pierre Henry-Labordere. 2019-04-09. From (Martingale) Schrodinger bridges to a new class of Stochastic Volatility Models. https://arxiv.org/abs/1904.04554

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