From (Martingale) Schrodinger Bridges to a New Class of Stochastic Volatility Model
From (Martingale) Schrodinger Bridges to a New Class of Stochastic Volatility Model
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从（鞅）薛定谔桥到一类新的随机波动率模型
DOI：
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发表时间：
2019
期刊：
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通讯作者：
P. Henry
中科院分区：
文献类型：
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作者：
P. Henry
紧随薛定谔桥的构建，我们构建了一类新的随机波动率模型，该模型完全根据市场工具（例如香草、已实现方差期权或 VIX 期权）进行校准。这些模型与众所周知的局部随机波动率模型有很大不同，特别是相关裸 SVM 的瞬时波动率在根据市场工具进行校准后就不会被修改。它们可以被解释为薛定谔桥的鞅版本。数值校准是使用 Sinkhorn 算法的动态版本来执行的。最后，我们强调与戴森非碰撞布朗运动的显着关系。
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.