Optimally Transported Schemes - Application to Mathematical Finance

Abstract :

This work applies the "Optimally Transported Schemes" framework into the context of Mathematical Finance. It fully reviews the one dimensional case, from the continuous to the numerical and algorithmic point of view.

From a continuous point of view, this method can be classified as a quantized method, usually considered as a Stochastic approach. However, we will be relying heavily over Partial Differential Equation (PDE) arguments. Thus, this method may be considered as an hybrid Stochastic / PDE one. From a numerical point of view, these schemes belong to the class of "Optimally Transported Schemes".

The overall methodology proposed in this paper eases the code production, allow to design faster and more accurate algorithms, gives a natural setting to the calibration problem, provide a completely unified stochastic/PDE computational framework for Financial Engineering in one dimension, and, finally, should be a good candidate to break the "Curse of Dimensions".

Ressources :

• Reference Paper : Optimally Transported Schemes : Applications to mathematical Finance
  
• Finance Forum. Math Forum.
• Code ressources :

 Related :

• Jean-Marc Mercier blog post.
• Optimally Transported Schemes Work Group.
• Transported Heston Work Group.

Status :

Almost finished. It remains to test numerically the Calibration algorithm.