Journal of Computational Finance

Risk.net

Quantization-based Bermudan option pricing in the foreign exchange world

Jean-Michel Fayolle, Vincent Lemaire and Thibaut Montes

  • The paper demonstrates the effectiveness of training an artificial neural network (ANN) to represent different implementations of the SABR stochastic volatility model – from the widely used SABR approximation to a full two-factor PDE implementation.
  • With respect to representing the two-factor PDE implementation the approach demonstrates significant performance acceleration while retaining a high degree of accuracy.
  • The method allows for richer models, which are currently too computationally expensive for practical purposes, to have ANN representations and be used effectively.

This paper proposes two numerical solutions based on product optimal quantization for the pricing of Bermudan options on foreign exchange rates. More precisely, we consider the pricing of Bermudan power reverse dual currency options, taking into account stochastic domestic and foreign interest rates in addition to stochastic foreign exchange rates; we therefore consider a three-factor model. For the two numerical methods, we give an estimation of the L^2 error induced by the approximations and we illustrate the methods with market-based examples that highlight their speed.

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