Quantization-based Bermudan option pricing in the $FX$ world

TL;DR

This paper introduces two quantization-based numerical methods for pricing complex FX Bermudan options considering stochastic interest rates and FX rates, providing error estimates and demonstrating efficiency with market examples.

Contribution

It presents novel quantization-based algorithms for FX Bermudan option pricing under a 3-factor stochastic model, including error analysis and practical market applications.

Findings

Methods achieve fast computation times

Error bounds are effectively estimated

Market examples validate practical efficiency

Abstract

This paper proposes two numerical solution based on Product Optimal Quantization for the pricing of Foreign Echange (FX) linked long term Bermudan options e.g. Bermudan Power Reverse Dual Currency options, where we take into account stochastic domestic and foreign interest rates on top of stochastic FX rate, hence we consider a 3-factor model. For these two numerical methods, we give an estimation of the $L^2$-error induced by such approximations and we illustrate them with market-based examples that highlight the speed of such methods.