Pricing Bermudan options under local L\'evy models with default

TL;DR

This paper introduces a fast, accurate Fourier-based method for pricing Bermudan options on defaultable assets modeled by local Le9vy processes, with error bounds and efficient Greeks computation.

Contribution

It develops an analytical approximation of the characteristic function tailored for local Le9vy models, enabling rapid Bermudan option pricing via FFT.

Findings

Fast Fourier Transform-based pricing algorithm with high accuracy.

Error bounds established for characteristic function approximation.

Greeks computed efficiently with minimal additional cost.

Abstract

We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential L\'evy-type martingale. This class of models allows for a local volatility, local default intensity and a locally dependent L\'evy measure. We present a pricing method for Bermudan options based on an analytical approximation of the characteristic function combined with the COS method. Due to a special form of the obtained characteristic function the price can be computed using a Fast Fourier Transform-based algorithm resulting in a fast and accurate calculation. The Greeks can be computed at almost no additional computational cost. Error bounds for the approximation of the characteristic function as well as for the total option price are given.