We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale. This class of models allows for a local volatility, local default intensity and a locally dependent Lévy 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.

Asymptotic expansion, Bermudan option, Defaultable asset, Fourier-cosine expansion, Local Lévy model
doi.org/10.1016/j.jmaa.2017.01.071
Journal of Mathematical Analysis and Applications
Applied mathematics for risk measures in finance and insurance, in the wake of the crisis
This work was funded by the European Commission 7th Framework Programme; grant id h2020/643045 - Applied mathematics for risk measures in finance and insurance, in the wake of the crisis (WAKEUPCALL)
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Borovykh, A.I, Pascucci, A, & Oosterlee, C.W. (2017). Pricing Bermudan options under local Lévy models with default. Journal of Mathematical Analysis and Applications. doi:10.1016/j.jmaa.2017.01.071