Pricing methods for $\alpha$-quantile and perpetual early exercise options based on Spitzer identities

TL;DR

This paper introduces novel numerical schemes for pricing perpetual Bermudan, American, and alpha-quantile options using Spitzer identities and Wiener-Hopf methods, achieving efficient and accurate results for various Levy processes.

Contribution

It develops a new direct calculation method for the optimal exercise barrier and combines identities for the first time to price alpha-quantile options.

Findings

Excellent error convergence observed across different Levy processes.

New methods outperform existing schemes in computational efficiency.

First-time combination of Dassios-Port-Wendel and Spitzer identities for quantile options.

Abstract

We present new numerical schemes for pricing perpetual Bermudan and American options as well as $\alpha$-quantile options. This includes a new direct calculation of the optimal exercise barrier for early-exercise options. Our approach is based on the Spitzer identities for general L\'evy processes and on the Wiener-Hopf method. Our direct calculation of the price of $\alpha$-quantile options combines for the first time the Dassios-Port-Wendel identity and the Spitzer identities for the extrema of processes. Our results show that the new pricing methods provide excellent error convergence with respect to computational time when implemented with a range of L\'evy processes.