A pure dual approach for hedging Bermudan options

TL;DR

This paper introduces a novel purely dual Monte Carlo algorithm for computing hedging portfolios and initial values of Bermudan options, emphasizing a new excess reward representation and convexification techniques.

Contribution

It presents a new dual approach relying solely on the dual pricing formula, improving hedging strategy computation for Bermudan options.

Findings

Convergence of the proposed algorithm is established.

The method assesses the relevance of financial instruments in hedging.

The impact of rebalancing frequency on hedging effectiveness is analyzed.

Abstract

This paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a "purely dual" algorithm following the spirit of Rogers (2010) in the sense that it only relies on the dual pricing formula. The key is to rewrite the dual formula as an excess reward representation and to combine it with a strict convexification technique. The hedging strategy is then obtained by using a Monte Carlo method, solving backward a sequence of least square problems. We show convergence results for our algorithm and test it on many different Bermudan options. Beyond giving directly the hedging portfolio, the strength of the algorithm is to assess both the relevance of including financial instruments in the hedging portfolio and the effect of the rebalancing frequency.