A backward dual representation for the quantile hedging of Bermudan options

TL;DR

This paper introduces a backward dual representation method for quantile hedging of Bermudan options, employing Fenchel transforms and duality to develop a numerical scheme that extends American option valuation techniques.

Contribution

It presents a novel backward numerical scheme using Fenchel transforms for quantile hedging of Bermudan options in a Markovian market, incorporating duality and stochastic target methods.

Findings

Numerical scheme effectively computes quantile hedging prices.

Algorithm extends American option backward induction with Fenchel transforms.

Numerical illustrations demonstrate practical applicability.

Abstract

Within a Markovian complete financial market, we consider the problem of hedging a Bermudan option with a given probability. Using stochastic target and duality arguments, we derive a backward numerical scheme for the Fenchel transform of the pricing function. This algorithm is similar to the usual American backward induction, except that it requires two additional Fenchel transformations at each exercise date. We provide numerical illustrations.