Local Risk-Minimization under the Benchmark Approach

TL;DR

This paper introduces a novel approach for pricing and hedging derivatives in incomplete markets using benchmarked local risk-minimization, which operates under weaker assumptions than traditional methods.

Contribution

It extends local risk-minimization to the benchmark approach, enabling more flexible modeling in incomplete markets.

Findings

Allows handling of a broader class of models

Operates under weaker assumptions than classical methods

Facilitates more robust derivative pricing and hedging

Abstract

We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization allows to handle under extremely weak assumptions a much richer modeling world than the classical methodology.