Utility based pricing and hedging of jump diffusion processes with a view to applications

TL;DR

This paper explores utility-based pricing and hedging for jump diffusion processes, addressing practical limitations by introducing the concept of implied drift and providing heuristic methods for pricing and hedging.

Contribution

It proposes a reinterpretation of the utility framework to overcome drift dependence and risk aversion issues, introducing the notion of implied drift and heuristic derivations.

Findings

Introduction of implied drift concept

Heuristic derivation of marginal indifference price

Practical applicability improvements

Abstract

We discuss utility based pricing and hedging of jump diffusion processes with emphasis on the practical applicability of the framework. We point out two difficulties that seem to limit this applicability, namely drift dependence and essential risk aversion independence. We suggest to solve these by a re-interpretation of the framework. This leads to the notion of an implied drift. We also present a heuristic derivation of the marginal indifference price and the marginal optimal hedge that might be useful in numerical computations.