Forward indifference valuation and hedging of basis risk under partial information

TL;DR

This paper develops a framework for valuing and hedging claims on non-traded assets in incomplete markets with partial information, using forward utility and stochastic control to derive optimal strategies and prices.

Contribution

It introduces a novel approach combining forward utility, partial information, and basis risk to derive indifference prices and hedging strategies for European and American claims.

Findings

Derived the optimal hedging strategy under partial information.

Obtained a PDE representation for the forward indifference price.

Provided asymptotic expansions of the indifference price in the European case.

Abstract

We study the hedging and valuation of European and American claims on a non-traded asset $Y$, when a traded stock $S$ is available for hedging, with $S$ and $Y$ following correlated geometric Brownian motions. This is an incomplete market, often called a basis risk model. The market agent's risk preferences are modelled using a so-called forward performance process (forward utility), which is a time-decreasing utility of exponential type. Moreover, the market agent (investor) does not know with certainty the values of the asset price drifts. This market setting with drift parameter uncertainty is the partial information scenario. We discuss the stochastic control problem obtained by setting up the hedging portfolio and derive the optimal hedging strategy. Furthermore, a (dual) forward indifference price representation of the claim and its PDE are obtained. With these results, the residual risk process representing the basis risk (hedging error), pay-off decompositions and asymptotic expansions of the indifference price in the European case are derived. We develop the analogous stochastic control and stopping problem with an American claim and obtain the corresponding forward indifference price valuation formula.