Pricing and hedging of derivatives based on non-tradable underlyings

TL;DR

This paper develops a framework for pricing and hedging derivatives based on non-tradable underlyings correlated with tradable assets, using FBSDEs and utility-based indifference pricing.

Contribution

It introduces a novel approach to hedge derivatives on non-tradable assets by extending classical delta hedging through FBSDE analysis and correlation considerations.

Findings

Derived explicit formulas for indifference prices.

Generalized delta hedge for non-tradable underlyings.

Established Markov property and differentiability of FBSDE solutions.

Abstract

This paper is concerned with the study of insurance related derivatives on financial markets that are based on non-tradable underlyings, but are correlated with tradable assets. We calculate exponential utility-based indifference prices, and corresponding derivative hedges. We use the fact that they can be represented in terms of solutions of forward-backward stochastic differential equations (FBSDE) with quadratic growth generators. We derive the Markov property of such FBSDE and generalize results on the differentiability relative to the initial value of their forward components. In this case the optimal hedge can be represented by the price gradient multiplied with the correlation coefficient. This way we obtain a generalization of the classical 'delta hedge' in complete markets.