Indifference prices and implied volatilities

TL;DR

This paper derives explicit approximations for indifference prices and implied volatilities in local-stochastic volatility models, providing practical tools for pricing and hedging European options on traded and non-traded assets.

Contribution

It introduces explicit formulas for indifference prices and implied volatilities, including error bounds for non-traded assets, advancing practical option pricing methods.

Findings

Explicit indifference price approximations for traded and non-traded assets

Error bounds for non-traded asset indifference prices

Implementation examples demonstrating practical applicability

Abstract

We consider a general local-stochastic volatility model and an investor with exponential utility. For a European-style contingent claim, whose payoff may depend on either a traded or non-traded asset, we derive an explicit approximation for both the buyer's and seller's indifference price. For European calls on a traded asset, we translate indifference prices into an explicit approximation of the buyer's and seller's implied volatility surface. For European claims on a non-traded asset, we establish rigorous error bounds for the indifference price approximation. Finally, we implement our indifference price and implied volatility approximations in two examples.