Indifference Pricing and Hedging in a Multiple-Priors Model with Trading Constraints

TL;DR

This paper develops a framework for indifference pricing and hedging of derivatives under model uncertainty and trading constraints, linking prices to modified Black-Scholes prices via stochastic control and differential equations.

Contribution

It introduces a novel approach combining stochastic control and PDE methods to analyze indifference prices under multiple-priors and trading constraints.

Findings

Bid and ask prices relate to modified Black-Scholes prices.

Prices coincide without trading constraints or model uncertainty.

Applications to European and American options are provided.

Abstract

This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein (2002). The price is determined by two optimal stochastic control problems (mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations. By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates. The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.