Pricing multi-asset contingent claims in a multi-dimensional binomial market

TL;DR

This paper develops a method to determine price bounds and hedging strategies for multi-asset options in an incomplete binomial market, providing closed-form formulas and algorithms for practical computation.

Contribution

It introduces a novel characterization of extremal martingale measures in multi-asset binomial models, enabling explicit bounds and efficient algorithms for pricing and hedging complex options.

Findings

Closed-form formulas for no-arbitrage price bounds

Efficient algorithms for computing bounds and hedging strategies

Application to basket and Asian options

Abstract

We consider an incomplete multi-asset binomial market model. We prove that for a wide class of contingent claims the extremal multi-step martingale measure is a power of the corresponding single-step extremal martingale measure. This allows for closed form formulas for the bounds of a no-arbitrage contingent claim price interval. We construct a feasible algorithm for computing those boundaries as well as for the corresponding hedging strategies. Our results apply, for example, to European basket call and put options and Asian arithmetic average options.