European baskets in discrete-time continuous-binomial market models

TL;DR

This paper analyzes a discrete-time multi-asset market with continuous jumps, providing explicit bounds for no-arbitrage prices of European basket options and describing optimal hedging strategies.

Contribution

It introduces a method to compute price bounds for basket options in jump models and explicitly constructs maximal hedging strategies, extending previous binomial model results.

Findings

Lower bounds coincide with Jensen's bound.

Upper bounds are computed via restricted binomial models.

Explicit maximal hedging strategies are derived.

Abstract

We consider a discrete-time incomplete multi-asset market model with continuous price jumps. For a wide class of contingent claims, including European basket call options, we compute the bounds of the interval containing the no-arbitrage prices. We prove that the lower bound coincides, in fact, with Jensen's bound. The upper bound can be computed by restricting to a binomial model for which an explicit expression for the bound is known by an earlier work of the authors. We describe explicitly a maximal hedging strategy which is the best possible in the sense that its value is equal to the upper bound of the price interval of the claim. Our results show that for any $c$ in the interval of the non-arbitrage contingent claim price at time $0$, one can change the boundaries of the price jumps to obtain a model in which $c$ is the upper bound at time $0$ of this interval. The lower bound of this interval remains unaffected.