Minimum Cost Super-Hedging in a Discrete Time Incomplete Multi-Asset Binomial Market

TL;DR

This paper derives explicit formulas for the minimum cost super-hedging strategies in a multi-asset binomial market model without assuming joint distribution, applicable to various European options.

Contribution

It extends previous work by providing explicit super-hedging formulas in a more realistic multi-asset incomplete market model without distribution assumptions.

Findings

Explicit formulas for super-hedging strategies for European multi-asset claims

Applicable to basket options and similar derivatives

Provides formulas for non-negative residuals in super-hedging strategies

Abstract

We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide explicit formulas for the minimum cost super-hedging strategies for a wide class of European type multi-asset contingent claims. This class includes European basket call and put options, among others. Since a super-hedge is a non-self-financing arbitrage strategy, it produces non-negative local residuals, for which we also give explicit formulas. This paper completes the foundation started in previous work of the authors for the extension of our results to a more realistic market model.