Improved Frechet bounds and model-free pricing of multi-asset options

TL;DR

This paper develops improved bounds on the dependence structure of bivariate distributions and applies these to derive model-free price bounds for two-asset options using additional dependence information.

Contribution

It introduces new methods for tighter copula bounds with partial information and applies them to multi-asset option pricing without assuming a specific model.

Findings

Enhanced copula bounds with partial data

Tighter model-free option price bounds using dependence info

Applicable to multi-asset financial derivatives

Abstract

Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of $[0,1]^2$, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.