Portfolio optimisation with options

TL;DR

This paper introduces a novel method for portfolio optimization with options, addressing distribution asymmetry, high dimensionality, and dependence, using a new dependency matrix based on conditional probabilities.

Contribution

It proposes a new dependency matrix derived from conditional probabilities and copula structures, enabling efficient and scalable portfolio optimization with options.

Findings

The approach is efficient and fast.

It scales well to large portfolios.

Empirical results demonstrate practical effectiveness.

Abstract

We develop a new analysis for portfolio optimisation with options, tackling the three fundamental issues with this problem: asymmetric options' distributions, high dimensionality and dependence structure. To do so, we propose a new dependency matrix, built upon conditional probabilities between options' payoffs, and show how it can be computed in closed form given a copula structure of the underlying asset prices. The empirical evidence we provide highlights that this approach is efficient, fast and easily scalable to large portfolios of (mixed) options.