Optimal Option Portfolios for Skew-Elliptical t Returns

TL;DR

This paper develops a method for optimizing option portfolios under skew-elliptical t-distributed returns, capturing skewness and heavy tails, with explicit weights and improved risk measures.

Contribution

It introduces explicit portfolio weights for skew-elliptical t-distributions and compares their impact on risk measures like variance and VaR.

Findings

Skewness significantly affects optimal portfolio weights.

Better VaR approximations lead to more distinct weights from variance-based ones.

Numerical optimization improves VaR-based portfolio risk assessment.

Abstract

This paper explores option portfolio optimization when the underlying returns are skew-elliptical t-distributed. We use the variance and value at risk (VaR) to measure portfolio risk. The novelty of our work is the departure from the traditional normal returns setting, allowing investors to capture both heavy-tailed and skewed market dynamics. We provide explicit portfolio weights for the variance and VaR approximation. Our second contribution is the numerical representation of portfolio weights, obtained from numerical optimization for better VaR approximations. The effect of skewness on the portfolio weights is quantified by comparing our optimal skew t weights with those generated in the Student t setting. We also find that, as expected, a better VaR approximation risk measure yields optimal portfolio weights which are more different than the variance optimal weights.