Optimal Option Portfolios for Student t Returns

ArXiv ID: 2601.07991 “View on arXiv”

Authors: Kyle Sung, Traian A. Pirvu

Abstract

We provide an explicit solution for optimal option portfolios under variance and Value at Risk (VaR) minimization when the underlying returns follow a Student t-distribution. The novelty of our paper is the departure from the traditional normal returns setting. Our main contribution is the methodology for obtaining optimal portfolios. Numerical experiments reveal that, as expected, the optimal variance and VaR portfolio compositions differ by a significant amount, suggesting that more realistic tail risk settings can lead to potentially more realistic portfolio allocations.

Keywords: Value at Risk (VaR) minimization, Student t-distribution, Option portfolios, Portfolio optimization, Variance minimization, Equities/Options

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper contains dense, advanced mathematics including multivariate Student t-distributions, delta-gamma approximations, moment generating functions, and explicit closed-form solutions for portfolio optimization. While it presents numerical experiments with real stock data, the summary and excerpt focus heavily on theoretical derivations and lack detailed implementation steps, code, or comprehensive backtesting results that would indicate high empirical rigor.

  flowchart TD
    A["Research Goal:<br>Optimal Option Portfolios for Student t Returns"] --> B["Key Methodology:<br>Solve for Min Variance & Min VaR"]
    B --> C["Data/Inputs:<br>Student t-distribution Parameters"]
    C --> D["Computational Process:<br>Explicit Analytical Solution"]
    D --> E{"Numerical Experiments"}
    E --> F["Key Finding 1:<br>Min Variance & Min VaR<br>Compositions Differ Significantly"]
    E --> G["Key Finding 2:<br>Realistic Tail Risk Yields<br>Realistic Portfolio Allocations"]