Sharpe Ratio and Return-VaR Ratio Maximization for Option Portfolios with Skew-Elliptical t Underlying Returns

Battle Count: 121

Highly relevant for quantitative trading desks managing options portfolios. The closed-form solutions enable efficient portfolio construction under realistic heavy-tailed and skewed return distributions. The distinction between Sharpe-optimal and R-VaR-optimal portfolios is practically important for risk-adjusted performance evaluation. However, the single-period framework and delta-gamma approximation limit direct applicability to high-frequency or dynamic trading strategies.

The closed-form solutions (Theorems 3.1 and 3.2) are relatively straightforward to implement once the distributional parameters (mu, Sigma, nu, omega) are estimated. The main complexity lies in: (1) fitting the multivariate skew-elliptical t-distribution to return data, (2) computing the delta-gamma Greeks for the option portfolio, (3) constructing the u and Q matrices from the moment formulas in Appendix A, and (4) solving the constrained optimization numerically when box constraints are imposed. The mathematical derivations are well-documented but require careful numerical implementation.

The paper provides explicit closed-form formulas (Theorems 3.1 and 3.2), detailed parameter tables (Table 1), and full proofs in Appendix B. However, no code repository is provided, and the raw data for the five stocks (DIS, XOM, PFE, MO, INTC) is not explicitly linked. The methodology is fully described mathematically, enabling reproduction by a skilled practitioner.