Dilmi C. W. Hettiachchi-Halpe-Kankanamalage

arXiv2026

Portfolio Optimization for Commodity ETFs under Heavy-Tailed Returns

This paper examines portfolio optimization for commodity exchange-traded funds (ETFs) under heavy-tailed return behavior. Using daily Bloomberg data for 30 U.S.-listed commodity ETFs from 12 December 2018 to 16 December 2024, we study funds spanning agriculture, energy, metals, and broad commodity index exposure. We compare a passive buy-and-hold portfolio with rolling-window optimized portfolios formed under mean--variance and conditional value-at-risk (CVaR) criteria, considering both long-only and restricted long--short strategies. The results showed substantial heterogeneity across commodity sectors, with energy and broad commodity index funds displaying pronounced volatility, skewness, and excess kurtosis. Historical optimization indicated that minimum-risk and CVaR-based portfolios provided more stable cumulative performance than tangent portfolios and generally improved Sharpe, Calmar, and STARR$_{0.95}$ ratios. Extreme-value diagnostics showed that optimized portfolios remained exposed to heavy downside tails, so improved risk-adjusted performance did not eliminate extreme-loss risk. A dynamic extension based on ARMA--GARCH marginal models, Student--$t$ copula dependence, and one-step-ahead predictive scenarios improved performance mainly when combined with minimum-risk or CVaR-based objectives. Dynamic mean--variance tangent portfolios performed less reliably, reflecting sensitivity to expected-return estimation error. Transaction-cost robustness checks further showed that the practical value of dynamic optimization depended on turnover control, with low-turnover dynamic CVaR tangent portfolios remaining more resilient to implementation costs. Overall, the analysis showed that commodity ETF allocation benefited most from conservative and downside-risk-aware optimization, while optimized portfolios continued to require explicit tail-risk and implementation diagnostics.

q-fin.PM↗

arXiv2026

Innovative Extensions to Option Pricing: Asymmetric Brownian Motion and Random Walk Approaches

Classical option pricing models, such as Bachelier and Black--Scholes--Merton, postulate symmetric Brownian diffusion, which limits their capacity to reflect empirical phenomena including return skewness, heavy tails, and volatility asymmetry. This paper develops an innovative extension: the Geometric Asymmetric Brownian Motion (GABM), unifying asymmetric Brownian motion and random walk methodologies within the Bachelier--Black--Scholes--Merton framework. The approach harnesses the Cherny--Shiryaev--Yor invariance principle (CSYIP) to define asymmetric random walk integrals, where local time at the origin generates skewness and state-dependent risk. Closed-form option pricing formulas are derived, and a discrete-time binomial tree algorithm is constructed and shown to converge rigorously to the GABM limit. By incorporating a smoothed functional form based on the normal inverse Gaussian distribution, the model allows for flexible, state-dependent volatility calibration. Numerical experiments demonstrate the resulting option price and implied volatility surfaces, highlighting the framework's enhanced ability to capture persistent market asymmetry and complex risk behaviors observed in empirical data.

q-fin.MF↗