Multivariate Affine GARCH with Heavy Tails: A Unified Framework for Portfolio Optimization and Option Valuation
Abstract
This paper develops and estimates a multivariate affine GARCH(1,1) model with Normal Inverse Gaussian innovations that captures time-varying volatility, heavy tails, and dynamic correlation across asset returns. We generalize the Heston-Nandi framework to a multivariate setting and apply it to 30 Dow Jones Industrial Average stocks. The model jointly supports three core financial applications: dynamic portfolio optimization, wealth path simulation, and option pricing. Closed-form solutions are derived for a Constant Relative Risk Aversion (CRRA) investor's intertemporal asset allocation, and we implement a forward-looking risk-adjusted performance comparison against Merton-style constant strategies. Using the model's conditional volatilities, we also construct implied volatility surfaces for European options, capturing skew and smile features. Empirically, we document substantial wealth-equivalent utility losses from ignoring time-varying correlation and tail risk. These findings underscore the value of a unified econometric framework for analyzing joint asset dynamics and for managing portfolio and derivative exposures under non-Gaussian risks.
Keywords
Cite
@article{arxiv.2505.12198,
title = {Multivariate Affine GARCH with Heavy Tails: A Unified Framework for Portfolio Optimization and Option Valuation},
author = {Ayush Jha and Abootaleb Shirvani and Ali Jaffri and Svetlozar T. Rachev and Frank J. Fabozzi},
journal= {arXiv preprint arXiv:2505.12198},
year = {2025}
}