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arXiv · 2505.12198

Multivariate Affine GARCH with Heavy Tails: A Unified Framework for Portfolio Optimization and Option Valuation

Ayush Jha·Abootaleb Shirvani·Ali Jaffri·Svetlozar T. Rachev·Frank J. Fabozzi
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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.

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Ayush Jha, Abootaleb Shirvani, Ali Jaffri, Svetlozar T. Rachev, Frank J. Fabozzi. 2025-05-18. Multivariate Affine GARCH with Heavy Tails: A Unified Framework for Portfolio Optimization and Option Valuation. https://arxiv.org/abs/2505.12198

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