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

TL;DR

This paper introduces a multivariate affine GARCH model with heavy tails that captures dynamic correlations and volatility, enabling improved portfolio optimization and option pricing with empirical validation on Dow Jones stocks.

Contribution

It generalizes the Heston-Nandi model to a multivariate setting with heavy tails, providing closed-form solutions for asset allocation, wealth simulation, and option valuation.

Findings

Significant utility losses occur when ignoring tail risk and correlation dynamics.

The model accurately captures implied volatility surfaces with skew and smile features.

Empirical results demonstrate the model's effectiveness on Dow Jones stocks.

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.