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

2025-05-18

AI Summary

This paper addresses the challenge of jointly modeling time-varying volatility, heavy tails, and dynamic correlations in multivariate asset returns. We propose the first multivariate affine GARCH(1,1) model featuring Normal Inverse Gaussian (NIG) distributed innovations to capture tail thickness, and extend the Heston–Nandi framework—previously univariate and Gaussian—to a multivariate heavy-tailed setting. Theoretical contributions include: (i) deriving a closed-form dynamic portfolio allocation solution for CRRA investors; and (ii) constructing an implied volatility surface that replicates both skew and volatility smile. Empirical analysis using 30 Dow Jones Industrial Average constituents shows that neglecting dynamic correlations and tail risk incurs substantial wealth-equivalent losses. Our model significantly outperforms the Merton constant-proportion strategy in both Sharpe ratio and expected utility, demonstrating superior risk-adjusted performance and economic value.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Develops multivariate affine GARCH model for heavy-tailed asset returns
• Unifies portfolio optimization and option pricing under non-Gaussian risks
• Quantifies utility losses from ignoring dynamic correlation and tail risk

Innovation

• Multivariate affine GARCH model with heavy tails
• Dynamic portfolio optimization and option pricing
• Closed-form solutions for CRRA asset allocation