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

Paper: arXiv 2505.12198

Authors: Ayush Jha, Abootaleb Shirvani, Ali Jaffri, Svetlozar T. Rachev, Frank J. Fabozzi

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.0/10 (capped from 7.5: transaction costs not modelled; no out-of-sample test; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical extension of the Heston-Nandi framework to a multivariate affine GARCH model incorporating heavy-tailed Normal Inverse Gaussian innovations. It offers solid empirical application across 30 DJIA constituents, bridging closed-form option pricing, CRRA portfolio optimization, and wealth-equivalent loss metrics effectively.

Research Flowchart

  flowchart TD
    A[Research Goal: Unified Framework for Asset Allocation, Option Pricing & Non-Gaussian Risks] --> B[Input Data: Daily Returns of 30 DJIA Stocks & Option Prices]
    B --> C[Methodology: Multivariate Affine GARCH-NIG Model Construction]
    C --> D[Model Estimation: Capturing Dynamic Correlations & Heavy Tails]
    D --> E1[Financial App 1: Intertemporal CRRA Portfolio Optimization]
    D --> E2[Financial App 2: Path Simulation & Option Pricing / Volatility Surfaces]
    E1 & E2 --> F[Key Outcomes: Closed-Form CRRA Solutions & Utility Losses from Ignoring Tail/Correlation Risk]