Covariance dependent kernels, a Q-affine GARCH for multi-asset option pricing

• Published in: International review of financial analysis Vol. 87; p. 102622
• Main Authors: Escobar-Anel, Marcos, Rastegari, Javad, Stentoft, Lars
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-05-2023
• Subjects: Closed form solutions; Covariance dependent kernel; GARCH models; Maximum likelihood estimation; Multi-asset options; Pricing; GARCH models; Maximum likelihood estimation; C15; Pricing; Covariance dependent kernel; G13; G12; Multi-asset options; Closed form solutions
• ISSN: 1057-5219; 1873-8079
• DOI: 10.1016/j.irfa.2023.102622

This paper introduces a class of multivariate GARCH models that extends the existing literature by explicitly modeling correlation dependent pricing kernels. A large subclass admits closed-form recursive solutions for the moment generating function under the risk-neutral measure, which permits efficient pricing of multi-asset options. We perform a full calibration to three bivariate series of index returns and their corresponding volatility indexes in a joint maximum likelihood estimation. The results empirically confirm the presence of correlation dependance in addition to the well known variance dependance in the pricing kernel. The model improves both the overall likelihood and the VIX-implied likelihoods, with a better fitting of marginal distributions, e.g., 15% less error on one-asset option prices. The new degree of freedom is also shown to significantly impact the shape of marginal and joint pricing kernels, and leads to up to 53% differences for out-of-the-money two-asset correlation option prices.
•New class of GARCH with pricing kernels dependent on variances and correlation.•Closed-form solutions for the moment generating function under pricing measure.•Calibration to bivariate series via a joint maximum likelihood estimation.•Improvements in the likelihoods and lesser errors on one-asset option prices.•Up to 53% differences for OTM claims with short maturity for correlation options.