Valuation of VIX and Target Volatility Options with Affine GARCH Models

45 Pages Posted: 13 Aug 2020

See all articles by Hongkai Cao

Hongkai Cao

Stevens Institute of Technology - School of Business

Alexandru Badescu

University of Calgary

Zhenyu Cui

Stevens Institute of Technology - School of Business

Sarath Kumar Jayaraman

University of Calgary - Department of Mathematics and Statistics

Date Written: July 13, 2020

Abstract

In this paper we propose semi-closed-form solutions, subject to an inversion of the Fourier transform, for the price of VIX options and target volatility options (TVOs) under affine GARCH models based on Gaussian and Inverse Gaussian distributions. We illustrate the advantage of the proposed analytic expressions by comparing them with those obtained from benchmark Monte-Carlo simulations. The empirical performance of the two affine GARCH models is tested using different calibration exercises based on historical returns and market quotes on VIX and SPX options.

Keywords: VIX Options, Target Volatility Options, Heston-Nandi GARCH Model, Inverse Gaussian Model, Joint Calibration

JEL Classification: G12, G13, C13

Suggested Citation

Cao, Hongkai and Badescu, Alexandru and Cui, Zhenyu and Jayaraman, Sarath Kumar, Valuation of VIX and Target Volatility Options with Affine GARCH Models (July 13, 2020). Available at SSRN: https://ssrn.com/abstract=3650690 or http://dx.doi.org/10.2139/ssrn.3650690

Hongkai Cao

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

Alexandru Badescu

University of Calgary ( email )

University of Calgary
Calgary, Alberta
Canada

Zhenyu Cui (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://sites.google.com/site/zhenyucui86/publications

Sarath Kumar Jayaraman

University of Calgary - Department of Mathematics and Statistics ( email )

University of Calgary
Calgary, Alberta
Canada

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