Title: A regime switching quadratic model for VIX futures valuation

Authors: Zhigang Tong

Addresses: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

Abstract: We develop a continuous time model for the VIX futures valuation. In this model, the state variable follows a mean-reverting process and the logarithm of future price is a quadratic function of state variable with regime switching mean. The transition between regimes is governed by a continuous time Markov chain. We provide analytical solutions for future prices and show how the regime shifts and the nonlinearity introduced by the quadratic term affect the term structure of future prices. We estimate both single regime and regime switching models through the Kalman filter. In our empirical work, we document that, indeed, the regime switching quadratic model can improve the forecasting power of the existing models.

Keywords: VIX futures valuation; regime switching; quadratic model; Kalman filter; continuous time Markov chain; forecasting; modelling; CBOE Volatility Index.

DOI: 10.1504/IJFMD.2015.073484

International Journal of Financial Markets and Derivatives, 2015 Vol.4 No.3/4, pp.246 - 272

Received: 21 Jul 2015
Accepted: 28 Sep 2015
Published online: 09 Dec 2015 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article