A Regime-Switching Heston Model for VIX and S&P 500 Implied Volatilities

Quantitative Finance, Volume 14, Issue 10, (2014) pp. 1811-1827.

27 Pages Posted: 20 Oct 2012 Last revised: 21 Sep 2014

See all articles by Andrew Papanicolaou

Andrew Papanicolaou

NYU Tandon School of Engineering, Department of Finance and Risk Engineering

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Date Written: April 25, 2013

Abstract

Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular, there is growing interest in options on the VIX volatility index. A number of recent empirical studies examine whether there is significantly greater risk premium in VIX option prices compared with S&P 500 option prices. We address this issue by proposing and analyzing a stochastic volatility model with regime switching. The basic Heston model cannot capture VIX implied volatilities, as has been documented. We show that the incorporation sharp regime shifts can bridge this shortcoming. We take advantage of Fourier methods to make the extension tractable, and we present a fit to data, both in times of crisis and relative calm, which shows the effectiveness of the regime switching.

Keywords: Heston model, VIX Options

JEL Classification: G12, G13, G17

Suggested Citation

Papanicolaou, Andrew and Sircar, Ronnie, A Regime-Switching Heston Model for VIX and S&P 500 Implied Volatilities (April 25, 2013). Quantitative Finance, Volume 14, Issue 10, (2014) pp. 1811-1827.. Available at SSRN: https://ssrn.com/abstract=2164500 or http://dx.doi.org/10.2139/ssrn.2164500

Andrew Papanicolaou (Contact Author)

NYU Tandon School of Engineering, Department of Finance and Risk Engineering ( email )

6 Metrotech Center
Brooklyn, NY 11201
United States

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

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