A regime-switching Heston model for VIX and S&P 500 implied volatilities

Andrew Papanicolaou, Ronnie Sircar

Research output: Contribution to journalArticle

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 have 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 analysing 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 of sharp regime shifts can bridge this shortcoming. We take advantage of asymptotic and 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.

Original languageEnglish (US)
Pages (from-to)1811-1827
Number of pages17
JournalQuantitative Finance
Volume14
Issue number10
DOIs
StatePublished - Oct 1 2014

Keywords

  • Applied mathematical finance
  • Calibration of stochastic volatility
  • Model calibration
  • VIX options

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

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