Regime-switching stochastic volatility model: estimation and calibration to VIX options

Stéphane Goutte, Amine Ismail and Huyên Pham

Applied Mathematical Finance, 2017, vol. 24, issue 1, 38-75

Abstract: We develop and implement a method for maximum likelihood estimation of a regime-switching stochastic volatility model. Our model uses a continuous time stochastic process for the stock dynamics with the instantaneous variance driven by a Cox–Ingersoll–Ross process and each parameter modulated by a hidden Markov chain. We propose an extension of the EM algorithm through the Baum–Welch implementation to estimate our model and filter the hidden state of the Markov chain while using the VIX index to invert the latent volatility state. Using Monte Carlo simulations, we test the convergence of our algorithm and compare it with an approximate likelihood procedure where the volatility state is replaced by the VIX index. We found that our method is more accurate than the approximate procedure. Then, we apply Fourier methods to derive a semi-analytical expression of S&P500 and VIX option prices, which we calibrate to market data. We show that the model is sufficiently rich to encapsulate important features of the joint dynamics of the stock and the volatility and to consistently fit option market prices.

Date: 2017
References: Add references at CitEc
Citations: View citations in EconPapers (25)

Downloads: (external link)
http://hdl.handle.net/10.1080/1350486X.2017.1333015 (text/html)
Access to full text is restricted to subscribers.

Related works:
Working Paper: Regime-switching Stochastic Volatility Model: Estimation and Calibration to VIX options (2017)
Working Paper: Regime-switching stochastic volatility model: estimation and calibration to VIX options (2017)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:apmtfi:v:24:y:2017:i:1:p:38-75

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RAMF20

DOI: 10.1080/1350486X.2017.1333015

Access Statistics for this article

Applied Mathematical Finance is currently edited by Professor Ben Hambly and Christoph Reisinger

More articles in Applied Mathematical Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().