Regime-switching Stochastic Volatility Model: Estimation and Calibration to VIX options

Stéphane Goutte, Amine Ismail and Huyên Pham ()
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Amine Ismail: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique
Huyên Pham: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité

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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 (CIR) 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&P 500 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.

Keywords: EM algorithm; Regime-switching model; Stochastic volatility; VIX index; Baum-Welch algorithm. (search for similar items in EconPapers)
Date: 2017-05-31
Note: View the original document on HAL open archive server: https://hal.science/hal-01212018v2
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Citations: View citations in EconPapers (6)

Published in Applied Mathematical Finance, 2017, 24 (1), pp.38-75. ⟨10.1080/1350486X.2017.1333015⟩

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Journal Article: 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)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01212018

DOI: 10.1080/1350486X.2017.1333015

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