A Stochastic Volatility Model With Realized Measures for Option Pricing

Abstract

Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence—the crucial parameter in pricing Standard and Poor’s 500 Index options.

Keywords:

• Bayesian inference
• High-frequency data
• Monte Carlo Markov chain
• Option pricing
• Realized volatility

ACKNOWLEDGMENTS

All authors warmly thank Drew D. Creal for helpful comments on the implementation of the algorithm for computing the Bessel function of the second kind and Dario Alitab for support during the development of the pricing code. All authors thank Mark Jensen, Christian P. Robert, Francesco Ravazzolo, Herman K. van Dijk for helpful comments and fruitful discussion. We also thank all the participants of the European Seminar on Bayesian Econometrics 2016 in Venice, of the 1st DEM Workshop in Financial Econometrics 2016 in Verona.

Additional information

Funding

The research of RC used the SCSCF multiprocessor cluster system at University Ca’ Foscari of Venice and is part of the research activities of the Venice Center in Economic and Risk Analytics for public policies (VERA) at Ca’ Foscari University of Venice. GL acknowledges research support from the Scuola Normale Superiore Grant SNS_14_BORMETTI and CI14_UNICREDIT_MARMI.