Available online at www.sciencedirect.com Mathematics and Computers in Simulation 81 (2011) 1247–1256 Monte Carlo option pricing with asymmetric realized volatility dynamics David E. Allen a , Michael McAleer c,d,e , Marcel Scharth b,d,∗ a School of Accounting, Finance and Economics, Edith Cowan University, Australia b Department of Econometrics, VU University Amsterdam, The Netherlands c Econometric Institute, Erasmus University Rotterdam, The Netherlands d Tinbergen Institute, The Netherlands e Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics, University of Tokyo, Japan Received 2 December 2009; received in revised form 28 May 2010; accepted 1 June 2010 Available online 30 June 2010 Abstract What are the advances introduced by realized volatility models in pricing options? In this short paper we analyze a simple option pricing framework based on the dually asymmetric realized volatility model, which emphasizes extended leverage effects and empirical regularity of high volatility risk during high volatility periods. We conduct a brief empirical analysis of the pricing performance of this approach against some benchmark models using data from the S&P 500 options in the 2001–2004 period. The results indicate that as expected the superior forecasting accuracy of realized volatility translates into significantly smaller pricing errors when compared to models of the GARCH family. Most importantly, our results indicate that the presence of leverage effects and a high volatility risk are essential for understanding common option pricing anomalies. © 2010 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: Realized volatility; Option pricing; Volatility of volatility; Leverage effects 1. Introduction The advent of high frequency stock market data and the subsequent introduction of realized volatility measures represented a substantial step forward in the accuracy with which econometric models of volatility could be evaluated and allowed for the development of new and more precise parametric models of time varying volatility. Several researchers have looked into the properties of ex post volatility measures derived from high frequency data and developed time series models that invariably outperform latent variable models of the GARCH (Generalized Autoregressive Conditional Heteroskedasticity) or stochastic volatility family of models [3] in forecasting future volatility, to the point that the comparison has been dropped altogether in recent papers. Recent contributions to the realized volatility modeling and forecasting literature are exemplified by Andersen et al. [3], the HAR (heterogeneous autoregressive) model of Corsi [10], the MIDAS (mixed data sample) approach of Ghysels et al. [15] and the unobserved ARMA component model of Refs. [18,23]. Martens et al. [20] develop ∗ Corresponding author at: Department of Econometrics, VU University Amsterdam, The Netherlands. Tel.: +31 20 5986013. E-mail addresses: d.allen@ecu.edu.au (D.E. Allen), michael.mcaleer@gmail.com (M. McAleer), mscharth@feweb.vu.nl (M. Scharth). 0378-4754/$36.00 © 2010 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.matcom.2010.06.010