Abstract
A simulation technique known as empirical martingale simulation (EMS) was proposed to improve simulation accuracy. By an adjustment to the standard Monte Carlo simulation, EMS ensures that the simulated price satisfies the rational option pricing bounds and that the estimated derivative contract price is strongly consistent with payoffs that satisfy Lipschitz condition. However, for some currently used contracts such as self-quanto options and asymmetric or symmetric power options, it is open whether the above asymptotic result holds. In this paper, we prove that the strong consistency of the EMS option price estimator holds for a wider class of univariate payoffs than those restricted by Lipschitz condition. Numerical experiments demonstrate that EMS can also substantially increase simulation accuracy in the extended setting.
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References
Bams, D., Lehnert, T., Wolff, C.C.P. Loss functions in option valuation: a framework for model selection. 2005 (Working paper)
Barraquand, J. Numerical valuation of high dimentional multivariate Euorpean securities. Management Sci., 41: 1882–1891 (1995)
Billingsley, P. Convergence of Probability Measures. Wiley, New York, 1968
Black, F., Scholes, M. The pricing of options and corporate liabilities. J. Polit. Econ., 81: 637–659 (1973)
Boyle, P., Broadie, M., Glasserman, P. Monte Carlo methods for security pricing. J. Econ. Dynamics and Control, 21: 1267–1321 (1997)
Christoffersen, P., Jacobs, K., Mimouni, K. An empirical comparison of affine and non-affine models for equity index options. 2005 (Working paper)
Culot, M., Goffin, V., Lawford, S., De Menten, Y. An affine jump diffusion model for electricity, 2006 (Working paper)
Demir, S., Tutek, H. Pricing of options in emerging financial markets using martinagle simulation: an example from turkey. Compuational Finance and its Applications, WIT Press, Southampton, Boston, 143–156 (2004)
Duan, J.C. The GARCH option pricing model. Math. Finance., 5: 13–32 (1995)
Duan, J.C., Simonato, J.G. Empirical martingale simulation for asset prices. Management Sci., 44: 1218–1233 (1998)
Duan, J.C., Wei, J.Z. Pricing foreign currency and cross-currency options under GARCH, 2006. (Working paper)
Harikumar, T., De Boyrie, M. Evaluation of Black-Scholes and GARCH models using currency call options data. Review of Quantitative Finance and Accounting., 23: 299–312 (2004)
Harrison, J., D. Kreps. Martingale and arbitrage in multiperiod securities markets. J. Econ. Theory., 20:381–408 (1979)
Hawlistschek, K., Dorfleitner, G. A general Green’s function approach to option pricing. 2006 (Working paper)
Hogg, R.V., McKean, J.W., Craig, A.T. Introduction to mathematical statistics. Sixth Edition, Pearson Prentice Hall, 2005
Musiela, M., Rutkowski, M. Martingale methods in financial modelling. Springer-Verlag, Berlin, 1997
Papapantoleon, A. and Eberlein, E. 2006. Symmetries and pricing of exotic options in Lévy models. Working paper.
Yan, S., Liu, X. Measure and Probability. First Edition, Beijing Normal University Press, Beijing, 1994
Yuan, S.C., Henry, T. Probability Theory. Third Edition. Springer-Verlag, Berlin, 1997
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The second author’s research is supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
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Yuan, Zs., Chen, Gm. Strong consistency of the empirical martingale simulation option price estimator. Acta Math. Appl. Sin. Engl. Ser. 25, 355–368 (2009). https://doi.org/10.1007/s10255-008-8801-7
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DOI: https://doi.org/10.1007/s10255-008-8801-7