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Empirical Martingale Simulation for Asset Prices

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Author Info

  • Jin-Chuan Duan
  • Jean-Guy Simonato

Abstract

This paper proposes a simple modification to the standard Monte Carlo simulation procedure for computing the prices of derivative securities. The modification imposes the martingale property on the simulated sample paths of the underlying asset price. This procedure is referred to as the empirical martingale simulation (EMS). The EMS ensures that the price estimated by simulation satisfies rational option pricing bounds. The EMS also yields a substantial error reduction for the price estimate. The EMS can be easily coupled with the standard variance reduction methods to obtain greater computational efficiency. Simulation studies are conducted for European and Asian call options using both the Black and Scholes and GARCH option pricing frameworks. The results indicate that the EMS yields substantial variance reduction particularly for in- and at-the-money options. Cette étude propose une modification simple aux procédures traditionnelles de calcul de prix des produits dérivés par simulation de Monte Carlo. La modification impose la propriété de martingale aux trajectoires simulées de la variable d'état sous-jacente. L'utilisation de cette procédure assure que l'estimé de prix respecte les bornes rationnelles d'option tout en diminuant de façon substantielle la variance des estimés de prix. La procédure peut aisément être jumelée aux méthodes traditionnelles de réduction de variance afin d'obtenir une plus grande efficacité. Une étude de simulation est présentée pour des options d'achat Européennes et Asiatiques. Les résultats indiquent que la méthode obtient des réductions substantielle de la variance des estimés de prix et ce, particulièrement pour les options in et at the money .

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 95s-43.

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Date of creation: 01 Oct 1995
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Handle: RePEc:cir:cirwor:95s-43

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Related research

Keywords: Martingale; Option Pricing; Monte Carlo Simulation; GARCH; Asian Options; Martingale; Evaluation des Options; Simulation de Monte Carlo; GARCH; Options Asiatiques;

References

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  1. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
  2. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  3. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
  4. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
  5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  6. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  7. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  8. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
  9. Peter Ritchken & L. Sankarasubramanian & Anand M. Vijh, 1993. "The Valuation of Path Dependent Contracts on the Average," Management Science, INFORMS, vol. 39(10), pages 1202-1213, October.
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Citations

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Cited by:
  1. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for general GARCH models," Papers 1209.5976, arXiv.org, revised Sep 2012.
  2. Christian Wolff & Dennis Bams & Thorsten Lehnert, 2008. "Loss Functions in Option Valuation: A Framework for Selection," LSF Research Working Paper Series 08-11, Luxembourg School of Finance, University of Luxembourg.
  3. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2009. "Martingalized historical approach for option pricing," Documents de travail du Centre d'Economie de la Sorbonne 09021, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  4. Paul H. Kupiec & James M. O'Brien, 1997. "The pre-commitment approach: using incentives to set market risk capital requirements," Finance and Economics Discussion Series 1997-14, Board of Governors of the Federal Reserve System (U.S.).
  5. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
  6. Paul H. Kupiec & James M. O'Brien, 1998. "Deposit insurance, bank incentives, and the design of regulatory policy," Economic Policy Review, Federal Reserve Bank of New York, issue Oct, pages 201-211.
  7. Paul H. Kupiec & James M. O'Brien, 1997. "Deposit insurance, bank incentives, and the design of regulatory policy," Finance and Economics Discussion Series 1998-10, Board of Governors of the Federal Reserve System (U.S.).
  8. Thorsten Lehnert & Bart Frijns & Remco Zwinkels, 2009. "Behavioral Heterogeneity in the Option Market," LSF Research Working Paper Series 09-07, Luxembourg School of Finance, University of Luxembourg.
  9. Masato Ubukata & Toshiaki Watanabe, 2013. "Pricing Nikkei 225 Options Using Realized Volatility," Global COE Hi-Stat Discussion Paper Series gd12-273, Institute of Economic Research, Hitotsubashi University.
  10. Peter Christoffersen & Kris Jacobs, 2002. "Which Volatility Model for Option Valuation?," CIRANO Working Papers 2002s-33, CIRANO.
  11. Bams, Dennis & Lehnert, Thorsten & Wolff, Christian C, 2005. "Loss Functions in Option Valuation: A Framework for Model Selection," CEPR Discussion Papers 4960, C.E.P.R. Discussion Papers.
  12. Christian Wolff & Thorsten Lehnert & Cokki Versluis, 2009. "A Cumulative Prospect Theory Approach to Option Pricing," LSF Research Working Paper Series 09-03, Luxembourg School of Finance, University of Luxembourg.
  13. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers 2012-50, School of Economics and Management, University of Aarhus.
  14. Jin-Chuan Duan & Genevieve Gauthier & Caroline Sasseville & Jean-Guy Simonato, 2002. "Seize the Moments: Approximating American Option Prices in the GARCH Framework," Finance 0206005, EconWPA.
  15. Matthias Fengler & Helmut Herwartz & Christian Werner, 2010. "A dynamic copula approach to recovering the index implied volatility skew," University of St. Gallen Department of Economics working paper series 2010 1132, Department of Economics, University of St. Gallen, revised Nov 2011.
  16. repec:hal:journl:hal-00308687 is not listed on IDEAS
  17. Joan del Castillo & Juan-Pablo Ortega, 2011. "Hedging of time discrete auto-regressive stochastic volatility options," Papers 1110.6322, arXiv.org.
  18. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2007. "Models for S&P500 Dynamics: Evidence from Realized Volatility, Daily Returns, and Option Prices," CREATES Research Papers 2007-37, School of Economics and Management, University of Aarhus.

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