Advertisement

Hedging with Monte Carlo Simulation

  • Jaksa Cvitanić
  • Levon Goukasian
  • Fernando Zapatero
Part of the Applied Optimization book series (APOP, volume 74)

Abstract

Monte Carlo simulation provides a simple procedure to price securities numerically; however, it does not immediately yield the weights necessary to construct a replicating portfolio. The procedure commonly used consists in approximating the derivatives by perturbing the price of the underlying. Here we suggest an alternative procedure that exploits the semimartingale representation of the dynamics of any redundant security and consists in retrieving the volatility term of that representation. Compared to the alternative procedure, the method we suggest has the advantage that the computational cost is independent of the number of dimensions (unlike the traditional procedure where the cost increases linearly with the number of dimensions).

Keywords

Monte Carlo hedging options 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boyle, P., 1977, “Options: a Monte Carlo Approach,” Journal of Financial Economics 4, 323–338.CrossRefGoogle Scholar
  2. Boyle, P., M. Broadie and P. Glasserman, 1997, “Monte Carlo Methods for Security Pricing,” Journal of Economic Dynamics and Control, 21, 1267 1321.Google Scholar
  3. Broadie, M. and P. Glasserman, 1996, “Estimating Security Price Derivatives Using Simulation,” Management Science 42, 269–285.CrossRefGoogle Scholar
  4. Duffle, D. and P. Glynn, 1995, “Efficient Monte Carlo Simulation of Security Prices,” Annals of Applied Probability, 5, 897–905.CrossRefGoogle Scholar
  5. Fournie, E., Lasry J-M., Lebuchoux J., Lions P-L. and N. Touzi, 1999, “Applications of Malliavin calculus to Monte Carlo methods in finance,” Finance & Stochastics, 4, 391–412.Google Scholar
  6. Fu, M. and J.-Q. Hu, 1995, “Sensitivity Analysis for Monte Carlo Simulation of Option Pricing,” Probability in the Engineering and Informational Sciences, 9, 417–446.CrossRefGoogle Scholar
  7. Glynn, P., 1989, “Optimization of stochastic systems via simulation.” Proceedings of the Winter Simulation Conference, The Society for Computer Simulation, San Diego, CA, 90–105.Google Scholar
  8. Harrison, J.M. and D. Kreps, 1979, “Martingales and Arbitrage in Multiperiod Securities Markets,” Journal of Economic Theory, 20, 381–408.CrossRefGoogle Scholar
  9. Harrison, J.M. and S. Pliska, 1981, “Martingales and Stochastic Integrals in the Theory of Continuous Trading,” Stochastic Processes and Their Applications, 11, 215–260.CrossRefGoogle Scholar
  10. Ibanez A. and F. Zapatero, 1999, “Monte Carlo Valuation of American Options through Computation of the Optimal Exercise Frontier,” working paper, University of Southern California.Google Scholar
  11. Kloeden, P. and E. Platen, 1992, Numerical Solutions of Stochastic Differential Equations, Springler-Verlag, New York.CrossRefGoogle Scholar
  12. Longstaff, F. and E. Schwartz, 2001, “Valuing American Options by Simulation: A Simple Least-Squares Approach,” Review of Financial Studies, 14, 113148.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Jaksa Cvitanić
    • 1
  • Levon Goukasian
    • 1
  • Fernando Zapatero
    • 2
  1. 1.Department of MathematicsUSCUSA
  2. 2.Finance and Business Economics DepartmentUSCUSA

Personalised recommendations