The pricing of spread option using simulation

  • Authors

    • Hamid Reza Erfanian University of Science and Culture, Tehran, Iran
    • Seyed Jaliledin Ghaznavi Bidgoli University of Science and Culture, Tehran, Iran
    • Parvin Shakibaei
  • Monte Carlo Simulation, Multilevel Monte Carlo, Spread Options Pricing.
  • Monte Carlo simulation is one of the most common and popular method of options pricing. The advantages of this method are being easy to use, suitable for all kinds of standard and exotic options and also are suitable for higher dimensional problems. But on the other hand Monte Carlo variance convergence rate is which due to that it will have relatively slow convergence rate to answer the problems, as to achieve  accuracy when it has been d-dimensions, complexity is . For this purpose, several methods are provided in quasi Monte Carlo simulation to increase variance convergence rate as variance reduction techniques, so far. One of the latest presented methods is multilevel Monte Carlo that is introduced by Giles in 2008. This method not only reduces the complexity of computing amount  in use of Euler discretization scheme and the amount  in use of Milstein discretization scheme, but also has the ability to combine with other variance reduction techniques. In this paper, using Multilevel Monte Carlo method by taking Milstein discretization scheme, pricing spread option and compared complexity of computing with standard Monte Carlo method. The results of Multilevel Monte Carlo method in pricing spread options are better than standard Monte Carlo simulation.

  • References

    1. [1] Wilmott, P., Frequently asked questions in quantitative finance. 2010: John Wiley & Sons.

      [2] Glasserman, P., Monte Carlo methods in financial engineering. Vol. 53. 2003: Springer Science & Business Media.

      [3] Huth, D., Application of Multilevel Monte Carlo simulation to Barrier, Asian and American options, in Mathematics2012, Technical University of Munich.

      [4] Giles, M.B., Multilevel monte carlo path simulation. Operations Research, 2008 a. 56(3): p. 607-617.

      [5] Giles, M., Improved multilevel Monte Carlo convergence using the Milstein scheme, in Monte Carlo and quasi-Monte Carlo methods 2006. 2008 b, Springer. p. 343-358.

      [6] Giles, M.B. and B.J. Waterhouse, Multilevel quasi-Monte Carlo path simulation. Advanced Financial Modelling, Radon Series on Computational and Applied Mathematics, 2009: p. 165-181.

      [7] Giles, M.B., D.J. Higham, and X. Mao, Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff. Finance and Stochastics, 2009. 13(3): p. 403-413.

      [8] Giles, M.B. Multilevel Monte Carlo for basket options. in Simulation Conference (WSC), Proceedings of the 2009 Winter. 2009. IEEE.

      [9] Primozic, T., Estimating expected first passage times using multilevel Monte Carlo algorithm, in Mathematical and Computational Finance2011, University of Oxford.

      [10] Ferreiro-Castilla, A., et al., Multilevel Monte Carlo simulation for Lévy processes based on the Wiener–Hopf factorisation. Stochastic Processes and their Applications, 2014. 124(2): p. 985-1010.

      [11] Zhang, P.G., Exotic Options: A Guide to Second Generation Options. 1998: World Scientific.

      [12] Andersson, M., Valuation of spread options using the fast Fourier transform under stochastic volatility and jump diffusion models. 2015.

      [13] Heinrich, S., Multilevel monte carlo methods, in Large-scale scientific computing. 2001, Springer. p. 58-67.

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  • How to Cite

    Erfanian, H. R., Ghaznavi Bidgoli, S. J., & Shakibaei, P. (2017). The pricing of spread option using simulation. International Journal of Applied Mathematical Research, 6(4), 121-124.