Determining the optimum confidence interval based on the hybrid Monte Carlo method and its application in financial calculations

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    The accuracy of Monte Carlo and quasi-Monte Carlo methods decreases in problems of high dimensions. Therefore, the objective of this study was to present an optimum method to increase the accuracy of the answer. As the problem gets larger, the resulting accuracy will be higher. In this respect, this study combined the two previous methods, QMC and MC, and presented a hybrid method with efficiency higher than that of those two methods.


  • Keywords


    Central Limit Theorem; Confidence Interval; Efficiency; Hybrid Method; Pricing Model.

  • References


      [1] Giray Okten, Bruno Tuffin, Vadim Burago, 22 March 2006, A central limit theorem and improved error bounds for a hybrid-Monte Carlo sequence with applications in computational finance, Department of Mathematics, Florida State University, Tallahassee, FL 32306 USA.

      [2] Pierre L'Ecuyer, 23 July 2009, Quasi-Monte Carlo methods with applications in finance, this article is published with open access at Springerlink.com.

      [3] Peter Winker, Jenny X. Li, September 27, 2000, Time Series Simulation with Quasi Monte Carlo Methods, Departments of Mathematics and Economics, The Pennsylvania State University, University Park, PA, 16802, USA.

      [4] R. Caflisch, M. Morokoff, A. Owen, Valuation of mortgage backed securities using brownian bridges to reduce effective dimension, J. Comput. Finance 1 (1) (1997) 27–46.

      [5] Kahn, H., Marshall, A.W. (1953) Methods of reducing sample size in Monte Carlo computations, J.Oper.Res.Soc.Amer. 1, 263–271. http://dx.doi.org/10.1287/opre.1.5.263.

      [6] R. E. Caflisch, Monte Carlo and quasi-Monte Carlo methods, Acta Numerica vol. 7, Cambridge University Press, 1998, pp. 49-1.

      [7] tJ. Spanier, Quasi-Monte carlo methods for particle transport problems, in: H. Niederreiter, P.J.-S. Shiue (Eds.), Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Lecture Notes in Statistics, vol. 106, Springer, Berlin,1995, pp. 121–148. http://dx.doi.org/10.1007/978-1-4612-2552-2_6.

      [8] trL. Clewlow, C. Strickland, Implementing Derivatives Models,Wiley, NewYork

      [9] Parsiyan, A. Fundamentals of mathematic statistics. Tehran, Tehran University.


 

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Article ID: 3773
 
DOI: 10.14419/ijasp.v3i1.3773




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