Efficient computations of multivariate normal distributions with applications to finance

  • Authors:

  • Yongzeng Lai

  • Affiliations:

  • Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada

  • Venue:
  • MS'06 Proceedings of the 17th IASTED international conference on Modelling and simulation
  • Year:
  • 2006

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Abstract

This paper discusses the simulation of multivariate normal distributions with applications to Finance. We found that all the bivariate normal distributions can be converted into the one dimensional integrals and most cases of the trivariate normal distributions can be converted into 1- dimensional integrals provided |λi| i = 1, 2, 3), where ρij: = λiλj(i ≠ j) are correlation coefficients. If the dimension is higher than 3, the Monte Carlo and Quasi-Monte Carlo methods can be applied to estimate these distributions. And the quasi-Monte Carlo methods are more efficient than the Monte Carlo method. We also discuss the applications in finance since in many situations, financial derivatives, such as options, can be expressed in terms of multivariate normal distributions. Similar ideas can be applied to the computations of multivariate t-distributions.