Advanced stochastic approaches for option pricing based on Sobol sequence

Venelin Todorov, Ivan Dimov, Rayna Georgieva, Yu. Dimitrov, Stoyan Apostolov, Miroslav Stoenchev

Abstract

Recently Monte Carlo and quasi-Monte Carlo approaches have become a very attractive and necessary computational tools in finance. The field of computational finance is becoming more complicated with increasing number of applications. The pricing of options is a very important in financial markets today and especially difficult when the dimension of the problem goes higher. Monte Carlo and quasi Monte Carlo methods are appropriate for solving multidimensional problems, since their computational complexity increases polynomially, but not exponentially with the dimensionality. A comprehensive experimental study based on scrambling of the Sobol sequence is applied for the first time to evaluate European style options. The Sobol scrambling method is not only one of the best available algorithms for high dimensional integrals but also one of the few possible methods, because in this work we show that the deterministic algorithms need a huge amount of time for the evaluation of the multidimensional integral, as it was discussed in this paper. The numerical tests show that the method is efficient for multidimensional integration and especially for computing multidimensional integrals of a very high dimension.

Locations

• AIP conference proceedings - View - PDF