A New Optimized Stochastic Approach for Multiple Integrals in Option Pricing

—In the present paper we evaluate European style options with an exponential payoff function with an optimized lattice rule based on a new optimal generating vector. A brief introduction of the theory of lattice rule has been given. We compare the performance of the new stochastic approach with a new optimal generating vector for multiple integrals up to 50 dimensions.

[1]  Price forecasting and risk portfolio optimization , 2019, APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19.

[2]  Frances Y. Kuo,et al.  Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation , 2016, Foundations of Computational Mathematics.

[3]  Puxiang Lai,et al.  Applications of Monte Carlo/Quasi-Monte Carlo Methods in Finance: Option Pricing , 1998 .

[4]  H. Keng,et al.  Applications of number theory to numerical analysis , 1981 .

[5]  P. Boyle.  Options: A Monte Carlo approach , 1977 .

[6]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[7]  A. Stroud.  Approximate calculation of multiple integrals , 1973 .