文档介绍：Numerical Algorithms Group
Title: Multi-Asset Derivative Pricing Using Quasi-Random Numbers and Monte
Carlo Simulation
Summary: This article discusses using NAG software to estimate the value of some (simple) financial
derivatives. Here instead of generating uniform pseudo-random and uniform quasi-random
sequences as previously presented (see white paper titled “An Introduction to Quasi-
random Numbers), we generate multivariate Normal pseudo-random and multivariate
Normal quasi-random sequences with a given mean and covariance matrix. The current
price of the financial derivative is estimated by evaluating an integral which represents the
expected (discounted) value of the derivative’s pay-off at maturity.
In a previous Financial Engineering News article [1] the author gave introductory details concerning the
use of quasi-random numbers for Monte Carlo simulation. The benefits to be gained by using quasi-
random numbers instead of pseudo-random numbers were illustrated by using different random
sequences to estimate the known value of a six-dimensional integral. The sequences were obtained
using both the NAG pseudo-random number generators and the NAG quasi-random generators [2][3],
and the integral was estimated by uniformly sampling the six-dimensional unit hypercube. The results
illustrated that quasi-random numbers can gi