On the error in the Monte Carlo pricing of some familiar European path-dependent options

This paper studies the relative error in the crude Monte Carlo pricing of some familiar European path-dependent multiasset options. For the crude Monte Carlo method it is well known that the convergence rate O(n(-1/2)), where n is the number of simulations, is independent of the dimension of the integral. This paper also shows that for a large class of pricing problems in the multiasset Black-Scholes market the constant in O( n(-1/2)) is independent of the dimension. To be more specific, the constant is only dependent on the highest volatility among the underlying assets, time to maturity, and degree of confidence interval.