On the Error in the Monte Carlo Pricing of Some Familiar European Path‐dependent Options

Abstract

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.

Geometric bounds on certain sublinear functionals of geometric Brownian motion

“…The inequality (3) follows at once from Corollary 2 in [14]. However, in order to make the paper more self-contained and since [14] has not been published, (3) will be proved in this paper as well.…”

“…The inequality (3) gives that ψ(u) ≤ 0 for all u > u * . In combination with (14) this yields that ∞ s u r 0 −1 ψ(u) du ≤ 0 for each s ≥ 0.…”