Constructing discrete approximations algorithms for financial calculus from weak convergence results

摘要

A general method for generating approximation algorithms for integral cal-culations is proposed here, starting from weak convergence results and then adjusting the integral calculations such that the gaussian probability kernel appears inside the integral. While this technique can be applied in a wide ap-plied mathematical context we focus here on European option pricing as a class of applications. We prove that the weak convergence characterizing condition can still be applied under some mild assumption on the payoff function of fi-nancial options. It is also shown that the approximation grid is a dense set in the set of real numbers.