abstract:
Consider the solution of a scalar stochastic differential equation (SDE). We study approximation of the expected value of a function of the solution at a fixed time, which is motivated by pricing of pathindependent options. We present a deterministic quadrature rule for this problem, which is based on iterative quantization of the Euler scheme. We discuss its worst case error taken over a class of functions and a class of drift and diffusion coefficients, and the cost of constructing this rule. The latter is particularly relevant since the distribution of the solution is only given implicitly via the SDE. |