Efficient Computation of the Quasi Likelihood function for Discretely Observed Diffusion Processes

TL;DR

This paper presents a novel, efficient method for computing moments needed for quasi maximum likelihood estimation in discretely observed stochastic differential equations, with sublinear complexity and robustness to sampling intervals.

Contribution

It introduces a general, fast, and unbiased computational approach for moments in discretely observed diffusions, applicable across various dynamics and sampling schemes.

Findings

Computational complexity is sublinear in the number of observations.

Method is unbiased for practical sampling designs.

Faster than Euler-Maruyama for moderate and large datasets.

Abstract

We introduce a simple method for nearly simultaneous computation of all moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations commonly seen in finance. The method proposed in this papers is not restricted to any particular dynamics of the differential equation and is virtually insensitive to the sampling interval. The key contribution of the paper is that computational complexity is sublinear in the number of observations as we compute all moments through a single operation. Furthermore, that operation can be done offline. The simulations show that the method is unbiased for all practical purposes for any sampling design, including random sampling, and that the computational cost is comparable (actually faster for moderate and large data sets) to the simple, often severely biased, Euler-Maruyama approximation.