How to Estimate Parameters of a Multivariate Model?

Abstract

We are now concerned with the estimation and (very briefly) calibration of multivariate stochastic models. This task is crucial for applications, but quite challenging for various reasons that we illustrate in the following. As a general problem one could say that the amount of data needed to estimate the parameters of a multi-dimensional model is often larger than it is for the univariate marginal laws. In reality, one often has the situation that data is incomplete for some dimension during some periods of time, or that, say, returns of different stocks are known for different time periods. For instance, if some index constitutions change, this problem arises naturally. So only rarely does one have a long set of data with the same data quality in all dimensions.