On Conditional least squares estimation for the AD(1,n) model

TL;DR

This paper investigates the conditional least squares estimation of AD(1, n) affine diffusion models, analyzing asymptotic properties for both continuous and high-frequency discrete observations, with applications to financial models.

Contribution

It provides new asymptotic results for parameter estimation in AD(1, n) models using different observation schemes, extending the understanding of their statistical properties.

Findings

Asymptotic properties established for ergodic and non-ergodic cases.

Moment results for AD(1, n) models derived.

Estimation methods applicable to financial models like Vasicek and Heston.

Abstract

This paper deals with the problem of global parameter estimation of AD(1, n) where n is a positive integer which is a subclass of affine diffusions introduced by Duffie, Filipovic, and Schachermayer. In general affine models are applied to the pricing of bond and stock options, which is illustrated for the Vasicek, Cox-Ingersoll-Ross and Heston models. Our main results are about the conditional least squares estimation of AD(1, n) drift parameters based on two types of observations : continuous time observations and discrete time observations with high frequency and infinite horizon. Then, for each case, we study the asymptotic properties according to ergodic and non-ergodic cases. This paper introduces as well some moment results relative to the AD(1, n) model.