Limit Laws in Transaction-Level Asset Price Models

TL;DR

This paper develops limit laws for transaction-level asset price models with jumps, cointegration, and various market effects, providing new asymptotic distributions for estimators in complex, realistic settings.

Contribution

It introduces asymptotic distribution results for log-price processes and cointegrating parameter estimators in advanced transaction-level models with multiple market features.

Findings

Asymptotic distribution of log-price process derived

Asymptotic distribution of OLS estimator for cointegration obtained

Distribution results for tapered estimator in fractional cointegration

Abstract

We consider pure-jump transaction-level models for asset prices in continuous time, driven by point processes. In a bivariate model that admits cointegration, we allow for time deformations to account for such effects as intraday seasonal patterns in volatility, and non-trading periods that may be different for the two assets. We also allow for asymmetries (leverage effects). We obtain the asymptotic distribution of the log-price process. We also obtain the asymptotic distribution of the ordinary least-squares estimator of the cointegrating parameter based on data sampled from an equally-spaced discretization of calendar time, in the case of weak fractional cointegration. For this same case, we obtain the asymptotic distribution for a tapered estimator under more