Joint analysis and estimation of stock prices and trading volume in Barndorff-Nielsen and Shephard stochastic volatility models

TL;DR

This paper proposes a new stochastic volatility model linking trading volume and stock prices, providing explicit estimators and demonstrating their consistency and normality through empirical analysis of IBM and Microsoft stocks.

Contribution

It introduces a novel variant of the Barndorff-Nielsen and Shephard model that models trading volume instead of variance, with explicit estimation methods and theoretical properties.

Findings

Estimator is consistent and asymptotically normal.

Explicit expressions for the asymptotic covariance matrix.

Empirical analysis on IBM and MSFT stocks over five years.

Abstract

We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model where the non Gaussian Ornstein-Uhlenbeck process describes some measure of trading intensity like trading volume or number of trades instead of unobservable instantaneous variance. We develop an explicit estimator based on martingale estimating functions in a bivariate model that is not a diffusion, but admits jumps. It is assumed that both the quantities are observed on a discrete grid of fixed width, and the observation horizon tends to infinity. We show that the estimator is consistent and asymptotically normal and give explicit expressions of the asymptotic covariance matrix. Our method is illustrated by a finite sample experiment and a statistical analysis on the International Business Machines Corporation (IBM) stock from the New York Stock Exchange (NYSE) and the Microsoft Corporation (MSFT) stock from Nasdaq during a history of five years.