Drift in Transcation-Level Asset Price Models

16 Pages Posted: 22 Nov 2012

See all articles by Wen Cao

Wen Cao

New York University (NYU) - Leonard N. Stern School of Business

Clifford M. Hurvich

Stern School of Business, New York University; New York University (NYU) - Department of Information, Operations, and Management Sciences

Philippe Soulier

Université d'Évry

Date Written: November 2012

Abstract

We study the effect of drift in pure-jump transaction-level models for asset prices in continuous time, driven by point processes. The drift is assumed to arise from a nonzero mean in the efficient shock series. It follows that the drift is proportional to the driving point process itself, i.e. the cumulative number of transactions. This link reveals a mechanism by which properties of intertrade durations (such as heavy tails and long memory) can have a strong impact on properties of average returns, thereby potentially making it extremely difficult to determine growth rates. We focus on a basic univariate model for log price, coupled with general assumptions on durations that are satisfied by several existing flexible models, allowing for both long memory and heavy tails in durations. Under our pure-jump model, we obtain the limiting distribution for the suitably normalized log price. This limiting distribution need not be Gaussian, and may have either finite variance or infinite variance. We show that the drift can affect not only the limiting distribution for the normalized log price, but also the rate in the corresponding normalization. Therefore, the drift (or equivalently, the properties of durations) affects the rate of convergence of estimators of the growth rate, and can invalidate standard hypothesis tests for that growth rate. Our analysis also sheds some new light on two longstanding debates as to whether stock returns have long memory or infinite variance.

Suggested Citation

Cao, Wen and Hurvich, Clifford M. and Soulier, Philippe, Drift in Transcation-Level Asset Price Models (November 2012). NYU Working Paper No. 2451/31652. Available at SSRN: https://ssrn.com/abstract=2179403

Wen Cao

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

Clifford M. Hurvich

Stern School of Business, New York University ( email )

44 West 4th Street
New York, NY 10012-1126
United States

New York University (NYU) - Department of Information, Operations, and Management Sciences

44 West Fourth Street
New York, NY 10012
United States

Philippe Soulier

Université d'Évry ( email )

F-91025 Evry Cedex
France
33 (0)1 69 47 02 28 (Phone)
33 (0)1 69 47 02 18 (Fax)

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