Correlated Squared Returns

58 Pages Posted: 14 Apr 2020 Last revised: 26 Dec 2020

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

King Wang

Morgan Stanley

Date Written: March 24, 2020


Joint densities for a sequential pair of returns with weak autocorrelation and strong correlation in squared returns are formulated. The marginal return densities are either variance gamma or bilateral gamma. Two dimensional matching of empirical characteristic functions to its theoretical counterpart is employed for dependency parameter estimation. Estimations are reported for 3920 daily return sequences of a thousand days. Path simulation is done using conditional distribution functions. The paths display levels of squared return correlation and decay rates for the squared return autocorrelation function that are comparable to these magnitudes in daily return data. Regressions of log characteristic functions at different time points are used to estimate time scaling coefficients. Regressions of these time scaling coefficients on squared return correlations support the view that autocorrelation in squared returns slows the rate of passage of economic time.

Keywords: Correlated Gamma Processes, Joint Characteristic Functions, Digital Moment Estimation, Path Simulation

JEL Classification: Gii, G13, G17.

Suggested Citation

Madan, Dilip B. and Wang, King, Correlated Squared Returns (March 24, 2020). Available at SSRN: or

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

King Wang

Morgan Stanley ( email )

1585 Broadway
New York, NY 10036
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics