Waiting for Returns: Using Space-Time Duality to Calibrate Financial Diffusions

24 Pages Posted: 31 Dec 2004  

Mark J. Kamstra

York University - Schulich School of Business

Moshe A. Milevsky

York University - Schulich School of Business

Date Written: December 20, 2004

Abstract

In this brief paper we propose an alternative methodology for testing and calibrating diffusion processes for financial time-series. The methodology focuses on the duality that exists between time and space for any given stochastic process. More specifically, we use the First Passage Time (FPT) which is the amount of time required by a stochastic process to travel a pre-specified distance. Thus, for example, we demonstrate that testing the hypothesis that (logarithmic) investment returns are independent and normally distributed is equivalent to testing the hypothesis that the FPT is Inverse Gaussian distributed. We apply this idea to calibrate geometric Brownian motion (GBM) parameters for the S&P 500 index over the period 1952 - 2004.

Keywords: Diffusion, duality, inverse guassian, GBM, First Passage Time

JEL Classification: G10, G13

Suggested Citation

Kamstra, Mark J. and Milevsky, Moshe A., Waiting for Returns: Using Space-Time Duality to Calibrate Financial Diffusions (December 20, 2004). Available at SSRN: https://ssrn.com/abstract=638283 or http://dx.doi.org/10.2139/ssrn.638283

Mark J. Kamstra (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

Moshe Arye Milevsky

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

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