Dynamic Index Tracking and Risk Exposure Control Using Derivatives

Applied Mathematical Finance, August 2018

26 Pages Posted: 30 May 2017 Last revised: 27 Feb 2019

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Brian Ward

Columbia University

Date Written: June 8, 2017

Abstract

We develop a methodology for index tracking and risk exposure control using financial derivatives. Under a continuous-time diffusion framework for price evolution, we present a pathwise approach to construct dynamic portfolios of derivatives in order to gain exposure to an index and/or market factors that may be not directly tradable. Among our results, we establish a general tracking condition that relates the portfolio drift to the desired exposure coefficients under any given model. We also derive a slippage process that reveals how the portfolio return deviates from the targeted return. In our multi-factor setting, the portfolio's realized slippage depends not only on the realized variance of the index, but also the realized covariance among the index and factors. We implement our trading strategies under a number of models, and compare the tracking strategies and performances when using different derivatives, such as futures and options.

Keywords: slippage, index tracking, exposure control, realized covariance, derivatives trading

JEL Classification: G11, G13

Suggested Citation

Leung, Tim and Ward, Brian, Dynamic Index Tracking and Risk Exposure Control Using Derivatives (June 8, 2017). Applied Mathematical Finance, August 2018, Available at SSRN: https://ssrn.com/abstract=2976500 or http://dx.doi.org/10.2139/ssrn.2976500

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Brian Ward

Columbia University ( email )

New York, NY
United States

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