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Assessing the Effectiveness of Local and Global Quadratic Hedging Under GARCH Models

42 Pages Posted: 16 Jun 2016 Last revised: 17 Jun 2016

Maciej Augustyniak

University of Montreal - Department of Mathematics and Statistics

Frédéric Godin

Concordia University; Laval University

Clarence Simard

UQAM

Date Written: June 14, 2016

Abstract

Local and global quadratic hedging are alternatives to delta hedging that more appropriately address the hedging problem in incomplete markets. The objective of this article is to investigate and contrast the effectiveness of these strategies under GARCH models, both experimentally and empirically. Our analysis centers on three important practical issues: (i) the value added of global over local quadratic hedging, (ii) the importance of the choice of measure (real-world or risk-neutral) when implementing quadratic hedging, and (iii) the robustness of quadratic hedging to model mis-specification. We find that a global approach to quadratic hedging significantly reduces the risk of hedging derivatives with long-term maturities (one year or more), provided that it is implemented under the real-world probability measure. Global quadratic hedging should therefore be advocated when hedging LEAPS and other long-term derivatives such as market-linked certificates of deposit.

Keywords: risk-minimization, quadratic hedging, variance-optimal hedging, mean-variance hedging, GARCH, model risk, LEAPS, dynamic programming

JEL Classification: C22, C61, G32

Suggested Citation

Augustyniak, Maciej and Godin, Frédéric and Simard, Clarence, Assessing the Effectiveness of Local and Global Quadratic Hedging Under GARCH Models (June 14, 2016). Available at SSRN: https://ssrn.com/abstract=2795785

Maciej Augustyniak (Contact Author)

University of Montreal - Department of Mathematics and Statistics ( email )

C.P. 6128, succursale Centre-ville
Montreal, Quebec H3C 3J7
Canada

HOME PAGE: http://dms.umontreal.ca/

Frédéric Godin

Concordia University ( email )

1455 De Maisonneuve Blvd. W.
Montreal, Quebec H3G 1M8
Canada

Laval University ( email )

2214 Pavillon J-A. DeSeve
Quebec, Quebec G1K 7P4
Canada

Clarence Simard

UQAM ( email )

Montreal, Québec H3C 3P8
Canada

HOME PAGE: http://www.uqam.ca

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