Assessing the Effectiveness of Local and Global Quadratic Hedging Under GARCH Models
34 Pages Posted: 16 Jun 2016 Last revised: 26 Oct 2019
Date Written: December 15, 2016
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: Suggested Citation