A Profitable Modification to Global Quadratic Hedging

Abstract

Recent research has shown that global quadratic hedging, also known as variance-optimal hedging and mean-variance hedging, can significantly reduce the risk of hedging call and put options with long-term maturities (one year or more), such as Long-Term Equity AnticiPation Securities (LEAPS). We propose a modification to global quadratic hedging that is more profitable on average to the hedger without substantially increasing his downside hedging risk, if at all. We prove mathematically that the expected terminal hedging gain of our modified strategy is greater than that of the global quadratic hedging strategy. The performance of our strategy is evaluated under simulated return paths from GARCH and regime-switching models, and under empirical S&P 500 return paths.

Keywords: Risk Management, Variance-Optimal Hedging, Mean-Variance Hedging, Global Risk-Minimization, LEAPS

JEL Classification: C22, C61, G32