Improving and Extending the Wu-Zhu Static Hedge

Abstract

Without considering the underlying risk dynamics and jumps, Wu and Zhu (2016) recently proposed an ingenious approach of hedging options statically with an option portfolio. We improve their scheme in three ways. First, we theoretically make the Wu-Zhu approach more accurate by utilizing the Black-Scholes-Merton dual equation. Second, we propose a better error measure, the so-called “true hedge error,” that takes the initial cost of the hedge into consideration. Finally, we suggest two measures of percentage hedge errors to assess hedge performance more precisely. With extensive simulations under both the Black-Scholes-Merton and Heston models, we show that our proposal significantly improves the hedge performance, especially for in-the-money and at-the-money options. Importantly, we extend Wu-Zhu to options with a payoff of homogeneous of degree one.