Dynamic Hedging in a Volatile Market

Abstract

In financial markets, errors in option hedging can arise from two sources. First, the option value is a nonlinear function of the underlying; therefore, hedging is instantaneous and hedging with discrete rebalancing gives rise to error. Frequent rebalancing can be impractical due to transaction costs. Second, errors in specifying the model for the underlying price movement (model specification error) can lead to poor hedge performance. In this article, we compare the effectiveness of dynamic hedging using the constant volatility method, the implied volatility method, and the recent volatility function method [3]. We provide evidence that dynamic hedging using the volatility function method [3] produces smaller hedge error. We assume that there are no transaction costs, and both the risk-free interest rate r and the dividend rate q are constant.