一個利用等分機率的改良式靜態避險方法

Abstract

This paper further adjusts the static replication method of Derman, Ergenger,and Kani. (1995, DEK) and modi ed DEK method of Chung, Shin, and Tsai. (2010,modi ed DEK) to reduce hedging errors. Chung et al. hedge continuous barrier options under the Black and Scholes (1973) model. In those previous methods, the value of the static replication portfolio, consisting of many options with varying maturities, matches the boundary value of the barrier option at n evenly time-spaced points when the stock price equals to the barrier (and zero theta in modi ed DEK). We need to calculate the rst passage time density under risk-neutral probability measure when we want to derive the fair price of the barrier option (closed-form). The mathching points by using the quantile are more intuitive than those by even space. In the modi ed single PDEK method we construct a portfolio of standard options with uneven maturities (time points) and one binary option at last time point to match the boundary value, and we just match the theta at the last point on the barrier. Our numerical results indicate that the modi ed single PDEK approach improves the performance of static hedges.