A Simple Approach to Option Valuation and Hedging in the Black-Scholes Model

Most practitioners use some variant of the Black-Scholes model as the basis for valuing and hedging European-style options. Unfortunately, the model remains somewhat complicated. It can be explained in a simplified manner by neutralizing the effects of the time value of money on the exercise price and focusing on the insurance feature of options. For options whose striking price equals the forward price of the underlying asset, option value is an approximately linear function of volatility. Using this property of linearity, one can obtain surprisingly accurate estimates of option values and risk factors such as hedge ratio, convexity, time decay and volatility sensitivity.