Many financial institutions hold derivative securities in their portfolios, and frequently these securities need to be hedged for extended periods of time. Failure to hedge properly can expose an institution to sudden swings in the values of derivatives, such as options, resulting from large, unanticipated changes in the levels or volatilities of the underlying asset. Understanding the basic techniques employed for hedging derivative securities and their advantages and pitfalls is therefore of crucial importance. ; This article examines the popular valuation model for options developed by Black and Scholes (1973) and Merton (1973). The model, while elegant from a theoretical perspective, is often fraught with problems when implemented in the real world. Nevertheless, because of its simplicity and tractability, the model is widely used by options traders and investors. ; The authors consider ways that users try to circumvent some of these problems-for example, with certain ad hoc pricing rules. Using the Standard and Poor's 500 index options market, the authors compare the hedging efficacies of various models. Their findings suggest that ad hoc rules do not always result in better hedges than a very simple and internally consistent implementation of the Black-Scholes-Merton model.