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The Black-Scholes option pricing model (1973) can be intimidating for the novice. By rearranging and combining some of the variables, one can reduce the number of parameters in the valuation problem from five to two: 1) the option's moneyness ratio and 2) its time-adjusted volatility. This allows the computationally complex Black-Scholes formula to be collapsed into an easy-to-use table similar to those in some popular textbooks. The tabular approach provides an excellent tool for building intuition about the comparative statics in the Black-Scholes equation. Further, the pricing table can be used to price options on dividend-paying stocks, commodities, foreign exchange contracts, futures contracts, and exchanges of assets, and can be inverted to generate implied volatility. Formulas for reproducing the tables in Excel are included. [JEL: GIO, GI3]
*Although three decades old, the option pricing model of Black and Scholes (1973) defines many aspects of option pricing today. With the explosion in financial derivatives and risk management contracts, the development of real option analysis, and the growing popularity of options in compensation packages, many more people (and a more diverse population) need to understand the Black-Scholes model. Cox and Rubinstein (1985) show how to create a simple two-dimensional table for easy calculation of BlackScholes European call values.' Armed with this table and a basic calculator, we need only three simple calculations to price any European call option. The pricing tables that were once quite popular have been superceded by inexpensive personal computers that can use spreadsheet programs to evaluate the necessary components of the Black-Scholes model (e.g., the cumulative normal distribution function).2
Our purpose is to show that the option pricing tables described in Cox and Rubinstein (1985) still have tremendous pedagogical value. First, we show how we can use the tables to help students build intuition about the comparative statics of the Black-Scholes model (i.e., the "greeks") without reference to partial derivatives. Second, we demonstrate that the tables can be used to easily price a wide variety of options beyond plain vanilla calls: options on dividend-paying stocks, commodities, foreign exchange, futures, and asset exchanges; put options can also be priced either by put-call parity or by a similar table. Third, we present a way to invert the tables so that implied volatilities can...