In May 1973, Fischer Black and Myron Scholes published their seminal article on option valuation. Because of its complexity, the user of their formula normally relies on a computer or on a set of option value tables. Unfortunately, these methods provide little feeling for the sensitivity of the option value to changes in inputs. How will an option value change if the stock is more volatile than assumed, or if its price falls, or if the exercise price changes? What underlying stock volatility does a known option price imply?
This article presents nomograms for calculating the Black-Scholes value of any option, along with the position in the underlying stock required to hedge it and the probability of exercise. Using the nomograms involves no mathematical calculations—only a pencil and a ruler.
The nomogram method is fast and easy to use. For most traded put and call options, it provides accuracy comparable to that of published option value tables. It is also versatile: It can be used to evaluate stocks paying dividends, short-lived warrants and the value to a corporate issuer of a standby agreement when it makes a rights offering on its common stock.