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7.1  Overview


he Black-Scholes model gives us formulas for the European call and put options.  Besides letting you determine the prices of options, the model is extremely useful in measuring the risk of a stock or option position.  In fact, it provides a precise way to measure the exposure of a position to different variables.  This makes it easy to hedge a position's exposure to these variables.

The variables that affect the value of an option are the price of the underlying stock, the volatility, the risk-free interest rate, the strike price, and the time to maturity.  (When we extend the model to options on currencies, you will find that another variable affects option prices.) 

Online, in the subject Option Sensitivities, you can see how these variables affect the price of an option in the Black-Scholes model.  (To see this, look at the option value on the Y-axis, and then select one variable for the X-axis.  The graph shows you the option price for a range of values of the selected variable.)  The mathematics underlying this analysis are covered here in the next topic Comparative Statics.