CHAPTER 7: HEDGE PARAMETERS and COMPARATIVE STATICS
7.1
Overview

he BlackScholes 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 riskfree 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 BlackScholes
model. (To see this, look at the
option value on the Yaxis, and then select one variable for the Xaxis.
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.