252 CHAPTER 7. THE BLACK-SCHOLES MODEL
Outside Readings and Links:
- Bradley University, School of Business Administration, Finance De-
partment, Kevin Rubash A very brief description on the development
history of option theory and the Black-Scholes model for calculating
option value, with the notations, Greeks and some explanatory graphs.
Also contains a calculators for the option value calculation. Submitted
by Yogesh Makkar, November 19, 2003.
7.5 Implied Volatility
Rating
Mathematically Mature: may contain mathematics beyond calculus with
proofs.
Section Starter Question
What are some methods you could use to find the solution off(x) =cforx
wherefis a function that is so complicated that you cannot use elementary
functions and operations to isolatex?
Key Concepts
- We estimate historical volatility by applying the standard deviation
estimator from statistics to the observations ln(Si/Si− 1 ). - We deduce implied volatility by numerically solving the Black-Scholes
formula forσ.
Vocabulary
- Historical volatilityof a security is the variance of the changes in
the logarithm of the price of the underlying asset, obtained from past
data. - Implied volatilityof a security is the numerical value of the volatility
parameter that makes the market price of an option equal to the value
from the Black-Scholes formula.