256 CHAPTER 7. THE BLACK-SCHOLES MODEL
Problems to Work for Understanding
- Suppose that the observations on a security price (in dollars) at the end
of each of 15 consecutive weeks are as follows: 30.25, 32, 31.125, 30.25,
30.375, 30.625, 33, 32.875, 33, 33.5, 33.5 33.75, 33.5, 33.25. Estimate
the security price volatility. - A call option on a non-dividend paying security has a market price of
$2.50. The security price is $15, the exercise price is $13, the time to
maturity is 3 months, and the risk-free interest rate is 5% per year.
What is the implied volatility?
Outside Readings and Links:
- Peter Hoadley, Options Strategy Analysis Tools has a Historic Volatility
Calculator that calculates and graphs historic volatility using historical
price data retrieved from Yahoo.com. Submitted by Bashar Al-Salim,
Dec. 2, 2003. - Analysis of asset allocation A calculator to compute implied volatility
using Black and Scholes. Submitted by Bashar Al-Salim, Dec. 2, 2003. - MindXpansion,a Tool for Option Traders This option calculator pack-
ages an enormous amount of functionality onto one screen, calculating
implied volatility or historical volatility with Midas Touch. Submitted
by Chun Fan, Dec. 3, 2003.
7.6 Sensitivity, Hedging and the “Greeks”
Rating
Mathematically Mature: may contain mathematics beyond calculus with
proofs.
Section Starter Question
Key Concepts
- The sensitivity of the Black-Scholes formula to each of the variables
and parameters is named, is fairly easily expressed, and has important