244 CHAPTER 7. THE BLACK-SCHOLES MODEL
Sources
This section is adapted from: Financial Derivatives by Robert W. Kolb,
New York Institute of Finance, Englewood Cliffs, NJ, 1993, page 107 and
following. Parts are also adapted fromStochastic Calculus and Financial
Applicationsby J. Michael Steele, Springer, New York, 2000, page 155.
Problems to Work for Understanding
- Calculate the price of a 3-month European put option on a non-dividend-
paying stock with a strike price of $50 when the current stock price is
$50, the risk-free interest rate is 10% per annum (compounded contin-
uously) and the volatility is 30% per annum. - What is the price of a European put option on a non-dividend paying
stock when the stock price is $69, the strike price is $70, the risk-
free interest rate is 5% per annum (compounded continuously), the
volatility is 35% per annum, and the time to maturity is 6 months?
Outside Readings and Links:
- Video with explanation of put-call parity.
- Option Research and Technology Services Provides important option
trading terms and jargon, here is the link to definition of “Put-Call
Parity”.
7.4 Derivation of the Black-Scholes Equation
Rating
Mathematically Mature: may contain mathematics beyond calculus with
proofs.
Section Starter Question
What is the most important idea in the derivation of the binomial option
pricing model?