USING THE BLACK-SCHOLES FORMULA TO VALUE OF SOME SIMPLE OPTIONS

Last Edit: Sept 2003

GOAL: Develop a working understanding of options valuation calculations.

NOTE:** **A spreadsheet that
calculates the value of European calls and puts using the Black-Scholes**
**model

is available on the website, under the Course Materials, Spreadsheets
link (
option_pricing_models.xls
).

The file also includes a set of spreadsheets allowing you to calculate
the value of different options using

the Binomial model. These spreadsheets will not be used until *Part
5* , but you can always compare the

results given by the two models if you are interested.

ACTION: Use the Black-Scholes
based spreadsheet to calculate the value of a European call option with

a strike price of $25, 2 years before expiration, a risk-free rate of
interest of 5%, current stock prices

ranging between $5 to $50 (in $5 increments), and volatilities ranging
between 20% and 60% (in 20% increments).

Create a graph of call option value versus stock price for varying volatility.
Include the immediate exercise

value of the option on the graph (e.g. Max [0, S-K]).

Perform a similar calculation for a European put option.

Create a graph using the put data that is similar to that developed
for the call option case. Note that the

immediate exercise value for the put is Max [0, K-S].

The spreadsheet model (
option_pricing_models.xls
or
option_pricing_models.wk1
) also contains some actual

quotes for call and put options on Netscape stock, which pays no dividends
(Source: October 30, 1997 *Wall Street Journal* ).

Information provided includes the current stock price, the time until
the options expire, the strike price of each option,

and the price for calls and puts. Assuming a risk free rate of interest
of 5%, use the data and the spreadsheet model

to estimate the implied volatility of these options.