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
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 (
) 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.