## S E

d1 d2

Rf = 4% per year, continuously compounded d1 = .60 d2 = .30 t = 9 months

Based on this information, what is the value of the call option, C?

To answer, we need to determine N(d1) and N(d2). In Table 24.3, we first find the row corresponding to a d of .60. The corresponding probability N(d) is .7258, so this is N(d1). For d2, the associated probability N(d2) is .6179. Using the Black-Scholes OPM, we calculate that the value of the call option is:

C = S X N(d1) - E X e-Rt X N(d2) = \$100 X .7258 - \$90 X e- 04(3/4) X .6179 = \$18.61

Notice that t, the time to expiration, is 9 months, which is 9/12 = 3/4 of one year.

As this example illustrates, if we are given values for d1 and d2 (and the table), then using the Black-Scholes model is not difficult. Generally, however, we would not be given the values of d1 and d2, and we must calculate them. This requires a little extra effort. The values for d1 and d2 for the Black-Scholes OPM are given by:

In these expressions, ct is the standard deviation of the rate of return on the underlying asset. Also, ln(S/E) is the natural logarithm of the current stock price divided by the exercise price.

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

VIII. Topics in Corporate Finance

24. Option Valuation

© The McGraw-Hill Companies, 2002

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