Problem

JetBlue Airways does not pay dividends. Using the data in Table 21.1, compare the price on July 24, 2009, for the December 2009 American call option on JetBlue with a strike price of $6 to the price predicted by the Black-Scholes formula. Assume that the volatility of JetBlue is 65% per year and that the risk-free rate of interest is 1% per year.

Solution

We use $5.03 (the closing price) for the per-share price of JetBlue stock. Because the December contract expires on the Saturday following the third Friday of December (December 19), there are 148 days left until expiration. The present value of the strike price is PV(K) = 6.00/(1.01)148/365 = $5.976. Calculating d1 and d2 from Eq. 21.8 gives

d1=In[S/PV(K)]T+T2=In(5.03/5.976)0.65148365+0.651483652=0.209

d2=d1T=0.2090.65148365=0.623

Substituting d1 and d2 into the Black-Scholes formula given by Eq. 21.7 results in

C=SN(d1)PV(K)N(d2)=5.030.4170.267=$0.50 (Berk 748)

Looking at the above example I am trying to figure out how the 5.03 x 0.417 x 0.267 was calculated. What is the value of N(d1) and N(d2) if d1 is 0.209 and d2 is 0.623. I'm just trying find out how N(d1)-PV(K) calculated to 0.417 and how N(d2) calculated to 0.267.