问题如下：
5.The value of the European-style call option on Beta Company shares is closest to:
选项：
A. 4.83.
B. 5.12.
C. 7.61.
解释：
A is correct.
Using the expectations approach, the risk-neutral probability of an up move is
π= [FV(1) - d]/(u - d) = (1.03 - 0.800)/(1.300 - 0.800) = 0.46.
The terminal value calculations for the exercise values at Time Step 2 are
c++ = Max(0,u2S - X) = Max[0,1.302(38) - 40] = Max(0,24.22) = 24.22.
c-+ = Max(0,udS - X) = Max[0,1.30(0.80)(38) - 40] = Max(0,-0.48) = 0.
c- - = Max(0,d2S - X) = Max[0,0.802(38) - 40] = Max(0,-15.68) = 0.
Discounting back for two years, the value of the call option at Time Step 0 is
c = PV[n2c++ + 2n(1 - n)c-+ + (1 - n)2c--].
c = [1/(1.03)]2[0.462(24.22) + 2(0.46)(0.54)(0) + 0.542(0)].
c = [1/(1.03)]2[5.1250] = 4.8308.
u 与 d,pai u 与pai d从概念上要怎么理解，常常搞错