请问这里的n就是πu吧？PV=1/(1+rf）？

问题如下：

The value of the Alpha Company call option is closest to:

选项：

A.

3.71.

B.

5.71.

C.

6.19.

解释：

A is correct.

The call option can be estimated using the no-arbitrage approach or the expectations approach. With the no-arbitrage approach, the value of the call option is

c = hS + PV(-hS^- + c^-).

h = (c⁺ - c^-)/(S⁺ - S^-) = (6 - 0)/(56 - 46) = 0.60.

c = (0.60 x 50) + (1/1.05) x [(-0.60 x 46) + 0].

c = 30 - [(1/1.05) x 27.6] = 30 - 26.286 = 3.714.

Using the expectations approach, the risk-free rate is r = 0.05, the up factor is u =S⁺/S = 56/50 = 1.12, and the down factor is d = S^-/S = 46/50 = 0.92. The value of the call option is

c = PV x [nc⁺ + (1 - n)c^-].

π= [FV(1) - d]/(u - d) = (1.05 - 0.92)/(1.12 - 0.92) = 0.65.

c = (1/1.05) x [0.65(6) + (1 - 0.65)(0)] = (1/1.05)(3.9) = 3.714.

Both approaches are logically consistent and yield identical values.

中文解析：

本题考察的是c₀ 的计算，两种方法都可以得到答案。但是建议使用预期法，即先求得c⁺ 和c^- ，然后按照π_u 和π_d 加权平均后折现到0时刻即可。