NO.PZ201702190300000308
问题如下:
Based on Exhibit 2 and the parameters used by Sousa, the value of the interest rate option is closest to:
选项:
A.5,251.
B.6,236.
C.6,429.
解释:
C is correct.
Using the expectations approach, per 1 of notional value, the values of the call option at Time Step 2 are
c++ = Max(0,5++ - X) = Max(0,0.050 - 0.0275) = 0.0225.
c+- = Max(0,5+- - X) = Max(0,0.030 - 0.0275) = 0.0025.
c-- = Max(0,5- - - X) = Max(0,0.010 - 0.0275) = 0.
At Time Step 1, the call values are
c+ = PV[nc++ + (1 - π)c+-].
c+= 0.961538[0.50(0.0225) + (1 - 0.50)(0.0025)] = 0.012019.
c- = PV[nc+- + (1 - π)c--].
c- = 0.980392[0.50(0.0025) + (1 - 0.50)(0)] = 0.001225.
At Time Step 0, the call option value is
c = PV[πc+ + (1 - π)c-].
c = 0.970874[0.50(0.012019) + (1 - 0.50)(0.001225)] = 0.006429.
The value of the call option is this amount multiplied by the notional value, or 0.006429 x 1,000,000 = 6,429.
中文解析:
本题考察的是利率二叉树,需要注意两点:一是利率二叉树下向上和向下的概率是已知且确定的,都为0.5;二是在折现的时候要注意使用的是节点利率,例如把c++ c+-向前折现求c+时,注意应该使用的是iu。
我看这道大题前面计算european和american option的时候,例如p++ = Max(0,X - u2S) = Max[0,40 - 1.3002(38)] = Max(0,40 - 64.22) = 0.
都乘以的是probability的平方,想问下计算Interest rate option为什么在t=2时刻也只是乘以0.5,而不是0.5^2