NO.PZ2020033001000092
问题如下：
A CMT (Constant Maturity Treasury) swap has a payoff of ($50,000/2) x ( - 8%) every six months. Binomial tree is constructed with initial of 8%. In the next 6 months, interest rate would either have a 60% probability of increasing to 8.6% or decrease to 7.4%. If the interest rate raises, it would have a 50% probability of increasing to 9.2% or decrease to 8% in the after 6 months. If the interest rate drops, it would have a 50% probability of increasing to 8% or decrease to 6.8% in the after 6 months. What is the value of this CMT swap?
选项：
A.$56.18
B.$27.34
C.$28.58
D.$0
解释：
A is correct.
考点：Binomial tree
解析：
在第二个6月，Ycmt有三种可能：9.2%，8.0%，6.8%。
当利率为9.2%， Price=50,000/2*(9.2%-8.0%)=300
当利率为8.0%， Price=50,000/2*(8.0%-8.0%)=0
当利率为6.8%，Price=50,000/2*(6.8%-8.0%)=-300.
接下来再计算第一个6月的价格，此时Ycmt有两种可能：8.6%，7.4%。
当利率为8.6%， Price=50,000/2*(8.6%-8.0%)+(300*0.5+0*0.5)/(1+8.6%/2)=293.82
当利率为7.4%， Price=50,000/2*(7.4%-8.0%)+(0*0.5-300*0.5)/(1+7.4%/2)=-294.65
最后计算CMT swap value=(293.82*0.6-294.65*0.4)/(1+8.0%/2)=56.18
因此选A
第一步明白，然后去到第二步，不明白为什么要用1+8.6%/2的利率来折算，为什么不用8.6%-8%利率来折算？
