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
折现的时候都是用期初利率去折现吗?例如在从9.2利率的时候折回8.6的时候,我用的是1.092/2去折现,但是答案用的是1.86/2去折现,为什么我那种算法不对