Use the fact that the pseudo-probability of default at time zero is (1 / 2)to answer the questions that follow.
-Consider a floorlet with maturity time 1 and strike price 0.035.What are the holdings in the three-period bond and money market account at time 0 that replicate the floorlet's time 1 payoffs in both the up and down nodes?

Question

Use the fact that the pseudo-probability of default at time zero is (1 / 2)to answer the questions that follow. 
-Consider a floorlet with maturity time 1 and strike price 0.035.What are the holdings in the three-period bond and money market account at time 0 that replicate the floorlet's time 1 payoffs in both the up and down nodes?

Quizplus · Accepted Answer

The pseudo-probability of default at time zero is (1/2), implying that there is an equal chance for the bond to default or not default.
Given that the floorlet has a strike price of 0.035 at time 1, the replicating portfolio needs to have the same payoffs in both the up and down nodes.
Let F1 be the face value of the bond, and S1 be the bond price at time 1 in the up state. Then, we need to solve for F1 and S1 such that:
F1 + S1 = 1 (since it is a two-period bond)
max(0, 0.035 - S1) = max(0, 0.035 - 0.5(F1 + S1))
Solving these two equations, we get F1 = 0.265 and S1 = 0.239428. 
Therefore, the holdings in the three-period bond and money market account at time 0 that replicate the floorlet's time 1 payoffs in both the up and down nodes are 0.265009 and F1F1F1S1-F1F1F100.239428, respectively.

Use the Fact That the Pseudo-Probability of Default at Time