Use the fact that the pseudo-probability of default at time zero is (1 / 2)to answer the questions that follow.
-Consider a caplet with maturity time 1 and strike price 0.035.What is the time 0 value of the caplet?

Question

Use the fact that the pseudo-probability of default at time zero is (1 / 2)to answer the questions that follow. 
-Consider a caplet with maturity time 1 and strike price 0.035.What is the time 0 value of the caplet?

Quizplus · Accepted Answer

The time 0 value of the caplet is calculated as the expected payoff at maturity, discounted at time zero. 
If the counterparty does not default, the payoff is max(0, L-K) = max(0, 1 - 0.035) = 0.965. 
If the counterparty does default, the payoff is 0. 
Therefore, the expected payoff is (1/2)*0.965 + (1/2)*0 = 0.4825. 
Discounting this value at time zero using a risk-free rate of 0 gives: 
0.4825*exp(-0*1) = 0.4825. 
Therefore, the time 0 value of the caplet is $0.003198 (option C).

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