A company buys a caplet today (time 0)with maturity T = 1 year and a strike rate of k = 3 percent on a notional of L N = $200 million.Suppose the six-month bbalibor rate realized after one year is 4.5 percent.Assume that there are 181 days in this six-month period and the year has 365 days.
-The caplet's payoff after 1.5 years:

Question

Quizplus · Accepted Answer

The caplet's payoff after 1.5 years can be calculated using the formula:

Max[0, L × (F – K) × (T/365)]

where:
L = notional value = $200 million
F = forward rate = 4.5%
K = strike rate = 3%
T = time period = 0.5 years (since the payoff is after 1.5 years, which is 1 year after the caplet is bought at time 0)

Substituting the values, we get:

Max[0, 200,000,000 × (0.045 – 0.03) × (181/365)]

= Max[0, 200,000,000 × 0.015 × 0.49589]

= Max[0, 1,487,670.5]

= $1,487,671 (rounded to the nearest dollar)

Therefore, the correct answer is D) $1,487,671.

A Company Buys a Caplet Today (Time 0)with Maturity T