Assume a binomial pricing model where there is an equal probability of interest rates increasing or decreasing 1 percent per year.
-What should be the net price of a $5,000,000 collar if the bank purchases a three-year 6 percent cap and sells a 5 percent floor, if the current (spot) rates are 6 percent?
A)The bank will receive net $2,010.
B)The bank will receive net $31,651.
C)The bank will pay net $31,651.
D)The bank will pay net $2,010.
E)price = $0

Question

Quizplus · Accepted Answer

First, we need to calculate the payoff for the cap and floor at each possible interest rate scenario over the three-year period:

- Scenario 1: Interest rates increase to 7%, 8%, and 9%: 
     - Cap payoff: $5,000,000 x (7% - 6%) x 3 years = $150,000
     - Floor payoff: $5,000,000 x (5% - 9%) x 3 years = -$600,000

- Scenario 2: Interest rates decrease to 5%, 4%, and 3%: 
     - Cap payoff: $0 (because interest rates do not exceed the cap rate of 6%)
     - Floor payoff: $0 (because interest rates do not fall below the floor rate of 5%)

The net payoff for the collar is the sum of the cap and floor payoffs in each scenario, multiplied by their respective probabilities. Since there is an equal probability of interest rates increasing or decreasing, each scenario has a probability of 0.5. Therefore, the net payoff for the collar is:

Net payoff = [0.5 x ($150,000 - $600,000)] + [0.5 x ($0 + $0)] 
           = -$225,000

Since the bank is purchasing the cap and selling the floor, the net price of the collar is the negative of the net payoff, which is $225,000. Therefore, the bank will pay a net price of $225,000 for the collar, which corresponds to answer choice C.

Assume a Binomial Pricing Model Where There Is an Equal