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

Using the binomial pricing model, we can calculate the possible interest rate outcomes over three years:

- If interest rates increase by 1% in year 1: the cap would be exercised and the bank would pay out $300,000 (6% on $5,000,000), while the floor would not be exercised. The bank would receive a net payment of $200,000 ($300,000 from cap payout minus $100,000 from floor premium received).
- If interest rates decrease by 1% in year 1: the cap would not be exercised and the floor would be exercised, resulting in a payment of $250,000 (5% on $5,000,000), while the bank would not pay out anything for the cap. The bank would receive a net payment of $100,000 ($250,000 from floor payout minus $150,000 from cap premium paid).
- If interest rates increase in year 1 and then decrease in year 2: the cap would be exercised in year 1, resulting in a payment of $300,000, but the floor would be exercised in year 2, resulting in a payment of $250,000. The net payment to the bank would be $50,000 ($300,000 from cap payout minus $250,000 from floor payout).
- If interest rates decrease in year 1 and then increase in year 2: the floor would be exercised in year 1, resulting in a payment of $250,000, but the cap would not be exercised in year 2. The net payment to the bank would be $100,000 ($250,000 from floor payout minus $150,000 from cap premium paid).

Based on these outcomes, we can calculate the expected net payment to the bank:

(0.5 x $200,000) + (0.5 x $100,000) + (0.25 x $50,000) + (0.25 x $100,000) = $162,500

Therefore, the net price of the collar should be $162,500. Since the bank is selling the floor and buying the cap, the net payment should be negative, meaning the bank will pay a net amount of $162,500 - $194,151 = -$31,651. Therefore, the correct answer is C.

Assume a Binomial Pricing Model Where There Is an Equal