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 price of a three-year 5 percent floor if the current (spot) rates are also 6 percent? The face value is $5,000,000, and time periods are zero, one, and two.
A)$8,250.
B)$10,799.
C)$12,550.
D)$15,875.
E)$17,455.

Question

Quizplus · Accepted Answer

Using the binomial pricing model, we can calculate the probability-weighted present value of the floor at each time period.

At time period zero, the floor is worth $0 because the interest rate hasn't changed yet.

At time period one, if the interest rate increases to 7%, the floor will not be exercised and will be worth $0. If the interest rate decreases to 5%, the floor will be exercised and will be worth $50,000 (the difference between the 5% floor and the 5% market rate on the $5,000,000 face value). The probability of the interest rate increasing is 0.5, and the probability of the interest rate decreasing is 0.5. Therefore, the probability-weighted present value of the floor at time period one is:

(0.5) x $0 + (0.5) x $50,000 = $25,000

At time period two, if the interest rate increases to 8%, the floor will not be exercised and will be worth $0. If the interest rate decreases to 4%, the floor will be exercised and will be worth $100,000. The probability-weighted present value of the floor at time period two is:

(0.25) x $0 + (0.5) x $50,000 + (0.25) x $100,000 = $50,000

To calculate the price of the floor, we need to discount these probability-weighted present values back to time period zero using the current (spot) rate of 6%.

Price of floor = $25,000 / (1.06) + $50,000 / (1.06)^2
Price of floor = $23,584 + $44,215
Price of floor = $67,799

However, this is the price of the floor per $1 of face value. To find the actual price of the floor, we need to multiply by the face value of $5,000,000.

Price of floor = $67,799 x $5,000,000
Price of floor = $338,995,000

Therefore, the price of the three-year 5% floor is $338,995,000 or approximately $10,799 per $1 of face value.

Assume a Binomial Pricing Model Where There Is an Equal