Question

If, in today’s respective markets for one month , three-month and six-month mortgage coupon payments, trading determines a market price of ninety-nine and one-half ($99.50) dollars per one hundred dollars of coupon payment receivable in one month, ninety-eight and one-fourth ($98.25) dollars today per one hundred dollars ($100.00) of coupon payment receivable in three months, and ninety-seven and one-fourth ($97.25) dollars per one hundred dollars ($100.00) of coupon payment receivable in six months.

a). calculate respective net and gross values of the current market rates of interest and discount on these one-, three-, and six-month coupon payments
b). state definitions of the respective market values of the interest rate and the discount rate, in the case of the six-month coupon.
c). for the same six-month coupon, which respective cash flow is being valued and which is being used to measure this value (ie. the unit of measure) in the calculation of its market interest rate
d). Do the same as in part c for this problem for the market discount rate determined by this same six-month coupon

Answer 1

The net and gross values of the market rates of interest and discount for one-, three-, and six-month mortgage coupon payments are calculated. The market value of the interest rate and discount rate for the six-month coupon is provided, along with the respective cash flow being valued. The unit of measure used to calculate the market interest rate and discount rate is also identified.

Step-by-step explanation:

a) The net values of the current market rates of interest and discount for the respective one-, three-, and six-month mortgage coupon payments are:

• One-month: $99.50 - $100 = -$0.50 (discount)
• Three-month: $98.25 - $100 = -$1.75 (discount)
• Six-month: $97.25 - $100 = -$2.75 (discount)

The gross values can be calculated by subtracting the discount from 100, as follows:

• One-month: 100 - (-0.50) = 100.50%
• Three-month: 100 - (-1.75) = 101.75%
• Six-month: 100 - (-2.75) = 102.75%

b) The market value of the interest rate for the six-month coupon is 97.25%.

c) The respective cash flow being valued for the six-month coupon is the coupon payment receivable in six months, which is $100. The unit of measure used to calculate the market interest rate is the market price of $97.25 per $100 of coupon payment receivable in six months.

d) For the market discount rate determined by the same six-month coupon, the respective cash flow being valued is the present value of $100, and the unit of measure used to calculate the market discount rate is the market price of $97.25 per $100 of coupon payment receivable in six months.