1.If in todays respective markets for one month, three month and six month mortgage coupon payments trading determines a market price of $99.50 per $100 of coupon payment receivable in one month. $98.25 today per $100 of coupon receivable in three months and $97.25 per $100 of coupon payment receivable in six months.

a) calculate the respective net and gross values of the current market rates of interest and discount on these one, three and six month coupon payments.

b) Using english only, state the definitions of the respective market values of the interest rate and the discount rate, in the case of the six month coupon.

c) Using english only, state for this same six month coupon, which respective cash flow is being valued and which is being used to measure this value( unit of measure) in the calculation of its market interest rate.

d) do the same as in part c of this problem for the market discount rate determined by this same six month coupon.

2.Consider again these same three markets with todays market values of their respective prices. A mortgage lender has just originated a twenty year, interest only Canadian mortgage with a balance of $500,000 and an announced annual mortgage coupon rate of 6%. He offers to sell either you or your classmate, today, a security composed of a single three month coupon plus a single six month coupon, each of which could alternatively be traded on an individual basis in these markets.

a) what should you offer to pay for this security today?

b) what would your classmate offer to pay for this same security if he used the announced annual coupon rate of 6% to calculate its present discounted value?

c) to whom would the lender sell the security?

d) if youre classmate buys the security at the price he calculates for its present discounted value, how much does he gain or lose( in dollars today) relative to what he would have paid by using the market prices in the three and six coupon markets above?

e) since you can trade in todays markets for three and six month coupons, you decide you can make an arbitrage profit from your classmates purchase by offering to trade each of the three and six month coupon payments composing the security he now owns. Assuming you and he limit your trading to just one coupon of each maturity, determine (i) how much of a profit you could make and (ii) whether you buy or sell the three month coupon you trade with him and analogously, whether you buy or sell the six month coupon you trade with him.

3.Three mortgage based securities are up for auction today in riskless, arbitrage free markets, by bond traders in toronto. the first is a single one year $5000 mortgage coupon and the second a single $7000 two year mortgage coupon payment, each sold off of interest only canadian residential mortgages of twenty years maturity. The third security consists of two coupon payments, with the first coupon paying in one year and the second in two years, each being taken from and interest only canadian residential morgage. This mortgage is also of twenty year maturity and has an announced annual coupon rate of 8% and an initial balance of $1,000,000. Unfortunately no one has yet bid for the second scurity, and consequently it does not yet have a market price, nor can corresponding market interest rate for two year coupons be directly observed. Your supervisor, who is known as someone whose trading acuity canot be underestimated, whishes howeever to bid on this second security and assigns you to estimate its market(no arbitrage) price so he should know what to bid for it. Assuming the first security( the single one year coupon) sells today for $98.80 per $100 of face value and the third security is selling today for $12,824.5541, then based on these observed sales, infer the following:

a) the respective market rates of interest and discount

b) the current market(no arbitrage) price of the second security