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 55000.00 mortgage coupon and the second a single $7000.00 two-year mortgage coupon payment, each sold off of interest-only Canadian residential mort- gages 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 an interest-only Cana- dian residential mortgage. This mortgage is also of twenty years maturity and has an announced annual coupon rate of 8.00% and an initial balance Bo of 81,000,000.00. Unfortunately, no one has yet bid for the second security, 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 knowt as some one whose trading acuity cannot be underestimated, wishes however 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 898.80 per one hundred dollars 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 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 55000.00 mortgage coupon and the second a single $7000.00 two-year mortgage coupon payment, each sold off of interest-only Canadian residential mort- gages 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 an interest-only Cana- dian residential mortgage. This mortgage is also of twenty years maturity and has an announced annual coupon rate of 8.00% and an initial balance Bo of 81,000,000.00. Unfortunately, no one has yet bid for the second security, 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 knowt as some one whose trading acuity cannot be underestimated, wishes however 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 898.80 per one hundred dollars 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
