Suppose that there is an ideal bank offering effective spot rates R.(.5) 2.5%, R.(1) = 3.5%,...

 

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Suppose that there is an ideal bank offering effective spot rates R.(.5) 2.5%, R.(1) = 3.5%, R. (1.5)=4%, and R. (2) = 4.25%,.. (a) Find the swap rate q[2] for an interest rate swap with maturity T = 2 with two swap dates per year (i.e. the counter parties make payments twice per year). (b) Suppose that you have agreed to act as the counter party in an interest rate swap with a client. The client will receive the fixed payments, so you are paying fixed. Under the contract, there will be two swap dates per year for two years. The notional face value of the contract is F = $10,000. Describe the payments you will make or receive. Use p[2] to refer to the spot rate (under the semiannual compounding convention) for deposits/loans between times and (c) Explain how you can hedge the risk of your position using a float note and a coupon bond with coupon rate equal to the swap rate. (d) As it turns out, there are no coupon bonds trading with coupon rate equal to the swap rate. There is a coupon bond with face value $1000, maturity 2 years, making two coupon payments per year at the coupon rate q[2] = .05. The price of this bond is P = $1015.55. 1 Explain how you can hedge your risk using this bond, an appropriate float note and an investment with the ideal bank. Suppose that there is an ideal bank offering effective spot rates R.(.5) 2.5%, R.(1) = 3.5%, R. (1.5)=4%, and R. (2) = 4.25%,.. (a) Find the swap rate q[2] for an interest rate swap with maturity T = 2 with two swap dates per year (i.e. the counter parties make payments twice per year). (b) Suppose that you have agreed to act as the counter party in an interest rate swap with a client. The client will receive the fixed payments, so you are paying fixed. Under the contract, there will be two swap dates per year for two years. The notional face value of the contract is F = $10,000. Describe the payments you will make or receive. Use p[2] to refer to the spot rate (under the semiannual compounding convention) for deposits/loans between times and (c) Explain how you can hedge the risk of your position using a float note and a coupon bond with coupon rate equal to the swap rate. (d) As it turns out, there are no coupon bonds trading with coupon rate equal to the swap rate. There is a coupon bond with face value $1000, maturity 2 years, making two coupon payments per year at the coupon rate q[2] = .05. The price of this bond is P = $1015.55. 1 Explain how you can hedge your risk using this bond, an appropriate float note and an investment with the ideal bank.