## Question 1

Swap代写 Let be a set of dates, on which payments of the floating leg of an interest rate swap occur. The payoff of the floating leg of the swap at time

Let  be a set of dates, on which payments of the floating leg of an interest rate swap occur. The payoff of the floating leg of the swap at time  is  where  is the reference rate of the floating leg and s is a constant spread. For simplicity, assume that the floating and fixed payments happen on the same dates. Also,  is the risk-free rate on the same tenor. Let N be the notional of the swap.

1) what is the fixed semiannual swap rate calculated from the risk-free rates? Please specify mathematical formula (no need for exact numerical result at the point).

2) Let the semiannual swap rate calculated in 1) be the fixed leg payment of the swap. What is the constant spread s which sets the present value of the swap position to be zero? Please specify mathematical formula (no need for exact numerical result at this point).Swap代写

Sol: 1) as  is spot rate of risk-free rate. based on two simultaneous bond positions, let’s donate the fixed semimanual swap rate by c.

At inception of the swap, it is convention to select the fixed payment, so that .

Then we can get,

2) at the inception of the swap, the value of the swap

What means,

Then we can get,

### Question 2 Swap代写

The risk-free curve and reference curve data can be found in the Excel file. Let’s support the analysis date is 12 June 2013 and both fixed and floating payment happens semiannually, with the first payment date half year from analysis date. The swap notional equals to USD 100,000, the maturity of the swap is 5 years, and the swap currency is USD.

1) the answer for the first two questions based on the input data given in the attached Excel file.

2) the PV of the swap position on 12 August 2013. Swap代写

3) the PV of the swap position on 12 February 2014.

Sol: 1) the semiannual swap rate is: 0.0072847;

2) the value of IRS on 12 August 2013 is: 3025.5464

3) the value of IRS on 12 February 2014 is: 3047.2092