Valuation of Variable-rate

Valuation of Variable-rate commitments Well, here we see a problem. If today is July 20, 2008, the commitment variable rate of the first period, which in our example we have to pay on 20 January 2009, is known as the 6-month Euribor rate in date today. But how do we value the commitment to pay the Euribor 6 months to be on 20 January 2009, payable on July 20, 2009, if you know now what will Nor do we know what are the successive 6-month Euribor rates to be fixed over the life of the contract. How do we do then to find the economic value (NPV) of the commitments of the variable leg Again an arbitration analysis will allow us to find a solution and find the formula we need. Suppose that the commitment of the leg is variable payment thereof.Thus, in our example, if we are the counterpart B we make the necessary financial transactions to pay the Euribor 6 months of each period, but now know what type to be set. The only way to ensure that we pay the floating rate on the notional lifetime of the contract is to have our hands on a notional amount equal to and reversing every 6 months to 6 months Euribor rate. The interest we receive from our invested capital are enabling us to pay for the commitment of our floating-rate swap agreement. But again, we is another problem we have in our hands the capital. So we ask borrowing this capital as of today and will return the date of expiry. That is the ability to pay the various Euribor futures have an economic cost (VE VA NPV) equal to the cost of borrowing over the life of notional contract.No matter what the rates will be 6 months Euribor future we will be able to pay today if we asked the notional loan swap agreement and return it to the due date. Then the economic value of the commitment of the floating leg is given by the value today of the interest we pay when contracts of notional loan requested. We now need a little math to put these concepts in order. If we now ask for a loan capital N and we have to return at the time v, the capital return Nves: Nv N (1 iv) v and therefore I interest we pay on the due date are: I Nv – N That interest is the economic value to the due date that is committed to pay the Euribor futures. To find the economic value today alone we must apply the formula we used to find the current value of a single fixed rate commitment, ie it will apply the discount factor for interest I.A bit of algebra leads us to find the economic value of the floating commitment (NPV): Although complex seemed just get the economic value of the commitments of the floating leg of the swap. The arbitration again assures us that the value should be because as we have shown in previous sections, any other value would allow a profit without risk.