In chapter 3 of the course, the notes suggest that you dont swap the principal in an interest rate swap. In chapter 11, valuation of a swap, the value is found by comparing the value of a bond (fixed) with the principal (which is tailored to represent the floating side). Both of these legs include the principal - are we just valuing exchange of the principal twice here to make the calculations easier - i.e use tools that we have to hand, or am i missing something a bit subtle?
You're correct in your conclusion. We value the principle in order to make the calculation easier. The principal is not swapped in practice as it would be a trivial process. It makes the calc easier in that if you include the redemption of capital with floating rate interest payments, you have all the components of a floating rate bond. Given the simplistic circumstances in the example, the value of the floating rate bond is equal to par value - no calculations required. This can then be compared with the fixed rate bond to get the value of the swap, which is really just the difference in the value of the coupon payments. You should take care when the circumstances are not simplified, i.e. if the floating rate payment is anything other than 1 year away or if the floating rate payment is not based on the discount rate applying over the period. In such cases, the floating rate bond will not be trivially equal to par - although you should be able to determine relatively easily what the value is. Best of luck.
Yes, the value of any floating rate bond is equal to its par value at the outset and also immediately after each coupon payment (at which point in time the remaining payments can be considered to represent a brand new floating rate bond). At other points in time, you need to use the argument outlined near the top of page 21 of Chapter 11 of the Course Notes. Here it suggests that the value of the floating rate bond is equal to the sum of the par value plus the next coupon, both discounted back to the valuation date using the appropriate spot yield.
