Y9

Consider the floating leg of a vanilla interest rate swap with notional principal F. Suppose the swap is settled every years, the previous -year BBSW rate was r , the current -year BBSW rate is r, and the fraction of the current settlement period remaining is w, ie. w = dTN /dPN . (i) Show that the value of the floating leg of the swap is Pf lo = F(1 + r ) (1 + r) w assuming that on any settlement date, the value of the floating leg of the swap is equal to the notional principal F. (ii) By substituting the above formula into the expression for modified duration Dmod = 1 P P r show that the modified duration of the floating leg of the swap is Dmod = w (1 + r)