Hello I would like to know how we obtain 11.044% (the calculation)?

Best regards,

Baptiste

Example 7.3 Consider again the situation in Example 7.2. Under the terms of the swap, financial institution has agreed to pay 6-month LIBOR and receive 8% per annui (with semiannual compounding) on a notional principal of $100 million. The swa has a remaining life of 1.25 years. The LIBOR rates with continuous compound ing for 3-month, 9-month, and 15-month maturities are 10%, 10.5%, and 11% respectively. The 6-month LIBOR rate at the last payment date was 10.2% (wit semiannual compounding). The calculations are summarized in Table 7.6. The first row of the table shows th cash flows that will be exchanged in 3 months. These have already been determine The fixed rate of 8% will lead to a cash inflow of 100 x 0.08 x 0.5 floating rate of 10.2% (which was set 3 months ago) will lead to a cash outflow 100 x 0.102 x 0.5 = $5.1 million. The second row of the table shows the cash flow 163 Table 7.6 Valuing swap in terms of FRAs ($ millions). Floating cash flows are calculated by assuming that forward rates will be realized. Time Fixed Floating Net Discount Present value cash flow cash flow cash flow factor of net cash flow 0.25 -5.100 -1.100 0.9753 -1.073 0.75 -5.522 -1.522 0.9243 -1.407 1.25 -6.051 -2.051 0.8715 -1.787 Total: -4.267 that will be exchanged in 9 months assuming that forward rates are realized. The cash inflow is $4.0 million as before. To calculate the cash outflow, we must first calculate the forward rate corresponding to the period between 3 and 9 months. From equation (4.5), this is 0.105 x 0.75 -0.10 x 0.250 1075 0.5 or 10.75% with continuous compounding. From equation (4.4), the forward rate becomes 11.044% with semiannual compounding. The cash outflow is therefore 100 x 0.11044 x 0.5 = $5.522 million. The third row similarly shows the cash flows that will be exchanged in 15 months assuming that forward rates are realized. The discount factors for the three payment dates are, respectively, -0.160.25 -0.105x0.75 -0.16x1.25