Answer: c) +$710,950

The **pay floating** counterparty is effectively **receiving fixed**, so: \[ \text{Swap value} = PV(\text{fixed leg}) - PV(\text{floating leg}) \] ### 1) Discount factors Flat continuously compounded rate = 4.0%. Remaining cash-flow dates are approximately: - 2 months = \(2/12\) years - 8 months = \(8/12\) years - 14 months = \(14/12\) years So: - \(P(0,2/12)=e^{-0.04\cdot 2/12}\approx 0.993356\) - \(P(0,8/12)=e^{-0.04\cdot 8/12}\approx 0.973686\) - \(P(0,14/12)=e^{-0.04\cdot 14/12}\approx 0.954084\) ### 2) Fixed leg A 5.0% fixed rate with semiannual compounding gives a 6-month coupon of: \[ 50,000,000 \times 0.05 \times 0.5 = 1.25\text{ million} \] With three remaining payment dates, the fixed-leg PV is approximately: \[ PV_{fixed} = 1.25P_1 + 1.25P_2 + 51.25P_3 \] \[ PV_{fixed} \approx 1.25(0.993356) + 1.25(0.973686) + 51.25(0.954084) \approx 51.35\text{ million} \] ### 3) Floating leg The next floating coupon was set four months ago at 4.0%, so the next coupon is: \[ 50,000,000 \times 0.04 \times 0.5 = 1.0\text{ million} \] With the curve flat at 4.0%, the following floating coupons are also effectively priced at 4.0%: \[ PV_{float} \approx 1.0P_1 + 1.0P_2 + 51.0P_3 \approx 50.63\text{ million} \] ### 4) Swap value \[ V = PV_{fixed} - PV_{float} \approx 0.71\text{ million} \] So the value to the pay-floating counterparty is positive, about **$710,950**.

Author: Manit Arora