Cmon guys give it one more chance Let’s say that two parties enter into a 1-year swap with quarterly fixed payments priced at 6.052%. At initiation, the 90-day LIBOR was 5.5%. 30 days later, we observe the following chart on a $30 million dollar notional 60-day LIBOR – 6.0% 150-day LIBOR – 6.5% 240-day LIBOR – 7.0% 330-day LIBOR – 7.5% What is the value of the swap? Step 1: Calculate the fixed payment at each payment period 6.052% X (90/360) = 1.513% It’s easier to calculate in terms of $1.00. After all, we’re trying to find the net amount Day 90 - $0.01513 Day 180 - $0.01513 Day 270 - $0.01513 Day 360 - $1.01513 Remember the principal is returned in the last payment Step 2: Calculate the present values of the fixed rate payments Now that we’re 30 days in, we need to calculate the discount factors for 60, 150, 240, and 330 days using the new LIBORS In 60 days - Z1 = 1 / 1 + (0.06 * (60/360) = 0.99010 In 150 days - Z2 = 0.97363 In 240 days - Z3 = 0.95541 In 330 days - Z4 = 0.93567 These are usually given so we don’t have to go through the process CF1 = $0.0153 * 0.99010 = 0.01498 CF2 = $0.0153 * 0.97363 = 0.01473 CF3 = $0.0153 * 0.95541 = 0.01446 CF4 = $1.0153 * 0.93567 = 0.94999 PV of Fixed-Payer = $0.99399 Step 2: Calculate the floating rate payment at each period. There are four payments for each of the 4 quarters. Because 30 days have passed, the payments are at 60, 150, 240, and 330. However, we only need to know 1 payment, and we already know it. How can that be? Unlike the fixed-payment, the floating-rate payment is reset to the market value every payment date, therefore the par value is always equal to 100. As for the payment, well that was identified in the question 5.5%. Remember the floating-rate payment is always set for the next payment date, therefore on day 90 (60 days away) the value of the payment will be 5.5%. Also, we add the value of the principal as well as discount back at the 60-day (first payment) discount factor. 0.055*(90/360) = $0.01375 This is the floating rate payment undiscounted. Since it is 60-days out, we need to discount it back + the $1.00 bond value immediately after the payment is made. CF1 = 1.01375 * 0.99010 = 1.00371 = PV of the floating-rate payer Remember that it doesn’t matter what the floating rate coupon payments are at the last three settlement dates because the floating rate bond will be worth $1.00 plus the coupon of $0.01375 at day 90 Step 3: Determine the value to the fixed-rate payment The present value of the floating-payments are greater than the present value of the fixed-payments, therefore, the fixed payer stands to gain Swap value to the fixed payer = 1.00371 – 0.99399 = 0.00972 Swap value to the fixed payer = $30,000,000 * 0.00972 = $291,630 Present value of the fixed payments + principal at the last payment period compared to the present value of the next floating payment (usually given) + principal at the next payment period. Just remember how to calculate the discount factors (which are usually given anyway) and to discount based on where you stand in the contract, 60 days away, 30 days away etc. And remember to stop valuing the floating rate after the next payment date.
Wow, I truly appreciate you doing that. I’m printing that out and I’m studying it. Thank you. Swaps, I may just give you another chance…
thx JScott24 you demystified the discounting of only 1 floating rate period for me
you are a God among men…
I am fine with plain vanilla swaps, but currency swaps?? -> I get a headache just looking at them!
That’s really helpful JScott. I know how to do them but your summary example is very good. lxada I agree. I think I’m sunk if we get a currency swap.
That’s very helpful Jscott24 but I still think I’m just going to resort to choosing A 
damn good explanation
Hey Jscott, I’ve been through your explanation all afternoon and I get it. You might have saved me like 3 point son exam day. Thanks. Now…(ahem)…would you mind doing the same for valuing a currency swap?
Alright let’s try it. Let’s consider a fixed-for-floating currency swap. The term is 1-year, the notional 5 million. The exchange rate at the beginning of the contract was 0.50 L/. The dollar is floating and the L is fixed at 6.8%. Payments are by quarter. Let’s say that 300 days have passed. At the last settlement date (30 days ago), the 90-day LIBOR for the and L;, was 5.6% and 6.4% respectively. Let’s say that after 300 days (meaning 60 days left), the LIBOR 60-day interest rate is 5.4% and the LIBOR 60-day L interest rate is 6.6%, and the exchange rate is 0.52 L/. Calculate the value of the swap to the L fixed payer, who receives floating. Okay wow, let’s start with what we know. Both the fixed and the floating have one payment left 60-days from now that is equal to the coupon payment + principal. The fixed pays the 6.8% which was set at the beginning of the contract plus the par value principal back. Because there are 60 days left in the contract, we use the 60-day L LIBOR to calculate our discount rate (although chances are they will provide this). Fixed Payment L Discount Factor: = 1 / 1 + [0.066 X (60/360)] = 0.98912 Payment = [0.068 X (90/360)] + 1 (principal) = 1.017 Discounted payment = 1.017 X 0.98912 = 1.00594 Now for the floating payment, we take the 90-day LIBOR rate (remember the floating payer is the guy) that was set at the last settlement day (30 days ago). The discount factor is the 60-day LIBOR rate. Floating Payment Discount Factor = 1 / 1 + [0.054 X (60/360)] = 0.99108 Payment = [0.056 X (90/360)] + 1 = 1.014 Discounted Payment = 1.014 X 0.99108 = 1.00496 Calculate the values of the floating payment Floating Payment = 1.00496 X 50,000,000 = $5,024,776 Remember in the case of currency swaps, the two parties exchange the currency at the beginning of the swap because the idea is to hedge the holding effect (FSA name-drop there). Therefore, when we are calculating the value to the fixed or the floating payer, we must take the entire payment including the principal into account when netting the amounts Calculate the values of the fixed payment. Now this is a little different because the fixed payment is in L, we need to first translate the notional amount over at the beginning exchange rate which was $0.50, multiply it by the discounted payment, and then translate it back at 0.52. This is extremely important to remember in currency swaps. If we were doing a fixed-for-fixed currency swap, this would be all that matters. However, in a fixed-for-floating currency swap, gains/losses are subject to both (a) fluctuations in the floating rate (b) appreciation/depreciation in the exchange rates. Initial principal in X Initial Exchange Rate = 5million X 0.5 L/ = L 2.5 million Initial principal in ₤ X discounted payment = L2.5 million X 1.00594 = L2,514,850 L value of discounted fixed payment X new exchange rate = L2,514,850 X 1 / 0.52 = 4,836,227 As we can see the dollar has appreciated from 0.5 L/ to 0.52 L/$, so the L fixed payer gains (on that front) because they are paying the depreciated currency and receiving the appreciated. Let’s think about the gains conceptually. To paint a picture, let’s assume that the floating payer is in the UK, and the fixed payer is in the US. At the initiation of the contract, there is $5 million dollars exchanged. The U.S. guy holds $5 million dollars worth of pounds, and the U.K. holds $5 million dollars. Also for simplicity, let’s assume for the moment that they both are paying fixed rates, contract value at initiation = 0. Then, over the course of the contract, as the pound depreciates and the dollar appreciates, the U.S. guy paying a fixed rate on the depreciated pound and receiving a fixed rate on the appreciated dollar is gaining. In the case of a fixed-for-floating, the gains/losses of the interest rate hedge and the currency hedge cumulate to the total gains/losses. So the first thing you do with a currency swap is value the swap like a plain vanilla swap. The next step would be taking into account the currency fluctuations, as I did above. Value to the fixed = 5,024,776 – 4,836,250 = $118,549 A question might be in the case of a fixed-for-floating currency swap, what are the gains attributable to currency fluctuations and what are the gains attributable to interest rate fluctuations? Also the number above won’t add completely due to the rounding.
I don’t know who you are, or where you’re from, or why you’ve decided to drop in on my life in this way, but all I can think of to say is thank you so very much.
smarshy. i feel uncomfortable. can is say with 95% confidence you might hug this guy? in all seriousness though, nice contribution.
schweser did most of the work, i just added the commentary
Can JScott or someone else just reiterate why you only need to calculate the one floating payment? Wouldn’t the payments of the floating keep changing? I think that’s my biggest sticking point.
kbakes, the point is that the floating rate is going to reset to make the value of the swap again equal to 0 at each reset date. therefore you only have to calc one floating rate pmt.
The floating payment will change with each settlement to equal market rates. i.e. when coupon rate = market rates, par value = 1,000 Therefore there is no need to calculate future floating payments if you know that your par value will always be 1,000 with each settlement. This is in effect an anticipation of all future floating payments.
Jscott…I think we all owe you a drink for doing that one…If you are ever in DC let me know. Thanks,
Some topics I am the pitcher…Swaps, I am definitely the catcher.
swaps have been conqered here here
*BUMP* for those having derivs difficulty- search out jscott24… he did one on FRA’s also last year- great posts.