Currency Swap Fixed USD receiver, Floating EUR payer question

[graff_legend]

My apologies for the length of this question. I’ve been trying to wrap my head around this for a while…question comes from an example that starts off like this:

One-year currency swap, quarterly payments. The two currencies are USD and EUR, and the current exchange rate is $1.25/€ (assume constant for the rest of this for simplicity). The current term structures of Libor (for USD) and Euribor (for EUR) are as follows:

Days Libor% Euribor%

90 3.25 3.80

180 3.75 4.65

270 4.25 5.90

360 4.60 6.75

Then the example calculates the periodic fixed rate for each currency using their respective rates, for a “fixed USD receiver, fixed EUR payer” swap. I am good till here. Then it provides rates 60 days into the tenor:

Days Libor% Euribor%

30 3.10 3.50

120 3.25 4.15

210 3.80 5.05

300 4.35 6.10

For the value of the swap, it maintains the same periodic rate (since it is fixed for fixed) but updates the PV factors for the change in rates. Then it applies a rate netting formula, with respective PV factors applied to each leg, and exchange rate to the EUR payer leg, converting everything into USD at the end. All this is understood.

My question…what if it was a fixed USD receive, FLOATING EUR payer swap? Would I be recalculating the periodic rate for the floating EUR payer leg with the new t = 60 rates? Or would I do something else? Other videos online seem to suggest that there’s no way to know what the future floating rates would be, so one should just apply the previous period’s floating rate to calculate the next periodic payment and PV that to find the value of the floating leg. But clearly, in this example, the future rates are already known hence it is possible to find the value of the whole leg?

Thank you for your help and guidance.

tl;dr In a fixed for floating currency swap, how do I find the value of the floating leg at a given point in time, given floating rates ahead?

[CEO10K-DAY]

@graff\_legend

My apologies for the length of this question. I’ve been trying to wrap my head around this for a while…question comes from an example that starts off like this:

One-year currency swap, quarterly payments. The two currencies are USD and EUR, and the current exchange rate is $1.25/€ (assume constant for the rest of this for simplicity). The current term structures of Libor (for USD) and Euribor (for EUR) are as follows:

Days Libor% Euribor%

90 3.25 3.80

180 3.75 4.65

270 4.25 5.90

360 4.60 6.75

Then the example calculates the periodic fixed rate for each currency using their respective rates, for a “fixed USD receiver, fixed EUR payer” swap. I am good till here. Then it provides rates 60 days into the tenor:

Days Libor% Euribor%

30 3.10 3.50

120 3.25 4.15

210 3.80 5.05

300 4.35 6.10

For the value of the swap, it maintains the same periodic rate (since it is fixed for fixed) but updates the PV factors for the change in rates. Then it applies a rate netting formula, with respective PV factors applied to each leg, and exchange rate to the EUR payer leg, converting everything into USD at the end. All this is understood.

My question…what if it was a fixed USD receive, FLOATING EUR payer swap? Would I be recalculating the periodic rate for the floating EUR payer leg with the new t = 60 rates? Or would I do something else? Other videos online seem to suggest that there’s no way to know what the future floating rates would be, so one should just apply the previous period’s floating rate to calculate the next periodic payment and PV that to find the value of the floating leg. But clearly, in this example, the future rates are already known hence it is possible to find the value of the whole leg?

Thank you for your help and guidance.

tl;dr In a fixed for floating currency swap, how do I find the value of the floating leg at a given point in time, given floating rates ahead?

if it was floating, you would only find the present value of the next floating rate payment, add in the present value of the notional (usually in terms of one currency unit) convert back to USD and compare the values. You don’t know what the future floating rate payments will be other than the next one. So, they’re going to be ignored since rates are floating and the present value of any payment divided by the same interest rate that’s going to be used to present value that payment will also be 1 - and since were comparing this on the terms of only $1.00 you can ignore them from valuation.

hope that made sense, I’m on my iPhone.

[graff_legend]

@CEO10K-DAY

@graff\_legend

My apologies for the length of this question. I’ve been trying to wrap my head around this for a while…question comes from an example that starts off like this:

One-year currency swap, quarterly payments. The two currencies are USD and EUR, and the current exchange rate is $1.25/€ (assume constant for the rest of this for simplicity). The current term structures of Libor (for USD) and Euribor (for EUR) are as follows:

Days Libor% Euribor%

90 3.25 3.80

180 3.75 4.65

270 4.25 5.90

360 4.60 6.75

Then the example calculates the periodic fixed rate for each currency using their respective rates, for a “fixed USD receiver, fixed EUR payer” swap. I am good till here. Then it provides rates 60 days into the tenor:

Days Libor% Euribor%

30 3.10 3.50

120 3.25 4.15

210 3.80 5.05

300 4.35 6.10

For the value of the swap, it maintains the same periodic rate (since it is fixed for fixed) but updates the PV factors for the change in rates. Then it applies a rate netting formula, with respective PV factors applied to each leg, and exchange rate to the EUR payer leg, converting everything into USD at the end. All this is understood.

My question…what if it was a fixed USD receive, FLOATING EUR payer swap? Would I be recalculating the periodic rate for the floating EUR payer leg with the new t = 60 rates? Or would I do something else? Other videos online seem to suggest that there’s no way to know what the future floating rates would be, so one should just apply the previous period’s floating rate to calculate the next periodic payment and PV that to find the value of the floating leg. But clearly, in this example, the future rates are already known hence it is possible to find the value of the whole leg?

Thank you for your help and guidance.

tl;dr In a fixed for floating currency swap, how do I find the value of the floating leg at a given point in time, given floating rates ahead?

if it was floating, you would only find the present value of the next floating rate payment, add in the present value of the notional (usually in terms of one currency unit) convert back to USD and compare the values. You don’t know what the future floating rate payments will be other than the next one. So, they’re going to be ignored since rates are floating and the present value of any payment divided by the same interest rate that’s going to be used to present value that payment will also be 1 - and since were comparing this on the terms of only $1.00 you can ignore them from valuation.

hope that made sense, I’m on my iPhone.

Gotcha, so the videos were correct. Thank you for jumping in and taking the time to clarify this for me, using a difficult iPhone keyboard no less. It is greatly appreciated.

Just to recap so I know I got this: using numbers above, 60 days into the tenor, I would use the t = 60, 30 day Euribor rate of 3.50%, unannualize it first, then calculate the upcoming periodic payment at t = 90. PV that amount using the 30 day Euribor rate. Then on to the notional that will be exchanged at the end of the swap, PV that all the way back to t = 60, apply the exchange rate and net against the fixed side.

Now, I hope I made sense, LOL.