Currency Swap Conversion Question

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ocgal

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Just did a problem on currency fixed-for-fixed swap….won’t be able to post the vignette here because of the length. The question asked for market value of the swap after 45 days. Didn’t quite understand the answer.
Basically after calculating PV of fixed payments on the foreign currency, there was two conversion back to the domestic currency: Exchange rate at the initiation of the swap was HK 11:42 to 1 EUR and after 45 days, it is HK 9.96 to 1 EUR.
Explanation Given:
Per 1 Euro of notional principal, the PV of fixed payments paid on the euro is 0.9878 (omitting calculation here)
*Note that based on the exchange rate of HK$11.42, the actual notional principal = 1/11.42 = Euro 0.08757
1. PV of euro fixed payments = 0.9878* 0.08757 = 0.08649
2. PV of euro fixed payments in HK$ = 0.08649 * 9.96 = 0.8615
I understand 2…but don’t understand 1. Why can’t we just do 0.9878*9.96?
 
ocgal wrote:Just did a problem on currency fixed-for-fixed swap….won’t be able to post the vignette here because of the length it would violate the owners’ copyright.
Click to expand...
Fixed that for you.
 
ocgal wrote:Just did a problem on currency fixed-for-fixed swap….won’t be able to post the vignette here because of the length. The question asked for market value of the swap after 45 days. Didn’t quite understand the answer.
Basically after calculating PV of fixed payments on the foreign currency, there was two conversion back to the domestic currency: Exchange rate at the initiation of the swap was HK 11:42 to 1 EUR and after 45 days, it is HK 9.96 to 1 EUR.
Explanation Given:
Per 1 Euro of notional principal, the PV of fixed payments paid on the euro is 0.9878 (omitting calculation here)
*Note that based on the exchange rate of HK$11.42, the actual notional principal = 1/11.42 = Euro 0.08757
1. PV of euro fixed payments = 0.9878* 0.08757 = 0.08649
2. PV of euro fixed payments in HK$ = 0.08649 * 9.96 = 0.8615
I understand 2…but don’t understand 1. Why can’t we just do 0.9878*9.96?
Click to expand...
That would give you the PV in HKD, not in EUR.
 
Apologies for reviving an old question, but my question is very relevant to the OP’s question. I’m having a bit of confusion around the conversion of the PV of Fixed Payment in the foreign currency.
Why is the currency being converted in 2 steps? In the solutions for this reading #50, they convert the PV Fixed payment using an inverse of the current exchange rate.
Then a # of days later (we are valuing the swap on that day), the currency exchange is different, but this new exchange rate is direct multiplication, yet the older exchange rate is multiplied first in its inverse (1/x) form. Why do they have to do this?
 
It’s a fixed for fixed currency swap. You simply need to calculate the PV of fixed payments in euros and the PV of fixed payments in HKD, and compute the difference to value the contract. If you receive HKD, you need to convert it using the current exchange rate. As HKD depreciates (and you pay euro while receiving HKD), you lose.
 
I guess maybe I should provide a bit more detail on where I’m confused at…
In reading 50, several of the problems for currency swaps has this wierd calculation where they multiply the floating rate by the inverse of the previous exchange rate, then multiply by the current exchange rate.
For example:
PV of Floating rate: 1.02465 GBP
Previous exchange rate: $1.41 per GBP
New current exchange rate: $1.35 per GBP
Calculation shown in solution: 1.02465 GBP x (1/$1.41) = 0.7206 GBP
Then, 0.7206 GBP x ($1.35/GBP) = $0.9728
I’m confused as to why they don’t just convert the 1.02465 GBP floating rate and multiply with the most current exchange rate of $1.35 per GBP, since wouldn’t I need to “cross-out” the GBP foreign currency to convert to the domestic (i.e. GBP x USD/GBP = USD)?
 
In order to be arbitrage-free, if the swap has 1 unit of domestic currency from the one side, the PV of the foreign payments will be 1/S0. As time passes and exchange rates changes, the PV of the foreign payments becomes (1/S0)*St.
 
Gebura wrote:
In order to be arbitrage-free, if the swap has 1 unit of domestic currency from the one side, the PV of the foreign payments will be 1/S0. As time passes and exchange rates changes, the PV of the foreign payments becomes (1/S0)*St.
Click to expand...
Sorry, but I still don’t quite understand. So are you saying that, (1/S0)*St is to simply make sure that the foreign payment cannot have an arbitrage opportunity due to the currency spread between exchange rates?
Why is the calculation performed this way?
 
Derivatives are not one of my strong topics but I’ll try to explain better:
At swap initiation (t0) the value of the swap is zero. Let’s see how to achive this when we have fixed-for-fixed:
1) for the domestic currency leg: the fixed rate is the coupon rate on a fixed-rate domestic bond that is trading at par (let’s say 100 units of domestic currency) at t0;
2) same for foreign currency leg- the fixed-rate is the rate of foreign currency fixed-rate bond trading at par ( 100 units of foreign currency) at t0;
3) since 100 units of domestic currency are not equal to 100 units of foreign curency, at swap initiation the PV of the future foreign currency payments are agreed to be equal to the PV of the domestic currency payments. That’s why we use S0.
4) as time passes the spot exchange rate change and the domestic currency payer realize gain or loss.
For example:
The present value of the fixed-rate domestic currency payments are 100 DC;
The present value of the fixed-rate foreign currency payments are 100 FC;
Spot rate at t0 is 2 DC/ FC;
The foreign payer agree to pay 100 DC / 2 DC/ FC = 50 FC.
At time Tt: St = 2,1 DC/ FC.
The foreign payer will still have to pay 50 FC but now that will equal 105 DC.
From the domestic currency payer perspective: he will pay 100 DC and will receive 105 DC.
In short, the foreign currency payer will pay at time Tt (1/S0)*St.
 
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