| Математика
Key words: Cross-currency interest rate swaps, CCIRS, Interest rate swap, IRS, Interest rate risk, Currency risk
FX Delta calculation

Swap is a financial contract in which two parties agree to exchange “something” for “something” within an agreed time period, parties swapping things between each other. Often, there are cash flows, so called periodic payments swapped at a reasonable predetermined price.

Interest rate swap (IRS) and cross currency interest rate swap (CCIRS) are classified as plain vanilla swaps.
Usually, it means that interest rate is set at advance with payments on the quarterly basis and payments are fixed for float.
These products can be used to express some of the common views on the market; they are building blocks and often liability management products.

The difference between these two swaps is that CCIRS usually involves exchange of notional amounts because amounts are in different currencies.
IRS payments are in the same currency and thus simple netting is applied as it is shown in my previous article.
As it follows, market risks are different as well.
IRS is sensitive to interest rates changes while CIRS has sensitivity to interest rates and foreign exchange rate.

First of all, it should be understood that depending on the needs of the counterparty, the initial exchange may be omitted in CCIRS but the final exchange at the end gives FX risk exposure.

CCIRS can be fixed to fixed, fixed to floating or floating to floating.

Case 1: No initial exchange of notional amounts

1) A building company has EUR loan
2) Company bought equipment, paid EUR
3) Company has USD revenue(generated by using the equipment) and thus willing to pay USD rate and USD nominal (at the end) but unfortunately has EUR exposure to the bank (if EUR will rise, the company needs to buy EUR at higher rates by converting more dollars)
4) In order to eliminate the EUR exposure, the company swapped EUR for USD with the same periodic payments as the loan payments
5) Now the company receives EUR interest rate payments from the swap provider and sends them to the bank. The company pays only USD interest rate payments to the swap provider
6) At maturity, the company is obliged to return USD to the swap provider and will receive EUR under the swap agreement. Finally, the EUR amount will be paid to the bank

Case 2: Exchange and re-exchange of notional amounts

This is a straightforward and easily understood case. In order to improve the difference in the interest rates or simply to have funding in another currency, counterparties may enter into CCIRS.
As been already stated, a gain may be realized due to the lower interest rates of another currency but a loss may occur due to FX exposure.
FX risk results from uncertainty concerning future flows of nominal amounts in different currencies.

In the previous article I explained interest rate sensitivities.
DV01 is used to measure interest rate risks. FX exposure can be calculated using net present value of all cash flows of CCIRS.

The following example is a little bit simplified because there are no interest rate payments (it actually makes CCIRS worthless) but we can easily show the FX risk calculation.
The same methods of FX risk calculation can be applied to CCIRS with coupon payments.

USD Notional Amount: USD 1 108 860 equivalent to EUR amount on effective date
EUR notional Amount: EUR 1 000 000
Maturity: 1 year (20 Aug 2015 – 22 Aug 2016)
Day count: Act/360
Payment frequency: annually
Counterparty A (c/p A): pays fix in EUR. The coupon is 0% to simplify calculations
Counterparty B (c/p B): pays fix in USD. The coupon is 0% to simplify calculations as well

Cross currency swap

From Counterparty A side:
There is nominal amounts exchange on the effective date:
-receive fixed EUR amount, pay fixed EUR interest rate on the received amount
-pay fixed USD amount (@EUR/USD=1.10886), receive fixed USD interest rate on the paid amount

Cross currency swap payments

Forward FX = 1.11855.

NPV shows that totally Counterparty A has to pay $1 111 872 and receive $1 102 237.
The difference is $9 634 that Counterparty A will require from Counterparty B in order to execute the deal today.

What is the FX risk in this trade?
The risk can be measured by FX delta, i.e. how much net NPV will change if EUR/USD will move 1%. Current EUR/USD = 1.10886, EUR/USD move by 1% = 1.11995.

Therefore, let’s revaluate our swap by using new EUR/USD spot =1.1200.

Cross currency interest rate swap payments

The NPV difference is NPV (EUR/USD=1.1200) – NPV (EUR/USD=1.10886) = -$20 805 – (-$9 634) = -$11 171.
This difference is FX delta, i.e. Counterparty A will lose $11 171 if the spot rate moves from 1.10886 to 1.1200.

Excel file with calculation is attached.