A cross currency real rate swap is an inflation-linked swap in which the inflation leg pays a fixed real interest rate on the inflation-adjusted notional in one currency, and the other leg pays a fixed or floating nominal interest rate in a different currency.
In addition, note that, because there are two currencies involved in this instrument, the payments may not only include interest rate payments (on the set payment periods in the relevant currency on the respective principal) but may also include an exchange of principals.
And regardless of whether or not there is an exchange of principals on the end date, the inflation leg also includes the accretion payment, which is the payment of the inflation index (or CPI) change on the change in the principal amount/notional on a coupon’s payment date. The inclusion of this payment necessarily affects the leg’s present value (as seen in the Cash Flow PV column in the Swap Cash Flow Dates window) and therefore the instrument’s market value.
By default, the accretion payment is always calculated and paid in full on the last coupon's payment date, where the CPI change is measured from the instrument's base reference index1 to the CPI on this last payment date. However, you can choose to add an accretion payment to one or more of the inflation leg's other coupon payment dates in addition to the last coupon. For more information on this functionality, see Pricing A Cross Currency Real Rate Swap.
What is a fixed real interest rate? A fixed real interest rate is a fixed interest rate that is paid on an inflation-adjusted notional. It is "real" in that, for each coupon, irrespective of the realized inflation in that same period, the actual interest paid (i.e., the nominal interest rate) is the same in "real" terms. So for example, if there is high inflation over the period of a coupon, the actual interest paid, i.e., the nominal interest rate, is higher; if there is low inflation over the period of the coupon, the actual interest paid is lower.
This is achieved by applying the fixed interest rate to the inflation-adjusted notional. For each coupon, the inflation-adjusted notional is based on the instrument's base notional, adjusted to take into account the change in the inflation index, a change that for each coupon is measured from the instrument's start date to that coupon's end date2. Accordingly the actual notional for each coupon necessarily changes relative to the inflation index change in that period-if the inflation is high, the notional is higher; if the inflation is low, the notional is lower.
Which inflation indexes are supported for the inflation leg? Each currency has one or more standard inflation indexes. Currently in SDX Interest Rates you can price this instrument for the following currencies—USD which is based on USCPI; EUR which can be based on any of the following indices—HICPxT, FRCPIxT, HICP, ITCPI, SPCPI, FRCPI, DECPI; GBP which can be based on any of the following indices—UKRPI, LPI0-3, LPI 0-5, LPI 3-5, LPI Floor 0; JPY which is based on JPCPI; AUD which is based on AUCPI; ILS which is based on CPI/ILS.
Advantages Of A Cross Currency Real Rate Swap
A cross currency inflation swap is typically used by a corporation who wants to issue inflation linked debt in one currency and wishes to then swap this into ordinary nominal debt in another currency.
It is also used by pension funds who have natural exposure to inflation from their real rate annuity products, possibly in multiple currencies, and as such want to hedge this risk.
Pricing A Cross Currency Real Rate Swap
The system:
By default calculates the real rate that will result in a zero NPV. However, you can then edit this real rate if relevant.
By default assigns the accretion payment to the last coupon of the inflation leg.
However, you can also choose to include an accretion payback on one or more of the inflation leg’s other coupon payment dates in addition to the last coupon.
This is useful as it lets the receiver of the leg reduce the credit risk of its counterparty not being able to pay the CPI change on the notional in full on the last coupon.
You activate the accretion payment for an interim coupon using the relevant checkbox in the Acc. Payback column in the Swap Cash Flow Dates window as seen at 1 in Figure 1.
| Figure 1: | Enabling an Accretion Payment For Interim Coupons |
In order to calculate the accreted payment, you need to know what the CPI change is.
If an accretion payment is only made on the last coupon, the CPI change is measured from the instrument's base reference index to the CPI on that coupon's payment date. However, if there are additional accretion payback payments, i.e., on the interim coupon payment dates, then the CPI change used to calculate the accreted payment is only measured from the instrument's base reference index for the first accretion payment; for subsequent accretion payments, it is measured from the last accretion payment date to the coupon’s payment date.
You can see the base CPI, i.e., the CPI from which the CPI change on the coupon's payment date is measured, in the Base CPI column. This is the actual index, not the change in CPI. For a coupon for which there was no accretion payback in any of the previous coupons, this is the instrument's base reference index. For a coupon for which there was an accretion payback in a previous coupon, this is the CPI on that previous coupon's payment date.
Needs to know which forward index interpolation method to use.
For more information see the Selecting the Forward Index Interpolation Method for Inflation Instruments.
By default sets the instrument to include an exchange of principals on both the start date and the end date.
However, you can then change this setting so that notionals should be exchanged on the start date only, on the end date only, or on neither date. You do this using the Exchange Notionals At dropdown list.
Needs to know how to deal with seasonality.
For more information, See "Customizing the Seasonality Adjustment for Inflation Instruments".
Needs to know from when to calculate the seasonality.
For more information, see Defining Which Reference Index to Use to Calculate the Seasonality.
Uses inflation rates which are taken by lag definition, even if more recently published rates are available. When you define the instrument's tenor, the system automatically displays the default inflation lag for the selected index in the Inflation Lag field.
However, you can then edit this value if required. This lets you instruct the system to price the instrument using a non-default inflation lag.
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If you are using seasonality and you have also instructed the system to measure the seasonality using the newest index available, the system does not use the inflation lag for the seasonality calculation, even if you have manually defined the inflation lag in the pricing page itself (in the Inflation Lag field). |
In the Swap Cash Flow Dates window:
The Implied CPI column displays
For a future date what the market thinks the defined inflation index (or CPI) will be on each coupon’s payment date.
For a historical date what the actual inflation index was on that coupon’s payment date.
The Base CPI column displays the CPI from which the CPI change on the coupon's payment date is measured.
For a coupon for which there was no accretion payback in any of the previous coupons, this is the instrument's base reference index—as displayed in the pricing page in the Reference Index (Start) field. For a coupon for which there was an accretion payback in a previous coupon, this is the CPI on that previous coupon’s payment date.
The Accreted Notional column displays the inflation-adjusted notional for this coupon.
This is calculated as follows:
notional x (change in inflation index measured from the instrument's base reference index or, if relevant, from the last accretion payment date to the coupon’s end date)
The Actual Payments PV column displays the actual amount to be paid on each coupon.
For each coupon in a real rate swap it is calculated as follows:
Cash flow PV + (if activated for this coupon) the accretion payback payment PV
Where the cash flow PV is the present value of the interest payment on the accreted notional, which is the amount displayed in the Cash Flow PV column.
For each coupon in a cross currency real rate swap, this calculation also includes any principal payment PV—as long as there is an exchange of notionals on the end date (and then this is the present value of the amount seen in the Principal Payment column).