Rates, Calls and Rate Projection

This page sets out three cash flow calculation rules: the composition of a coupon rate (base rate and spread), the treatment of call dates, and the projection of floating rates not yet fixed.

Fixed rate with spread

The spread is an additive margin on the base rate, whatever the rate type:

\[\text{all-in rate} = \text{base rate} + \text{spread}\]

The base rate depends on the rate type of the transaction:

Rate type Base rate
FIXED The contractual rate of the transaction.
FLOATING The index rate read on the curve for the coupon period, or the known fixing of the current coupon when the transaction carries one.

A “fixed rate with spread” transaction is therefore well defined: its coupon is calculated on the fixed rate plus the margin. The coupon paid carries the all-in rate; its analytical breakdown places the fixed rate in the RATE component and the spread (less the liquidity component) in the MARGIN component.

Example — a bullet loan of EUR 1,000,000 at a fixed rate of 2% with a spread of 0.5%, annual coupon, 30/360 basis:

  • all-in rate: 2% + 0.5% = 2.5%;
  • annual coupon: 1,000,000 × 2.5% = EUR 25,000;
  • of which EUR 20,000 for the fixed rate (RATE) and EUR 5,000 for the spread, split between LIQUIDITY and MARGIN.

Swaps

Each leg of a swap applies the same rule, with one difference in how the rate value is read:

  • Fixed leg: the coupon is calculated on the rate value plus the spread, as for a loan.
  • Floating leg: the coupon is calculated on the index rate read on the curve plus the spread. The rate value carried by the leg (the last fixing provided in the import file) is for information only: it is added neither to the index rate nor to the spread, including for the current coupon.

Example — a floating leg EURIBOR 3M + 0.3% whose file shows a last fixing of 3.1%: if the forward rate for the period is 2.6%, the coupon is calculated at 2.6% + 0.3% = 2.9%. The 3.1% fixing in the file plays no part in the calculation.

Issuer call / holder call

The engine does not distinguish who holds the prepayment option (issuer or holder). A call date means that the option is exercised with certainty on that date, and only in the behavioural projection (BEHAVIOURAL). The contractual projection (CONTRACTUAL) retains the contractual maturity of the transaction. A call date on or after maturity has no effect. A call date already past (on or before the reporting date) means the transaction has already been repaid: the behavioural projection of a bullet loan, a term deposit, a security or a repo then produces no cash flow.

Product CONTRACTUAL projection BEHAVIOURAL projection
Bullet loan / borrowing, term deposit Capital and coupons up to maturity. Capital repaid at the call date. A single coupon payable at maturity is recalculated over the period up to the call; with periodic coupons, the coupon straddling the call accrues up to the call date (next version; it was previously removed) and subsequent coupons are removed.
Securities (SecurityPosition) Capital and coupons up to maturity. Capital repaid at the call date; the coupon straddling the call accrues up to the call date; subsequent coupons are removed.
Swap Schedule truncated at the call date. Schedule truncated at the call date.

For swaps, the call date applies to both projections: on each of the two legs, the periodic coupons stop at the call date and the final exchange of nominal is dated on it. The CONTRACTUAL and BEHAVIOURAL projections of a callable swap are therefore identical.

Example — a security with a nominal of EUR 1,000,000, maturity 31/12/2030, annual coupon on 31/12, call date 30/06/2028: the contractual projection repays the nominal on 31/12/2030; the behavioural projection repays it on 30/06/2028 with a last coupon accrued from 01/01/2028 to 30/06/2028, and no further flows thereafter.

Importing the call date

The call date is read from the column associated with the callDate mapping key (DateCall column in the example mapping provided).

For securities, the solution also reads the issuer call date (DtCallEmet column, issuerCallDate mapping key):

  • it is used when DateCall is empty;
  • when both columns are populated and differ, the nearer of the two dates is used: the security cannot run past its first call. A warning on the transaction names both columns, their dates and the date used.
Note

Modelling of the option holder and of an exercise rule (for example, exercise conditional on the level of rates) is a planned enhancement. In the meantime, any imported call date is considered exercised.

Projection mode for uncertain rates

The uncertain (UNCERTAIN) interest periods of floating-rate transactions are those whose rate is not yet fixed at the evaluation date. By default, their rate is projected using the forward rate of the period, a simple rate in the coupon’s basis derived from the discount factors of the index curve (see Calculation framework, §1.4), securities included. The contractual spread is added to it, as described above.

Note

The following paragraphs describe a feature delivered with the next version.

When launching a cash flow generation, a new Rate projection mode option offers two values:

Mode Behaviour
Forwards (default) Each uncertain period is valued at the forward rate of the period, read on the curve.
Last known rate (LAST_FIXING) The last known rate of the transaction is frozen over all future periods.

In Last known rate mode, the last known rate is determined in the following order:

  1. the prefixed rate of the transaction from the prefixing file, when a line applies (transaction reference, action date, rate, base rate frequency): the line is valid from its action date until that date plus the base rate frequency;
  2. failing that, the known fixing of the transaction (Interest Rate column of a floating-rate transaction);
  3. failing that, the current rate of the index read on the curve at the evaluation date.

Example — a loan indexed on EURIBOR 3M + 1%, with a known fixing of 2.9% and no applicable prefixing line. In Forwards mode, each future quarter is valued at its forward rate (for example 2.7%, then 2.6%…) + 1%. In Last known rate mode, all future quarters are valued at 2.9% + 1% = 3.9%.

Shock scenarios

The shock rule does not depend on the projection mode:

  • a certain flow (rate already fixed at the evaluation date) is never shocked: it keeps the same rate in all scenarios;
  • an uncertain flow is always shocked.

In Last known rate mode, the frozen rate of an uncertain period therefore receives the scenario shock: when it comes from prefixing or from the known fixing, it is increased by the difference between the current rate of the index in the shocked scenario and the same rate in the baseline scenario; when it is read on the curve, it is read directly on the scenario curve.

Example — the previous loan, in the +200 basis point parallel up scenario: the current quarter, already fixed, remains at 2.9% + 1%. Future quarters move from 3.9% to 2.9% + 2% + 1% = 5.9%.