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Use

An eonia swap ( E uro O ver n ight I ndex A verage) is a derivative financial instrument in which a fixed interest rate is swapped for a reference rate that is used for overnight money. An eonia swap has the following properties:

  • The term can be between two days and one year.

  • The term of the fixed side is the same as the term of the swap, which means that there is a payment on the fixed side upon maturity.

  • On the variable side, the average of the overnight money rates is used for the entirety of the term and to form a payment on maturity. The eonia swap takes the compound interest effect into account, and hence gives a depiction of the money market that is as realistic as possible. The formula for calculating the average interest rate (eonia rate) is:

    ( )

    where:

    r f :

    The eonia interest rate that is to be calculated

    t 0 :

    The start date of the eonia swap

    t n :

    The maturity of the eonia swap

    r i :

    Fixing rate for overnight money at time i

    d i :

    Number of days valid from r i (normally = 1, on weekends = 3)

    n:

    Total number of days

    The interest calculation method used is the euro method (actual/360).

  • At the end of the swap term, the cash flow is the difference between the fixed and variable sides. Since no payments take place during the term, transaction costs are greatly reduced.

Scope of functions/valuation

The fixed and variable sides of an eonia swap are priced separately. The NPV of the swap is the sum of the NPVs on both sides. The existing fixed payment on the fixed side is simply discounted to the valuation date. On the fixed side, the valuation takes place as follows:

  • m of n overnight fixings have already taken place. The remaining ( n - m ) fixings are determined from a yield curve using forward rates.

  • The eonia rate is calculated using the existing fixed interest rates and the forward rates.

  • The resulting interest payment Z = nominal value eonia rate days / 360 is discounted.

    Note Note

    Instead of calculating individual overnight money forward rates, which are then multiplied with each other, the product for all unknown overnight money rates n – m P(A n-m ) can be determined as follows:

    The following applies: Markup factor A n-m = 1 + r n-m d n-m / 360 = df n-m / df n-m+1

    (where df n-m is the discount factor at time n-m).

    Then the product of A n-m is

    P(A n-m ) = df 1 / df n

    This means it is sufficient to determine the forward rates between the time points n-m and n .

    End of the note.

Comments

In addition to eonia swaps, the function can price financial instruments that have the following characteristics:

  • More than one interest payment on the variable side

  • Any interest calculation method

  • The average interest calculation does not necessarily have to be based on overnight money rates. You can also put 12 monthly interest rates together.

Restrictions

The following parameters always have to be the same for a maturity date:

  • Nominal rate

  • Reference interest rate

  • Interest rate calculation method

  • Number of days/year

  • Nominal currency

  • Cash flow currency

At present, it is not permissible for the reference interest rate to be represented by a formula (for example, EURIBOR + 0.2).