Since the financial crisis during 2007, the pricing of derivatives has
been undergoing significant changes. Using the LIBOR rates for the discount
curves did not seem sufficient anymore since the OIS-LIBOR spread widened considerably
during the crisis and so did the EURIBOR-EONIA curve. For a long time,
counterparties utilized bilateral collateral for over the-counter (“OTC”)
derivative transactions for mitigating the credit risk of their counterparties.
The funding advantages from collateral which can be rehypothecated possesses a value and it should be
considered in derivative pricing (i.e. using the risk-free curve).

Source: Federal Reserve Bank of St. Louis

OIS Discounting uses the interbank overnight lending rates (for USD,
Fed-Fund rates) for the curve construction. Maturities longer than two years
can be constructed using the Swap rates on the market. For maturities longer
than 15 years, market data for certain currencies is often difficult to
construct. EONIA (EUR) and SONIA (GBP) rates can be derived from the Swaps which go out at 30 years. Beyond 10 years for the
Fed-fund rates (USD) curve, the basis swaps have to be considered.

Starting from two to ten years, OIS swaps have yearly coupons and can be
viewed similar to the fixed-float IRS where the index and discount curves are
both the OIS (risk-free) curve.

Often, firms value uncollateralized transactions
still using the LIBOR curve. This is controversial since using LIBOR
discounting will incorporate the counterparty risk twice, since it will be reflected
in the CVA calculation.

The CSA (Credit Support Annex) has been widely used for posting
collateral. The new CSA has been remodeled to reflect the risk free OIS
discounting. The new standard CSA agrees on daily collateral postings. If these
are failing, the transaction with that counterparty has to be be closed out. Due to these daily
collateral postings, the risk-free discount rate can be applied on the new
SCSA. This is referred to as “OIS discounting” or “CSA discounting”.

EURIBOR / LIBOR discounting

During pre-crisis, the discount curve was constructed using liquid
instruments such as futures, FRAs and interest rate swaps. The EURIBOR rates
are published at 11am daily and weighted average eliminating the top and bottom
15% from 40 contributing banks. 15 different maturities are published.
Effective from 1st of July 2014 all LIBOR/EURIBOR rates had a licensing change.

EONIA rates / OIS Rates used for OIS discounting

The EONIA or Fedfunds rate is the interest rate
which financial institutions use to move funds held at the Federal Reserve or
at the European Central Bank among each other, usually based on an overnight
terms. Financial institutions with excess funds in their accounts lend to other
institutions in need. The weighted average of all these
rate across among these transactions on a given day is the daily EONIA rate.

The related EONIA Swap Rate, which is used for the OIS discounting, is the
fixed rate exchanged for a floating overnight rate.

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