OIS Discounting – Part 1: Interest Rate Modeling

Prior to the credit crisis, interest rate modelling was generally well understood. The underlying fundamental principles had existed for over 30 years with steady evolution in areas that were most relevant to options and complex products.
12 Jun, 2013

Credit and liquidity were ignored as their effects were minimal. Pricing a single currency interest rate swap was straightforward. A single interest rate curve was calibrated to liquid market products and future cash flows were estimated and discounted using this single curve. There was little variation between implementations and results across the market were consistent. Following the credit crisis, interest rate modelling has undergone nothing short of a revolution. During the credit crisis, credit and liquidity issues drove apart previously closely related rates. For example, Euribor basis swap spreads dramatically increased and the spreads between Euribor and Eonia overnight indexed swaps diverged. In addition, the effect of counterparty credit on valuation and risk management dramatically increased. Existing modelling and infrastructure no longer worked and a rethink from first principles has taken place.

Today a new interest rate modelling framework is evolving based on OIS discounting and integrated credit valuation adjustment. Pricing a single currency interest rate swap now takes into account the difference between projected rates such as Euribor that include credit risk and the rates appropriate for discounting cash flows that are risk free or based on a funding cost. This approach is referred to as dual curve, OIS discounting, or CSA (Credit Support Annex) discounting and forces a re-derivation of derivatives valuation from first principles. In addition, the counterparty credit risk of uncollateralised over-the-counter transactions are measured as a CVA which takes into account the likelihood that the counterparty will default, along with expected exposures, volatility of these expected exposures, and wrong way risk.

Interest Rate Modelling Prior

Prior to the credit crisis, interest rate derivatives were valued with models that focused on the dynamics and term structure of interest rates but generally ignored other elements including:

  • Credit risk
  • Liquidity risk
  • Collateral agreements
  • Funding costs

Since the introduction of Black-Scholes in 1973, interest rate modelling has evolved steadily. There have been several key milestones with the most recent evolutions prior to the credit crisis relating to volatility skew modelling.

Valuing a single currency vanilla interest rate swap involved calculating forward rates and discounting expected cash flows from a single interest rate curve based on no-arbitrage assumptions. These curves were calibrated from liquid interest rate products including money market securities, Eurodollar futures, FRAs and interest rate swaps. A common reference rate for euro denominated swaps is Euribor. Euribor rates are published 11am Central European Time each day and are calculated as the average (excluding the top and bottom 15%) offer rates from over 40 contributing banks for Euro Interbank deposits. Fifteen different maturities are published. These deposits are unsecured but prior to the credit crisis were considered a proxy for a risk-free rate. Similar interbank deposit rates are calculated for other currencies.

Impact of the credit crisis on the rates market

As the credit crisis unfolded, there were significant impacts on the structure and dynamics of the rates market. Credit and liquidity drove segmentation and rates that were previously closely related diverged, causing a rethink of how these rates should be modelled.

Basis swaps spreads increased dramatically

Reflecting the different credit risk and market segmentation between different Euribor rate tenors, basis swap spreads blew out during the crisis from being fractions of a basis point (where they had been quoted for decades) to double digits in a matter of months. The three-month vs. six-month Euribor basis swap spread went from under a basis point to peak at over 44 basis points around October 2008, after the Lehman Brothers default.

OIS and LIBOR swap rates diverged

The basis widened dramatically from under 10 basis points to peak at 222.5 basis points around Lehman’s default in October 2008.The Euribor/Eonia spread has persisted even after the credit crisis and reflects the revised view of the different credit and liquidity characteristics between these two rates. The Eonia rate has now become the market standard proxy for a EUR market risk-free rate.

Graph showing the spread between the Euribor 6M deposit rate and the 6M Eonia OIS rate (source Bloomberg)

The relationship between forward rates of different tenors diverged

Prior to the credit crisis there were small but generally negligible differences between forward rates implied from interest rate products of different tenors. No-arbitrage arguments held and a six-month rate implied from a three-month rate and a three times six-month forward would match. As the credit crisis continued, the market segmented and this previously arbitrage-free relationship broke down.

Increased use of collateral agreements

Another effect of the credit crisis has been a dramatic increase in the use of collateral agreements as a method of managing counterparty risk. The 2010 International Swaps and Derivatives Association Margin Survey reports that 70% of OTC derivatives net credit exposure worldwide is covered by collateral, compared with 29% in 2003.

In part 2 we will explore the new interest rate modelling paradigm

Part 2

OIS Discounting – Part 2: The New Interest Rate Modeling Paradigm

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