The Overhaul of Interest Rate Modelling

A new generation of interest rate modelling is evolving, as an approach based on overnight indexed swap discounting and integrated credit valuation adjustment is becoming the market consensus.

Prior to the credit crisis, interest rate modelling was generally well understood. 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.

Today, a new interest rate modelling framework is evolving based on overnight indexed swap, or OIS, discounting and integrated credit valuation adjustment (CVA). 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 funding cost. This approach is referred to as OIS discounting. In addition, the counterparty credit risk of (uncollateralized) OTC transactions is measured as a CVA.  

Figure 1: Key milestones in the history of interest rate modelling

LCH’s decision to move to OIS discounting reflected the fact that most swaps cleared through its system were subject to standard CSAs with daily collateral calls and a collateral rate based on OIS rates. Further, the largest market-making banks are now pricing using OIS discounting, and their margining and collateral systems are being converted to reflect this practice.

The New Interest Rate Modelling Paradigm

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.

These changes have driven a rethink of how these rates should be modelled and profound shift in the way all OTC products are valued and risk managed. The result has been an abandonment of the classic derivatives pricing framework based on single interest rate curves and the introduction of a new approach that takes into account current interest rate dynamics and market segmentation using multiple curves.

[Related: "OIS Discounting: To Clear, or Not To Clear?" (video)]

Dual curve/OIS discounting

The old-style no-arbitrage, single-curve derivatives valuation framework, where Euribor was a reasonable proxy for a risk-neutral discount rate, has been permanently changed by the credit crisis. An understanding of the credit risk embedded in Euribor and similar rates and an increased importance in the modelling of funding have driven a separation between the index rates used for the floating legs of the swap (the projection rates) and the appropriate rates used for present value (the discount rates). The market-standard rate to discount future cash flows is now OIS rates.

The method of projecting rates using Euribor and discounting rates using Eonia changes the fundamental framework for existing derivative modelling. Pricing and risk managing even a vanilla single currency swap has become significantly more complex. Curve construction, pricing and hedging now involve multiple instruments and additional basis risks. These complexities are compounded for interest rate products such as cross currency swaps, Caps/Floors and Swaptions.

Counterparty risk and CVA

The measurement and management of counterparty risk is now something that impacts all market participants. Accurate valuation of OTC products now requires accurate valuation of the credit component of each transaction. In addition, regulatory initiatives such as Basel III and Solvency II, along with accounting rules such as ASC 820 (FAS 157) and IAS 39, have mandated more accurate counterparty risk valuation and risk management.

The larger banks have led the evolution of valuing and managing counterparty credit risk. Over time they have converged to generally consistent methods and processes. The concept of a Credit Value Adjustment (CVA) is now widely accepted and consistently calculated across the markets. And OTC transactions that carry counterparty exposure executed by all the larger institutions now have a CVA component as part of the valuation.

Dual-Curve OIS Discounting Curve Construction

Interest rate derivatives are now valued with models that reflect the observed market segmentation, counterparty risk, and interest rate dynamics. Valuing a single currency vanilla interest rate swap involves calculating forward rates based on Euribor rate curves and discounting expected cash flows using Eonia rates. As in the single-curve case, these curves are calibrated from liquid interest rate products. For the EUR curves this includes money market securities, futures, FRAs, IONA swaps, basis swaps and interest rate swaps. The process is complicated, however, by changes to the modelling principles around calculating the expected forward rates. These forward rates must be conditional on the EONIA rates used for discounting.

Dual currency pricing of cross currency swaps

Historically, cross-currency swaps were priced based on a single interest rate curve for each currency, a cross-currency basis spread and the current spot foreign exchange (FX) quote. Depending on the currency pair, different methods of calibration would be used to take advantage of the most liquid markets and quotes (for example, cross-currency swap versus FX forwards). Dual-curve pricing of cross-currency swaps adds challenges in terms of the relationship between the appropriate discount curves, projection curves and cross-currency basis.

Figure 2 below shows the process flow for calibrating interest rate curves for valuing a US$/euro fixed/floating cross-currency swap. The euro leg is discounted using the Eonia curve. The US$ leg would be projected using the cross-currency basis adjusted LIBOR interest rate curve and discounted using the Fed funds curve. The calibration process shown here is simplified. The calibration and pricing processes have significant implications for the hedging and risk management of these products and need to be carefully thought through.

Figure 2: Cross-currency curve construction in a dual-curve valuation framework

A new generation of interest rate modelling is evolving. An approach based on dual-curve pricing and integrated CVA has become the market consensus. There is compelling evidence that the market for interest rate products has moved to pricing on this basis, but not all market participants are at the stage were existing legacy valuation and risk management systems are up to date. The changes required for existing systems are significant and present many challenges in an environment where efficient use of capital at the business line level is becoming increasingly important.

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