Hyperbolic Framework: OIS Discounting + IBOR Forward Rates
Hyperbolic Framework: OIS Discounting + IBOR Forward Rates
1. Introduction
Prior to the 2007-2008 global financial crisis, the interest rate derivatives pricing field universally adopted a single-curve framework: using the same curve fitted from LIBOR/SHIBOR rates for both cash flow discounting and forward rate derivation. The crisis exposed two critical issues:
- Credit risk conflation: LIBOR/SHIBOR incorporates bank credit risk, making it potentially underestimate true collateral costs when used for discounting.
- Hedging rate mismatch: Most trades were governed by CSA agreements with collateral interest paid at overnight rates, yet still discounted using IBOR curves.
To resolve these contradictions, the market introduced the "dual-curve" framework: OIS Discounting + IBOR Forward Rates.
2. Background Concepts
OIS (Overnight Index Swap)
A swap contract referencing overnight rates (e.g., SOFR, EONIA, FR007), where the floating leg pays compounded overnight rates against a fixed rate.IBOR (Interbank Offered Rate)
Rates representing unsecured interbank lending costs, such as LIBOR, EURIBOR, and SHIBOR.
Under CSA agreements, counterparties pay interest on margin balances at overnight rates. Therefore:
- Cash flow discounting should use the OIS curve
- Forward rate derivation still requires the IBOR curve
3. Framework Construction
3.1 OIS Discount Curve
Underlying instruments
- OIS swap quotes
- Collateralized repos (e.g., FR007 repos)
- Short-term government bond repos
Bootstrapping procedure
- Derive discount factors from instrument quotes
- Ensure curve smoothness and arbitrage-free conditions
Output
- A discount curve for calculating present value of any cash flow:
- A discount curve for calculating present value of any cash flow:
3.2 IBOR Forward Curve
Underlying instruments
- FRAs (Forward Rate Agreements)
- Short-term IRS (Interest Rate Swaps)
- Eurodollar/SHIBOR futures
Pricing condition
- Price these instruments using the OIS discount curve from Section 3.1
Bootstrapping
- Derive IBOR forward rates sequentially
- Ensure instrument pricing matches market quotes
4. Pricing Principles
For a cash flow at time :
- For fixed cash flows:
- For floating cash flows (IBOR-linked):
where comes from the IBOR forward curve.
5. Practical Considerations
Hedging & CSA
- CSA agreements typically reference OIS rates for margin interest.
- Using OIS discounting aligns with actual hedging costs.
Data sources & liquidity
- OIS curves require sufficient maturity coverage; bond futures/repos can supplement long-end data.
- IBOR curves have abundant hedging instruments but require attention to bid-ask spreads.
Systems & tools
- Require dual-curve bootstrapping engines (QuantLib, Murex, etc.).
- Standardize historical/real-time data sources, curve interpolation, storage formats, and rebuild frequency.
6. Advantages & Challenges
6.1 Advantages
- Consistent discounting: Matches CSA collateral costs for proper risk pricing.
- Risk separation: OIS reflects "risk-free" rates while IBOR captures bank credit spreads.
- Pricing accuracy: Eliminates single-curve biases from discounting/hedging rate mismatches.
6.2 Challenges
- Data coverage: Some markets lack liquid OIS products, requiring models/alternatives for long-end.
- Computational complexity: Dual-curve bootstrapping demands higher performance.
- System upgrades: Legacy architectures need modifications for multi-curve support.
7. Chinese Market Application
- OIS equivalent → FR007 (7-day repo rate)
- IBOR equivalent → SHIBOR (3M/6M tenors)
China's interest rate derivatives market primarily uses FR007 for discounting and SHIBOR for forward curves. Post-LPR reform, some institutions experiment with LPR-based forward curves while maintaining FR007 discounting.
8. Conclusion
The dual-curve framework has become the global standard: "OIS discounting" ensures consistency while "IBOR forwards" preserve underlying pricing conventions. China's FR007+SHIBOR implementation offers liquidity, hedging, and regulatory capital advantages. As instruments and data governance improve, this framework will further solidify and expand to more derivatives pricing scenarios.