## Swap Curve

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FinPricing offers the following curves for various currencies via API. All the interest rate curves have data points up to 50 years.

- OIS curves
- RFR (risk free rate) curves
- SOFR, €STR (ESTR, ESTER), SONIA, TONA, CORRA, AONIA, SARON curves
- IBORs (LIBOR, EURIBOR, TIBOR, CDOR, EONIA, etc.) fallback rate curves
- Swap rate curves
- Basis curves
- Spot rate or zero rate curves
- Forward rate curves
- Discount curves
- Inflation Swap rate (CPI, RPI, HICP) curves
- Nordic electricity futures curve
- VIX futures curve
- S&P 500 futures curve

1. Swap Curve Introduction |

Interest rate curves have many different types. Sometimes they are quite confusing. There are two main categories in the market: market observed interest rate curves and derived interest rate curves.

Market observable interest rate curves are mainly swap curves and bond curves. They consist of market observable quotations, such as bond prices, swap rates, basis swap spreads, interest rate futures prices, or deposit rates. Bond curves are the term structure of market quoted bond prices, while swap curves are the term structures of swap rates, basis swap spreads, or Eurodollar futures. Swap curves can be futher divided into base swap curves and basis swap curves. Normally the 3 month swap curve is the base curve as all the basis curves are quoted against it. The market observable curves cannot be used for valuation directly. Thus they need to be bootstrapped into the derived curves that are essential for asset pricing.

Derived interest rate curves are mainly yield curves. Yield curve is the term structure of interest rate yields-to-maturity. Yield curve is widely regarded as the best proxy for risk-free curve and benchmark curve. Liquidity of underlying instrumennts is crucial. Since the swap market is a very liquid market with narrow bid-ask spreads and a wide selection of maturities, yield curves derived from swap curves offer several advantages over government curves (e.g., treasury yield curve). With the supply of government bond issues declining, yield curves are mainly bootstrapped from swap curves.

Zero rate curves, also called spot rate curves, are special and dominant type of yield curves. By definition, a zero rate curve is the term structure of the yields-to-maturity of zero coupon bonds. Given a zero rate, we can derive discount factor easily as:

D(t,T) = exp (-rT)

where D(t,T) is the discount factor at time t for maturity T and r is the continuously compounded zero rate or spot rate between time t and T.

Due to the simple relationship between zero rates and discount factors, zero rate curves become dominant valuation vehicle in the market. If people in financial market talk about interest rate curves, yield curves, zero rate curves, or spot rate curves, they actually mean the same thing. Without loss of generality, we will use zero rate curves representing all yield curves. Zero rate curves also have several different types. A zero curve derived from a base swap rate curve is used for discounting, so it is equivalent to discount curve. Similarly, a zero rate curve bootstrapped from a basis swap curve is used to compute forecasting rates. Understanding interest rate curves is essential in financial markets.

2. Swap Curve Data |

FinPricing provides more than 100 swap rate curves. The most commonly used swap curves are SOFR, LIBOR, ESTR, EURIBOR, OIS curves displayed below:

SOFR Swap Curve:

ValuationDate | Instrument | Tenor | Type | Value |
---|---|---|---|---|

2023-01-18 | USD.SOFR.30YR | 30YR | Swap | 2.88985 |

2023-01-18 | USD.SOFR.3WK | 3WK | Swap | 4.42412 |

2023-01-18 | USD.SOFR.4YR | 4YR | Swap | 3.35453 |

2023-01-18 | USD.SOFR.40YR | 40YR | Swap | 2.67518 |

2023-01-18 | USD.SOFR.5YR | 5YR | Swap | 3.21542 |

2023-01-18 | USD.SOFR.50YR | 50YR | Swap | 2.46311 |

2023-01-18 | USD.SOFR.6YR | 6YR | Swap | 3.14085 |

2023-01-18 | USD.SOFR.7YR | 7YR | Swap | 3.09991 |

2023-01-18 | USD.SOFR.8YR | 8YR | Swap | 3.07653 |

2023-01-18 | USD.SOFR.9YR | 9YR | Swap | 3.06922 |

2023-01-18 | USD.SOFR.1MO | 1MO | Swap | 4.48735 |

2023-01-18 | USD.SOFR.2MO | 2MO | Swap | 4.54812 |

2023-01-18 | USD.SOFR.3MO | 3MO | Swap | 4.63321 |

2023-01-18 | USD.SOFR.4MO | 4MO | Swap | 4.69833 |

2023-01-18 | USD.SOFR.5MO | 5MO | Swap | 4.74211 |

2023-01-18 | USD.SOFR.6MO | 6MO | Swap | 4.77626 |

2023-01-18 | USD.SOFR.9MO | 9MO | Swap | 4.82051 |

2023-01-18 | USD.SOFR.1DY | 1D | Cash | 4.31016 |

2023-01-18 | USD.SOFR.12MO | 12MO | Swap | 4.78401 |

2023-01-18 | USD.SOFR.10YR | 10YR | Swap | 3.06995 |

2023-01-18 | USD.SOFR.12YR | 12YR | Swap | 3.08309 |

2023-01-18 | USD.SOFR.15YR | 15YR | Swap | 3.10302 |

2023-01-18 | USD.SOFR.18MO | 18MO | Swap | 4.44481 |

2023-01-18 | USD.SOFR.1WK | 1WK | Swap | 4.31235 |

2023-01-18 | USD.SOFR.2YR | 2YR | Swap | 4.08508 |

2023-01-18 | USD.SOFR.20YR | 20YR | Swap | 3.07865 |

2023-01-18 | USD.SOFR.25YR | 25YR | Swap | 2.98435 |

2023-01-18 | USD.SOFR.2WK | 2WK | Swap | 4.33431 |

2023-01-18 | USD.SOFR.3YR | 3YR | Swap | 3.60507 |

3-Month LIBOR Swap Curve:

ValuationDate | Instrument | Tenor | Type | Value |
---|---|---|---|---|

2023-01-18 | USD.QT.3MO | 3MO | Cash | 4.72976 |

2023-01-18 | USD.QT.50YR | 50YR | Swap | 2.73604 |

2023-01-18 | USD.QT.6YR | 6YR | Swap | 3.42161 |

2023-01-18 | USD.QT.7YR | 7YR | Swap | 3.38175 |

2023-01-18 | USD.QT.8YR | 8YR | Swap | 3.35815 |

2023-01-18 | USD.QT.9YR | 9YR | Swap | 3.35125 |

2023-01-18 | USD.QT.1F | 1F | Future | 94.983 |

2023-01-18 | USD.QT.5F | 5F | Future | 96.082 |

2023-01-18 | USD.QT.10YR | 10YR | Swap | 3.35291 |

2023-01-18 | USD.QT.11YR | 11YR | Swap | 3.35762 |

2023-01-18 | USD.QT.12YR | 12YR | Swap | 3.36511 |

2023-01-18 | USD.QT.15YR | 15YR | Swap | 3.38665 |

2023-01-18 | USD.QT.2YR | 2YR | Swap | 4.35441 |

2023-01-18 | USD.QT.20YR | 20YR | Swap | 3.361653 |

2023-01-18 | USD.QT.2F | 2F | Future | 94.961 |

2023-01-18 | USD.QT.6F | 6F | Future | 96.582 |

2023-01-18 | USD.QT.3F | 3F | Future | 95.095 |

2023-01-18 | USD.QT.4F | 4F | Future | 95.485 |

2023-01-18 | USD.QT.25YR | 25YR | Swap | 3.26825 |

2023-01-18 | USD.QT.3YR | 3YR | Swap | 3.88016 |

2023-01-18 | USD.QT.30YR | 30YR | Swap | 3.17435 |

2023-01-18 | USD.QT.4YR | 4YR | Swap | 3.63413 |

2023-01-18 | USD.QT.40YR | 40YR | Swap | 2.95841 |

2023-01-18 | USD.QT.5YR | 5YR | Swap | 3.49621 |

Swap curves can be categoried into swap rate curves, basis curves, and OIS curves. Usully a swap rate curve is also called a base curve or standard curve or 3 month swap curve. The reason for calling 3 month curve as base curve is all the other (basis) curves are quoted against it.

**Swap Rate Curve**

The swap rate curve consists of a set of the most liquid and dominant interest rate products for certain time horizons. Normally the curve is divided into three parts. The short end of the term structure is determined by deposit rates. The middle part of the curve uses Eurodollar futures or FRAs. The far end is given by mid swap rates.

**Basis Curve**

The market quote of a basis spread is the spread over the associated 3 month reference rate. Typical basis curves are 1 month, 6 months, 12 months, Prime, FedFun, and OIS.

Check 1 month basis curve sample data here.

**OIS Curve**

In 2017 financial crises, people realized that credit risk is not negligible. Since then, OIS curves became the market standard for discounting collateralized products. The reason often given for using the OIS zero rate as the discount rate is that it is derived from the Fed funds rate and the Fed funds rate is the interest rate usually paid on collateral. As such the Fed funds rate and OIS rate are the relevant funding rates for collateralized transactions. A typical OIS basis curve looks like:

Check OIS curve sample data here.

3. Yield Curve Data |

Most commonly used yeld curves, called zero rate curves, are derived from swap curves. The zero rate curves are the benchmark interest rate curves and funding curves in the market.

**LIBOR Yield Curve for Discounting**

A yield curve or zero rate curve derived from a base swap rate curve is used for LIBOR discounting in the market. Therefore, it is equivalent to discount curve.

Check Libor yield curve.

**One Month Yield Curve**

Basis yield curve bootstraped from basis swap curve can be used to calculate forecasting float rate.

Check Basis yield curve.

**OIS Yield Curve**

OIS yield curve is the new market standard for discounting.

Check OIS yield curve.

4. Related Topics |