# SWAP Yield Curves

Swap -curve framework is based on OIS, FRA, SWAP Basis Spread and SWAP market prices.

Implementation uses calculated synthetic deposits, OTC FRA and SWAP rates to build curves which implement basis spread correctly from the beginning to end.

For example to build 6M Euribor Swap curve, first instrument that we can find is 6M Euribor Fixing or FRA0x6.

To apply deposit or shorter Euribor rates would implement basis spread incorrectly.

To create smooth short term curve, we need to create Synthetic deposits which are calculated from OIS forward rates and known OTC FRA rates.

To do that, we need to use backward extrapolation from the first known rate.

To solve short term interest rate, we use following equation:

To calculate Synthetic Deposit for unknown terms, we must approximate the ON-x basis by using polynomial function, which degree x (normally 3):

By solving coefficients (α,β,γ) we can get value for and synthetic deposits by using formula:

Last phase is to create SWAP curve by applying Synthetic deposits and OTC FRA rates by using discount calculation method.

Here light blue curve shows why this complex curve building matters and should be used in all valuations, if available.

Fully implemented curves

Following currencies and tenors are implemented at a moment.

To implement new curves require’s that all needed information is available, which is not a case always, e.g. SEK and NOK.

CAD

3M (1W – 15Y)EUR

1M (ON-50Y)

3M (ON-50Y)

6M (ON-50Y)

12M (ON-50Y)GBP

3M (ON-15Y)

6M (ON-15Y)USD

1M (ON-15Y)

3M(ON-15Y)

6M (ON-15Y)

12M (ON-15Y)