PYBOR

PYBOR is a multi-curve interest rate framework and risk engine based on multivariate optimization techniques, written in Python.

Please refer to the Jupyter notebook for the overview of main features.

Features

• Modular structure allows to define and plug-in new market instruments.
• Based on multivariate optimization, no bootstrapping.
• Supports arbitrary tenor-basis and cross-currency-basis relationships between curves, as long as the problem is properly constrained.
• Risk engine supports first-order (Jacobian) approximation to full curve rebuild when bumping market instruments.
• Supports the following curve optimization methods:
  • Linear interpolation of the logarithm of discount factors (aka piecewise-constant in forward-rate space)
  • Linear interpolation of the continuously-compounded zero-rates
  • Cubic interpolation of the logarithm of discount factors

Curve naming conventions

For the purpose of this project, the curves are named in the following way:

Projection curves

• USD.LIBOR.3M refers to USD BBA LIBOR reference rate with 3 month tenor
• GBP.SONIA refers to overnight GBP SONIA compound reference rate
• USD.OIS refers to overnight USD Federals Fund compound reference rate

Mono-currency discounting curves

In a mono-currency context, the reference rates above can be used also for discounting (e.g. USD.OIS curve used for discounting of collateralised USD trades and USD.LIBOR.3M curve for discounting of unsecured USD trades).

Cross-currency discounting curves

In a cross-currency context, the naming convention for discounting curves is as follows:

<CurrencyOfCashFlow>/<RatePaidOnCollateral>

Few examples:

• USD/USD.OIS Discounting curve for USD cash-flows of a trade which is collateralised in USD, paying collateral rate linked to USD.OIS. Names USD/USD.OIS and USD.OIS refers to the same curve.
• GBP/GBP.SONIA Discounting curve for GBP cash-flows of a trade which is collateralised in GBP, paying collateral rate linked to GBP.SONIA. Names GBP/GBP.SONIA and GBP.SONIA refers to the same curve.
• GBP/USD.OIS Cross-currency discounting curve for GBP cash-flows of a trade which is collateralised in USD, paying collateral rate linked to USD.OIS.

Screenshots

Interpolation

Illustration of different interpolation modes which are supported by PYBOR:

Jacobian Risk

First-order risk (instrument-to-curve pillar sensitivity) which is used to transform risk views.

Curve Risk

Effect of bumping 20Y Libor 3M Swap rate on different curves:

TODO

• Automatic resolution of solve stages for global optimizer
• Proper market conventions (day count and calendar roll conventions)
• Smoothing penalty functions
• Risk transformation between different instrument ladders
• Split-curve interpolators (different interpolation method for short-end and long-end of the curve)
• Jacobian matrix calculation via AD (performance gain)