Tuesday, May 9

PYBOR - multi-curve interest rate framework in Python

I have been recently working on a project PYBOR, a multi-curve interest rate framework and risk engine based on multivariate optimization techniques, written in Python (hence the name twist of a libor rate).

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

The entire project as well as the notebook above is available on GitHub.

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:
  • USDLIBOR3M refers to USD BBA LIBOR reference rate with 3 month tenor
  • GBPSONIA refers to overnight GBP SONIA compound reference rate
  • USDOIS refers to overnight USD Federals Fund compound reference rate

In a mono-currency context, the reference rates above can be used also for discounting (e.g. USDOIS curve used for discounting of collateralised USD trades and USDLIBOR3M curve for discounting of unsecured USD trades).

In a cross-currency context, the naming convention for discounting curves is as follows:
<CurrencyOfCashFlow>-<RatePaidOnCollateral>
Few examples:
  • USD-USDOIS Discounting curve for USD cash-flows of a trade which is collateralised in USD, paying collateral rate linked to USDOIS. Names USD-USDOIS and USDOIS refers to the same curve.
  • GBP-GBPSONIA Discounting curve for GBP cash-flows of a trade which is collateralised in GBP, paying collateral rate linked to GBPSONIA. Names GBP- GBPSONIA and GBPSONIA refers to the same curve.
  • GBP-USDOIS Cross-currency discounting curve for GBP cash-flows of a trade which is collateralised in USD, paying collateral rate linked to USDOIS.

TODO

  • Solve stages for global optimizer (performance gain)
  • 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)

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