Coding Interest Rates: FX, Swaps and Bonds

This book documents the architecture, formulae and algorithms of the Python package rateslib v2.0. Rateslib is a state-of-the-art fixed income and FX library used by multiple academic institutions and hedge funds, for trade analysis and valuation. The key chapters covered by this book are: 1) Objectives and Overview: An introduction to the general architectural design of rateslib and its decisions regarding a dual Python/Rust programming paradigm. 2) Automatic Differentiation: A discussion about rateslib's choice to implement an unstructured and flexible forward mode AD system to propagate gradients natively through all of its objects at any point in the code. 3) Interpolation and Splines: Outlining official and practical algorithms used in its pricing objects. 4) Business Day Calendars: Rateslib's novel approach to the joint issue of business day mathematics, date rolling and cross-referenced FX settlement versus the FED monetary system. 5) Scheduling: Thorough analysis of building fully nuanced instrument schedules while conforming to UI expectations when minimal and potential conflicting schedule information can be provided by a user. 6) Curves: establishing the principles and mathematics of the way rateslib treats interest rate and hazard curves. 7) FX Rates: integrating forward mode AD into FX rates solving so that it can incorporated into the wider risk sensitivity calculations, including issues surrounding construction of arbitrage free FX Forwards systems. 8) Periods: A discussion on the components that are composited to Legs. 9) Legs: A discussion on the components that comprise the various elements of fixed income and FX instruments. 10) Instruments: Details of how Legs are combines to yield the common, tradable financial market instruments, including special information regarding those instruments, such as bond conventions and yield-to-maturity, etc. 11) Curve Solving: A mathematical description of a central rateslib object: the Solver, which coordinates parameter estimation for pricing objects and risk sensitivity. 12) Risk Sensitivity: A treatise on the formulae rateslib adopts to create performant and scalable analysis of both delta and cross-gamma relative to the calibrating market data. 13) FX Volatility: A complete description of rateslib's implementation of FX Options, delta-vol smiles and surfaces and SABR smiles and surfaces, including the incorporation of AD and how these objects fit into the general Solver model. 14) Cookbook: certain select examples.