Journal of Economic Surveys

Abstract

Interest-rate modelling is often taught as a catalogue of competing stochastic equations, obscuring why models were created and why modern sell-side desks use several simultaneously.This survey reorganises the field around five layers of a pricing architecture: curve construction; arbitrage-free dynamics; volatility-smile representation; collateral, multi-curve and risk-freerate conventions; and numerical implementation.Within this framework, the progression from Vasicek and Cox-Ingersoll-Ross to Hull-White, HJM, the LIBOR market model, SABR and post-LIBOR forward market models is interpreted as a sequence of responses to new products, quotation practices, computational constraints and market institutions-not as a tournament won by one equation.We derive the core equations, compare the principal model families, connect calibration choices to hedging instruments, and map models to major rates products and XVA applications.Particular attention is paid to risks concealed by exact vanilla calibration, including correlation, conditional curve dynamics, future smile behavior and numerical error.An open Python/C ++ companion repository provides reproducible illustrations for selected stages.The resulting framework offers a systematic introduction for new quantitative analysts and a practical reference for researchers, traders, model developers and validators."An interest-rate model is not merely an equation for rates; it is a disciplined account of which market quantities must agree today, how they may evolve tomorrow, and which risks remain when calibration is complete." Introduction: An Interest-Rate Model is a Pricing Architecture, not a Single EquationFew areas of quantitative finance contain so many famous models and so little agreement about what the word model denotes.A macroeconomist may use an interest-rate model to describe expectations, term premia, and monetary-policy transmission.A bond investor may want a parsimonious representation of level, slope, and curvature.A derivatives trader needs prices and hedge ratios consistent with today's curve and option market.A model-validation team asks whether the implementation is stable outside calibration instruments.An XVA engine needs joint future scenarios under collateral and netting conventions.These are related problems, but they do not have the same state variables, probability measure, loss function, or standard of success.The distinction is especially sharp between buy-side and sellside modelling.Under the physical measure, an investor cares about forecasts and risk premia; under a pricing measure, a dealer primarily cares about replication, calibration,

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