korkomalli

Korkomalli, literally meaning "interest rate model" in Finnish, is a class of mathematical models used to describe the evolution of interest rates over time. They are used to price interest-rate derivatives, manage interest-rate risk, and perform scenario analysis.

Models are broadly categorized into short-rate models and forward-rate models. Short-rate models specify a stochastic process for the instantaneous short rate r(t) and derive all rates from it. Prominent examples include the Vasicek model (mean-reverting Ornstein–Uhlenbeck process), the Cox–Ingersoll–Ross (CIR) model (square-root diffusion ensuring nonnegative rates), and the Hull–White model (a time-dependent drift extension of Vasicek that can fit the current yield curve).

Forward-rate models describe the evolution of the entire forward rate curve, often within the Heath–Jarrow–Morton framework. The LIBOR Market Model (LMM) is a widely used forward-rate model for pricing interest-rate derivatives such as caplets and swaptions; Black’s model is used for certain products under simplifying assumptions.

Calibration and use: Parameters are estimated to fit observed market data, including the initial term structure, cap/floor volatilities, and swaptions. Models are used to price bonds and a wide range of derivatives and to run risk scenarios; some models are preferred for tractability or market-consistency for particular instruments.

Limitations: All korkomallit rely on assumptions and simplifications. They may struggle to capture regime changes or extreme movements, leading to model risk if misapplied or overextended.