Short-rate models versus market models
Question
Interest rate models are usually grouped into two broad classes. What are they, and how do they compare?
Short answer
Short-rate models and market (forward-rate) models. Short-rate models (Vasicek, CIR, Hull-White, Black-Karasinski) specify the instantaneous rate, are low-dimensional and Markovian, and work well on trees and PDEs, but fit caps and swaptions only loosely. Market models (HJM, LIBOR market model) evolve the whole forward curve directly, calibrate naturally to quoted caplet and swaption vols and allow rich correlation, but are high-dimensional and usually require Monte Carlo.
Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q4.6, p.148; question and answer rewritten by SelfMadeQuant.com.
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- Expectations, Volatility, and the Shape of the Term Structure
- Exponential Growth, Decay, and Continuous Compounding
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