Short-rate models

Short-rate models are a class of mathematical models used in finance to describe the evolution of interest rates over time. In these models, the short rate, which is the interest rate for a very short period (often taken to be instantaneous), serves as the key variable. The models often aim to capture the dynamics of interest rates to assist in pricing fixed income securities, managing interest rate risk, and understanding the term structure of interest rates.

The Black–Derman–Toy (BDT) model is a term structure model used in finance to describe the evolution of interest rates over time. Specifically, it is a single-factor model that assumes that short-term interest rates follow a mean-reverting stochastic process. This model is particularly useful for pricing interest rate derivatives and managing the risk associated with interest rate changes.

The Black–Karasinski model is a mathematical model used in finance to describe the dynamics of interest rates. It is specifically used for modeling the evolution of the logarithm of interest rates, leading to log-normal distributions. The model is a variation of the popular Vasicek and Cox-Ingersoll-Ross (CIR) models, and it captures the behavior of interest rates with mean reversion, which is a characteristic of many interest rate processes.

The Chen model often refers to a specific framework or model in finance and economics developed by Xiangyu Chen and his colleagues, primarily used to analyze the implications of various factors on asset pricing, performance measurement, and risk assessment. It typically focuses on the interplay between macroeconomic variables, investor behavior, and asset returns.

The Cox-Ingersoll-Ross (CIR) model is a mathematical model used to describe the dynamics of interest rates. It is part of the class of affine term structure models and is particularly known for its ability to capture the behavior of interest rates in a way that ensures non-negative rates. The CIR model was introduced by economists David Cox, Jonathan Ingersoll, and Stephen Ross in the early 1980s.

The Ho–Lee model is a mathematical model used in finance to describe the dynamics of interest rates. Developed by Thomas Ho and Sang-Bin Lee in 1986, this model is notable for its simplicity and ability to handle the term structure of interest rates, making it useful for pricing various interest rate derivatives and managing interest rate risk.

The Hull-White model is a popular term structure model used in finance to describe the evolution of interest rates over time. Named after its creators, John Hull and Alan White, the model is particularly useful for pricing interest rate derivatives and managing interest rate risk. ### Key Features of the Hull-White Model: 1. **Single Factor Model**: The original Hull-White model is a single-factor model, meaning it relies on one state variable to describe the dynamics of interest rates.

The Rendleman–Bartter model, developed by Dale Rendleman and William Bartter in the early 1980s, is a financial model used to estimate the term structure of interest rates, particularly for zero-coupon bonds. This model is part of the broader class of term structure models, which seek to explain how interest rates vary with different maturities of debt instruments.

The Vasicek model is a popular mathematical model used in finance and economics to describe the dynamics of interest rates, as well as asset prices. Developed by Oldrich Vasicek in 1977, the model is particularly noted for its ability to capture the mean-reverting behavior of interest rates, which is a common characteristic observed in real-world financial markets. ### Key Features of the Vasicek Model 1.