# Questions tagged [short-rate]

A short-rate model is a mathematical model that describes the evolution of interest rates

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### Differences between main classes of interest pricing derivatives models

There seems to be 3 main classes of interest rate pricing models: 1) Short rate models, 2) Heath Jarrow models and 3) Libor Market Model. My book doesnt seem to explain why we need all these different ...
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### QuantLib - Calibrating Hull White one-factor on negative interest rates

I have been working with the QuantLib Python package for some days now. Currently, I am working on calibrating a Hull White one-factor model for short rates. I am calibrating the model on the yield-...
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### Hull-White model: match between HJM framework and short model formulation

I need to show that the Hull-White model $$dr=(\theta(t)-ar)dt+\sigma dW^Q$$ corresponds to the Heath-Jarrow-Morton formulation $$df(t,T)=\alpha(t,T)dt+\sigma e^{-a(T-t)}dW^Q.$$ I obtained the drift ...
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### Negative Libor Simulation

Can LIBOR rates be simulated using short rate models? If no, what is the reason behind it? What is a simple model to simulate LIBOR rates? Especially in a negative rate environment.
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### Short rate models

On the short rate model in Wikipedia https://en.m.wikipedia.org/wiki/Short-rate_model Why is the first function, the P(t,T) given? This is not the short rate model this is generating prices for a ...
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### Obtaining the dynamics of the Vasicek model using Itô

Consider the following expression for the short-term interest rate $$r_t=r_0 e^{\beta t}+\frac{b}{\beta}\left(e^{\beta t}-1\right)+\sigma e^{\beta t}\int_0^te^{-\beta s}dW_s \tag{1},$$ which is ...
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