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Questions tagged [short-rate]

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

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Ho and lee derivation for short rates model

A silly question that is bugging me. I am working my way through Baxter and Rennie (again) and I am getting my wires crossed on the short rate models in particular the straight forward Ho and Lee ...
Chinny84's user avatar
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1 answer
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How to get set the theta function in the Hull-White model to replicate the current yield curve

I want to calibrate the HW one factor model to current market data. How do I set the function $\theta(t)$ in $$ \mathrm{d}r(t) = \kappa(\theta(t)-r(t))\mathrm{d}t+\sigma\mathrm{d}W(t) $$ to ...
lbf_1994's user avatar
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2 answers
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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 ...
Trajan's user avatar
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CIR model: is the short rate really non-central $\chi^2$ distributed?

Probably simple question. Consider the CIR (1985) model for interest rates $$ dr = k(\theta - r)dt + \sigma \sqrt{r}dz $$ Then it is known in closed form the conditional pdf $f(r(s),s|r(t),t)$ ($s \...
Gabriele Pompa's user avatar
5 votes
1 answer
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Bond dynamics in Ho Lee model

The short rate in the Ho-Lee model is given by : $$dr_t=\left( \frac{df(0,t)}{dt} +\sigma^2t\right)dt + \sigma dW_t$$ I'm trying to find the bond dynamics given by : $$dP(t,T)/P(t,T)=r_tdt-\sigma(...
JohnLord's user avatar
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5 votes
2 answers
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Extensions of CIR

I could need some advice on extensions of the CIR model. The standard CIR reads $dr(t)=\kappa(\theta-r(t))dt + \sigma \sqrt{r(t)} dW(t)$. A possible extension, if we would like the short-rate to ...
A.Boh's user avatar
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4 votes
1 answer
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How to determine components of Affine Term Structure for an Ohrnstein-Uhlenbeck process?

I wonder how I can determine the components $A(t,T)$ and $B(t,T)$ for the zero-coupon bond price process $p(t,T)=e^{A(t,T)-r(t)B(t,T)}$? The components are defined in the following link: https://en....
Dreason94's user avatar
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4 votes
1 answer
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Vasicek model: joint simulation with discount factor

In Vasicek model, we have the following relation to get Discount factors given the value of short rate: $$P(t\,,T)={{e}^{A(t,T)\,-\,B(t,T){{r}_{t}}\,}}$$ So, Discount factors are known as soon as we ...
InnocentR's user avatar
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2 votes
1 answer
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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 ...
Giulio Carlo Venturi's user avatar
2 votes
2 answers
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Ho Lee model in Baxter&Rennie

I am currentyl reading Baxter&Rennie and I have a difficulty with understanding a derivation of formula for one function, $g(x,t,T)$ (this can be found on page 152 in the book). I know that there ...
siwy9's user avatar
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1 vote
2 answers
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Calculating the short rate from the discount curve

I'm currently looking at some code that implements the Hull-White model. As one of the inputs, the code accepts a table of discount factors at various dates. Time in Years Discount Factor 0 1 0.003 ...
user54908's user avatar
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