Questions tagged [short-rate]
A short-rate model is a mathematical model that describes the evolution of interest rates
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Cox-Ingersoll-Ross
I am looking at a displaced CIR model and try to calibrate it to market data. I think my results looks reasonable but would like to sense-check with other studies. Does anyone know what "reasonable" ...
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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 ...
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simulating from the CIR++
I am looking at the CIR++ model which is described in interest rate models by Brigo et al, and was wondering on how to actually simulate from this model. The model reads
$$r_t=x_t+\phi(t),$$
where $...
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Concept Question Regarding Short Rate Model
I have a conceptual question that needs help. Does anyone know whether the short rate model generate discount rate or forward rate?
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Timesteps in Vasicek model
When simulating stocks one can easily use GBM with only one random variable per simulation to create a new stock price in say 5 years, you don't need to create the whole asset paths if you don't need ...
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Zero Coupon Bond Forward Price
I'm currently working on the Coursera Financial Engineering and Risk Management course. In one of the questions I was asked to build a binomial pricing model for fixed-income securities. Specifically ...
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Callable bond price sensitivity to Hull-White volatility changes
I'm using classic Hull-White model for short term interest rate dynamic:
$$dr(t)=[\theta(t)-\alpha(t)r(t)]dt+\sigma(t)dW(t)$$
(Notation is quite intuitive, anyway I am using the same as Wikipedia ...
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CallableFloatingRateBond in QuantLib: just a matter of multiple inheritance?
I would like to know what are the issues related to a possible CallableFloatingRateBond class in QuantLib and to have some hints on implementation.
My (very ...
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Basic LIBOR curve question
I'm new to the quant finance and have a very basic question about LIBOR curve.
LIBOR is published every day for 4 different tenors (1M, 3M, 6M, 1Y), and each rate means how much annual interest ...
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Term Structure and short rates
If I have a term structure/yield curve given by:
$$f(t, T) = f(0, T) + σ^2t(T − \frac{t}{2}) + σB_t $$
and want to find the short/spot rate $r_t$, is this simply:
$$f(t,t) = f(0,t) + \sigma^2t(t-\...
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CIR model: is the short rate really non-central $\chi^2$ distributed?
Probably simple question. Consider the CIR (1985) model for interest rates
$$
dr = k(\theta - r)dt + \sigma \sqrt{r}dz
$$
Then it is known in closed form the conditional pdf $f(r(s),s|r(t),t)$ ($s \...
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For the Dothan model $E^Q[B(t)]=\infty$?
How can I show that for the Dothan short rate model We have $E^Q[B(t)]=\infty$ ?
Where Dothan short rate model is " $dr_t=ar_tdt+\sigma r_tdW_t$ ".
I appreciate any help.
Thanks.
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Ho and lee derivation for short rates model
A silly question that is bugging me. I am working my way through Baxter and Rennie (again) and I am getting my wires crossed on the short rate models in particular the straight forward Ho and Lee ...
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Forward rates formulae
I am now working with forward rates and have somehow been asked to use an "intuitive" formula for forward rates.
$$ \frac{F(0,s,T)}{F(0,t,T)} = \frac{F(s,s,T)}{F(s,t,T)} $$
I can understand the ...
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Solving the Jamshidian Zhu (1997) PCA short rate model
This is my first time posting a question. I have very limited experience in the field of stochastic calculus and interest rate modelling. I have been tasked with implementing the short rate model ...
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Black–Karasinski - Market Price of Risk
In the past I have calibrated simple short rate models to the term structure by using maximum likelihood to get the parameters of the Vasicek/CIR sde, and then use the ZCB formula and the current ...
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How to price zero coupon bonds with short term rates model?
I want to find the price of Zero coupon bond given a short rate model.
I think about Merton, Vasiceck, CIR, Ho & Lee models.
1) Given a simulation of $r_t$ how can I calculate $ P(t,T) = \mathbb{...
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HJM simulation problem
I'm trying to simulate a 3-factor HJM model. I got the algorithms from Glasserman book. In my case, I have $3$ maturity:$ 0.25y, 0.5y, 0.75y$. So my time grid is: $t_0=0,t_1=0.25,t_2=0.5,t_3=0.75$.
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