# Questions tagged [short-rate]

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

118 questions
Filter by
Sorted by
Tagged with
724 views

### 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" ...
348 views

### 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 ...
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 $... 1 vote 1 answer 99 views ### 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? 1 vote 1 answer 733 views ### 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 ... 1 vote 1 answer 1k views ### 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 ... 6 votes 0 answers 806 views ### 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 ... 2 votes 1 answer 785 views ### 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 ... 3 votes 3 answers 5k views ### 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 ... 1 vote 0 answers 129 views ### 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: $$f(t,t) = f(0,t) + \sigma^2t(t-\... 5 votes 1 answer 2k views ### CIR model: is the short rate really non-central \chi^2 distributed? Probably simple question. Consider the CIR (1985) model for interest rates$$ dr = k(\theta - r)dt + \sigma \sqrt{r}dz $$Then it is known in closed form the conditional pdf f(r(s),s|r(t),t) (s \... 1 vote 2 answers 602 views ### For the Dothan model E^Q[B(t)]=\infty? How can I show that for the Dothan short rate model We have E^Q[B(t)]=\infty ? Where Dothan short rate model is " dr_t=ar_tdt+\sigma r_tdW_t ". I appreciate any help. Thanks. 9 votes 2 answers 2k views ### Ho and lee derivation for short rates model A silly question that is bugging me. I am working my way through Baxter and Rennie (again) and I am getting my wires crossed on the short rate models in particular the straight forward Ho and Lee ... 1 vote 2 answers 512 views ### Forward rates formulae I am now working with forward rates and have somehow been asked to use an "intuitive" formula for forward rates.$$ \frac{F(0,s,T)}{F(0,t,T)} = \frac{F(s,s,T)}{F(s,t,T)}$$I can understand the ... 3 votes 1 answer 436 views ### 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 ... 2 votes 1 answer 443 views ### 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 ... 1 vote 1 answer 2k views ### 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{...
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: $t_0=0,t_1=0.25,t_2=0.5,t_3=0.75$. ...