Questions tagged [cox-ingersoll-ross]
The Cox-Ingersoll-Ross model is a one-parameter model describing the evolution of interest rates. A square root does not allow negative interest rates.
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Sampling change in the driving brownian motion of a CIR process
I have volatility driven by a CIR process:
$$\mathrm{d}v_t = \kappa (\bar{v}-v_t)\mathrm{d}t + \omega \sqrt{v_t}\mathrm{d}W_v\text{.}\tag{1}$$
I am working with several (complicated) approximations of ...
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1answer
63 views
Boundedness in Square Root Process
Consider the following square root diffusion price process:
$$ dV_t = \kappa_V(\bar{V}-V_t)dt+\sigma_V\sqrt{V_t}dW_t $$
It is my understanding that $\kappa_V$ is the rate at which the process reverts ...
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0answers
42 views
Derivation of the distribution for a CIR process
Where is it possible to find a complete derivation of the distribution of a CIR process?
There is a number of papers that claim that it is a noncentrical chi-squared distribution.
However, I cannot ...
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0answers
48 views
Implicit Scheme for Cox-Ingersoll-Ross Model PDE
I am considering the PDE for the price of a bond $V(r,t)$ with maturity $T$ under the Cox-Ingersoll-Ross model,
$$V_t+\frac12\sigma^2rV_{rr}+\nu(\theta-r)V_r-rV=0\quad r>0, t\in(0,1)$$
with ...
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22 views
How to initialize a UKF for term structures?
How I’can initialize a UKF (unscented kalman filter) in a CIR model for a Term structure of CDS spread?
Are the sample mean and sample covariance matrix the firsts values that I’ve to set in the ...
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1answer
226 views
Does my Python code correctly simulate realizations of a CIR process?
I've written the following function which should simulate realizations of a CIR process:
...
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1answer
72 views
Affine term structure for CDS
in papres such as https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2686284 (Exploring Mispricing in the Term Structure of CDS Spreads by Robert A. Jarrow, Haitao Li, Xiaoxia Ye, and May Hu) a ...
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0answers
159 views
Vasicek Short rate simulation - analytical formula vs discretization
I've been using two approaches to simulate Vasicek short rate paths and I'm wondering if one of them is more correct than the other.
The first approach is based on the analytical formula (see code ...
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2answers
91 views
How do I pricing a ZCB using CIR (Cox-Ingersoll-Ross) model
Please see the codes below
My question is about input parameters (a, b and sigma)and their calculation.
For the long term mean "b", do we use effective Fed Fund rates? or 3m T-bills?
Also, ...
1
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0answers
275 views
CIR model. Is there a closed-form solution or even a good proxy of analytical solution?
Is there a closed-form (analytical) solution for the Cox-Ingersoll-Ross SDE
\begin{equation}
dr_t=k_r(\theta_r-r_t)dt+\sigma_r\sqrt{r_t}dW_t\tag{1}
\end{equation}
?
Notice that $\{r_t\}$ is our ...
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votes
1answer
91 views
Choosing which interest rate model to go with?
I've been assigned with the task of modelling zero rate curve. I did it with two models: Vasicek and CIR. Looking at the two curves produced, I can see that one is closer to the observed curve than ...
