# 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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### How to exactly sample two Cox-Ingersoll-Ross processes that share the same Brownian motion

Lets say that I have two CIR processes \begin{align} dX_t &= b_x(a_x - X_t)dt + s_x \sqrt{X_t}dB_t \newline dY_t &= b_y(a_y - Y_t)dt + s_y \sqrt{Y_t}dB_t \end{align} And I want to sample from ...
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### Calibration for CIR Model Discretization for Predictor Corrector and Milstein method

I'm new to Quantitative Finance. I've data which I need to fit a CIR model and estimate its parameters. $dX_{t+1} = a(b-X_{t})dt + \sigma \sqrt{X_t}dW_{t}$ While I can fit and obtain ...
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### Binomial tree with time dependent volatility

In the Cox approach for binomial trees, the up move $u$ and down move $d$ are given by: $u = e^{\sigma \sqrt{dt}}$ and $d = e^{-\sigma \sqrt{dt}}$. In this approach the volatility $\sigma$ is assumed ...
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### Estimating market price of interest rate risk under CIR model

My goal is to find the market price of risk associated with the interest rate under the CIR model whose stochastic differential equation under the physical measure is given: \begin{eqnarray}\label{...
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### Nonlinear Constrained optimization for a CIR model

I want to calibrate a CIR model which is commonly used to model the evolution of interest rates. Briefly speaking, we know that its dynamics is of the form dr_t = \kappa (\theta - r_t)...
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### Including Exogeneous variables in short rate models

I am trying to use short rate models (e.g. Vasicek, CIR or Hull-White) to forecast next one or two months yield curve. In this context, is there a way that I can include some exogenous economic or ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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, ...
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Is there a closed-form (analytical) solution for the Cox-Ingersoll-Ross SDE $$dr_t=k_r(\theta_r-r_t)dt+\sigma_r\sqrt{r_t}dW_t\tag{1}$$ ? Notice that $\{r_t\}$ is our ...