A copula is a multivariate distribution with uniform marginal distributions. Copulas are mostly used to represent/model the structure of dependence between random variables, separately from the margins.

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Copula models and the distribution of the sum of random variables without Monte Carlo

There is a vast literature on copula modelling. Using copulas I can describe the joint law of two (and more) random variables $X$ and $Y$, i.e. $F_{X,Y}(x,y)$. Very often in risk management (credit ...
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copula-marginal algorithm

has there been any interesting work or advances on the copula-marginal algorithm (CMA) as proposed by Attilio Meucci. I am unable to find anything on the web other then the original article, here is ...
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Is there a copula that can estimate negative tail dependence?

I have encountered numerous copula estimators that can estimate time-invariant and time-varying linear and non-linear correlations on the interval $[-1,1]$, and these estimators are fully consistent ...
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Generate correlated random variables from Normal and Gamma distributions

I want to generate a random vector $z$ of dimension $k+m$ with some given correlation matrix $\Sigma$, such that the first $k$ elements of the vector are distributed normally and the last $m$ elements ...
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Simulate (imaginary) asset prices using random numbers that follow a Frank Copula

I didn't understand how to simulate asset prices by using non normal random numbers. I am assuming that it would be incorrect to use the standard Geometric Brownian Motion, since it is based solely ...
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Portfolio VaR with Copula?

Let the portfolio be given by: $$X=X_1+X_2$$ $(X_1,X_2)$ are dependent through a Copula function $C(u_1,u_2)$, such that the joint distribution is given by: $$F(x_1,x_2)=C(F(x_1),F(x_2))$$ What is ...
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Estimation of ranks of log-returns via copula

I have successfully chosen and estimate a copula for the ranks of the log-returns of my actions. My question is, since I have worked with the ranks instead of directly the log-returns (in order to be ...
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Copulas simply explained

I try to understand the basic idea of copulas, however I am still struggling and hope that someone can help me. I understood that in general a copula is a function which links several marginal ...
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Do I need a copula to accurately estimate the VaR of a portfolio of risky assets?

I need to estimate the daily VaR of a portfolio of various exposures in $n$ risky assets (say equity futures). The simplest approach, I think, would be to just estimate VaR from a multivariate normal ...
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Copula- AR simulation

I am estimating different copulas for bond factors that i also fit AR(1) models on. Now i would like to test and compare durations and VaRs with my model vs empiric. But how can i simulate AR(1) ...
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162 views

Convolution copula?

Using copula formulation for the following probability: $$\mathbb{P}(X\leq x,y_{1}\leq Y\leq y_{2})=\mathbb{P}(X\leq x,Y\leq y_{2})-\mathbb{P}(X\leq x,Y\leq y_{1})$$ ...
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Ito integrals and copulas

Let $X_{t}$ and $Y_{t}$ be two brownian motions and let their joint distribution be given by $F$. So in regularly correlated BM's where $dX_{t}dY_{t}=\rho dt$, we have a bivariate normal distribution ...
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Properties of a Symmetric Copula

I am working with the following copula, and have a few questions about it: $C(x,y) = xy + \theta (1-x)(1-y)xy$ Here $\theta \in [-1,1]$ and $x,y \in [0,1]$ First, I am trying to show this copula is ...
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how to apply a simple copula model

I'm playing around with copulas and wanted to generate some sample based on copula techniques in R. For this purpose I applied the following algorithm: Generate three sample vectors coming from ...
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1answer
130 views

Where does this copula come from?

In a paper I encountered the following notation $$P(Z\leq z,u\leq Y\leq v)=C(F_{Z}(z),F_{Y}(v)-F_{Y}(u))$$ However I don't see why this holds in relation to uniform random variables. Usually ...
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445 views

Empirical copula

I am trying to find the empirical copula linking two random variables $X$ and $Y$. I have some data available but it's limited with respect to the variable $Y$ and I am not convinced it's enough data ...
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What are the general limitations of Gaussian copulas with regards to the range of joint pdf's it can approximate?

I'm working with the nataf transformation - AkA Gaussian copula - and trying to establish the range of joint bivariate pdf's it can approximate, and what limitations it puts on those joint pdf's. I've ...
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Gaussian Time-varing copula in R

I want to estimate the parameters of time-varing Normal Copula using R. A bivariate Normal copula is defined as following: The dynamic equation of dependance parameter ρ is : So I need the ...
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Creditworthiness indicator for copula one-factor model

In this paper in equation 15 on page 261 dealing with one factor copula model, one is using creditworthiness indicator as one of a variables. It is defined as \begin{equation} Y_c = \sqrt{\rho_c} Z ...
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How to combine Gaussian marginals with Gaussian copula to obtain multivariate normals?

in the book "Numerical Methods and Optimization in Finance" I red the following: "Combining the Gaussian copula with Gaussian marginal gives a fancy way of expressing multivariate normals. However, ...
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Where can I find implementations of the time-varying copula (BBX) in Matlab or R?

I want to construct some time-varying BBX copulas, however, I found that patron's package does not contain time-varying BBX copula. Anybody know where I can download them?
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Simulate from time-dependent copula in MatLab using COPULARND

I would like to simulate from a t-copula with time-dependent correlation matrices. Say I have a series of 2000 correlation matrices (obtained from a copula-DCC model for data consisting of 2000 ...
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Gaussian Copula with t margins

I am trying to fit a Gaussian Copula with t margins to my data (log returns of two stocks). It has already worked for a Gaussian Copula with normal margins with: normcopula_dist = ...
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copulas and time series

Can anbody explain how Copulas are used to describe the dependency between, for example, the return on two different stocks? I understand how Copulas are the "glue" that binds the two marginals ...
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Time-Varying Copulas (GAUSS)

Could anyone suggest me how to begin with Time-varying Copulas or Stochastic Copulas? I'm looking for the GAUSS code, however it seems there are only MATLAB code available over the internet. I'm ...
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Effect of kernel smoothing on correlation

Instead of deriving correlation matrix on standardized returns (z scores) would it not be more accurate to kernel smooth the cdf and then norminv the cdf values for the return z score and then ...
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Fitting Copula and Simulation

I would greatly appreciate any insights into the problem described below, regarding using the data obtained from applying the functions of the 'rugarch' package into those from the 'copula' package. ...
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Relation of survival and non-survival Marshall-Olkin copula

Let us have two random variables $A$ and $B$ representing lifetimes of two elements of a system, where $A$ has cdf $F_A(x)$, $A \sim Exp(\lambda_1 + \lambda_{12})$ and $B$ has cdf $F_B(y)$, $B \sim ...
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Clayton-Gumbel (BB1) and Joe-Clayton (BB7) time-varying copulas

I'm trying to estimate parameters for Mixed Dynamic Copulas (Clayton-Gumbel and Joe-Clayton) Is there any code in MATLAB? Thanks for any help.
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How to fit a copula to empirical data?

There are numerous types of Copulas one can choose to fit empirical data. My question is wow to select the 'best' copula to fit the data. More specifically, let's assume empirical data ...
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Estimating Credit VaR using a simulation of joint defaults with a copula

I'm trying to follow the steps Malz gives to calculate Credit VaR using simulation of joint defaults with a copula. I'm having trouble understanding some of the steps. My math knowledge is rather ...
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Copula Value At Risk

Let's suppose I have two asset in my portfolio. I want to compute Copula Value At Risk. Can you help me? This is the code I wrote: ...