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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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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475 views

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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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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Copula and Correlation

I am intending to use the copula distribution to generate a transition matrix for credit ratings. However, I am not sure exactly what correlation matrix to use. Can anybody help me
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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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130 views

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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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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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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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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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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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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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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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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120 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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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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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: ...
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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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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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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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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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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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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-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 ...