Questions tagged [copula]

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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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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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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Copula Correlations

It seems that the sample linear correlation coefficient $\hat{\rho}$ of samples generated by a copula that is parametrized by $\rho$ is unequal to $\rho$. For example, I construct a Normal copula with ...
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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 ...
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Simulating from a multivariate clayton copula

I am recently into copulas for finance, I've read several examples of how to generate dependent random variables with most kind of copulas. The problem for me is that all the books describe the case ...
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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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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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How to price this basket option?

Underlying assets are three global stock index : Eurostoxx 50, HSI, KOSPI 200 Maturity: 36 months with advanced redemption date in every 6 months if prices of indexes satisfy given conditions at each ...
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Why do we not use copula for forward starting options?

Why do we use copulas for spread options but do not use them to correlate random variables across time, such as in the forward starting option?
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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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Difference between Local Vol and Copula

Let's assume we have ATM European call on a basket of two stocks and price it with: 1) Multivariate Local Vol with constant correlation 2) Gaussian copula Assuming we use the same correlation ...
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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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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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How to sample from a copula in matlab

I have two random variables (say, X and Y). Each of these rv's are defined by their CDFs (CDF_X and CDF_Y). These CDFs were obtained empirically, so they are a "stair" graph. I also have a copula C ...
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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 P(Z\...
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Correlation sensitivity in multivariate $t$-copula for portfolio VaR of electricity futures using Kendall's tau-$b$ correlation matrix

My t-copula model captures the daily dollar returns of a portfolio of approximately 400 assets. I am curious if there's a generally accepted way to quantify the sensitivity of portfolio movements with ...
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(Reproducible example) Conditional returns in GARCH-EVT-Copula context (with R)

I'm estimating a time-varying correlation matrix for the normal copula using the rmgarch package from R. I've found this code in the rmgarch.tests folder. I use the ...
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Empirical bivariate copula when one variable is restricted

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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Portofolio optimization using ARMA-GARCH-EVT-Copula

I am currently trying to do some portfolio optimization by reproducing the methodology found in Sahamkhadam, Stephan & Östermark (2018) ("Portfolio optimization based on GARCH-EVT-Copula ...
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Convolution of Dependent Random Variables with Copulas

Lets say I have 2 different observations which are fitted to a parametric distribution. And lets say that they are dependent and can be modeled by one of the copulas. I want to calculate “a value” ...
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Historical quotes / prices of multiasset options

I am working on Lévy copulas, and I would like to try calibrating such techniques on real data. Where can I find quotes for multi-asset options? It could be exchange options or any other type of ...