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.

learn more… | top users | synonyms

0
votes
1answer
36 views

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 ...
3
votes
1answer
76 views

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 ...
0
votes
0answers
42 views

How to the compute the formula of Kendall's tau (please see this formula)

I am trying to compute the kendall's tau, but when facing the formula below, I don't know why the second line is this. Could anybody help me to interpret the reason to me? Thanks very much!
1
vote
0answers
24 views

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 ...
1
vote
1answer
77 views

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?
0
votes
1answer
122 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 ...
2
votes
1answer
71 views

Convolution copula?

Using copula formulation for the following probability: $$\mathbb{P}(X\leq x,y_{1}\leq Y\leq y_{2})=\mathbb{P}(X\leq x,Y\leq y_{2})-\mathbb{P}(X\leq x,Y\leq y_{1})$$ ...
2
votes
1answer
115 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 ...
0
votes
0answers
111 views

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: ...
2
votes
1answer
62 views

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 ...
2
votes
1answer
69 views

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 ...
4
votes
0answers
128 views

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 ...
11
votes
2answers
726 views

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 ...
4
votes
2answers
317 views

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 ...
4
votes
2answers
305 views

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 ...
3
votes
3answers
660 views

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 ...
9
votes
1answer
380 views

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 ...