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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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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How can we compute copula functions by using Fast Fourier transformation?

Q1. If a copula is expressed in terms of its moment generating function then how can this copula can be computed by using Fast Fourier Transformation? Q2. Can we use copula to evaluate spread option ...
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Is non-stationarity an issue during copula estimation?

In this paper (1), on page 14 (section 4), the author presents an empirical experiment on the computation of a copula through the use of kernels. To do so, he uses the following stochastic process (...
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Joint Distribution of Correlated Variables with Markov Switching

I am modeling a portfolio of correlated assets whose lack of liquidity can be reasonably described by a Markov-switching model. That is, not only is movement size among assets correlated, but so is ...
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Practical Use of Copulas and Sample Generation

I'm currently studying Copulas. However, i did not understand something. The very basic phases of Copula fitting is as follows i assume; Model each samples distribution with a parametric(or non-...
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'GARCH - extreme value theory - copula' approach to estimate risk measures in R

I'm reading about this approach of using GARCH-EVT-copula methodology to separate univariate and joint estimation and then estimate for example VaR and ES. I wanted to try something similar, but my ...
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233 views

Marginal Distribution using GARCH model: How to do inverse probability transform?

I have $n$ return series. I fitted AR(1)-GARCH(1,1) to each return series. Then used probability integral transform, PIT(residuals), to transform the residuals to have a uniform distribution. Then I ...
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370 views

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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133 views

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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92 views

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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126 views

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 ...
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Alternatives to Elliptical and Archimedean copulas for modelling dependency structure between stocks

Except from the well-know and well-documented Elliptical (i.e. Gaussian, Student-t) and Archimedean (i.e. Frank, Clayton, Gumbel) copulas used to model the dependency structure between stock returns, ...
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trying to better understand copulas

This topic is dense with notation that makes things a bit confusing. But is this the correct interpretation? Suppose we have two jointly distributed random variables – $X$ and $Y$ – of arbitrary (but ...
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129 views

Bivariate risk neutral distribution through copula

I want to build a bivariate risk-neutral distribution from two liquid assets (A and B) through the use of a copula. As A and B are liquid, I have the marginal distributions from the market. All I have ...
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Suggestions to build a copula to price Quanto options

I am willing to price a quanto option through the use of copulas. I will follow the following procedure: 1) Obtain the marginal distributions of the underlying asset and the exchange rate from ...
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311 views

Problems in computing VaR with GARCH-GPD-copula approach

I use a time-varying Gaussian copula (with GARCH-filtered standardized residuals modeled semiparametrically with Gaussian kernel interior and GPD tails, i.e. generalized pareto distributed) to ...
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68 views

False warning messages in R, is it possible?

I'm modeling GARCH-filtered standardized residuals via semiparametric distribution with Gaussian kernel and GPD (generalized pareto distribution) tails with thresholds at 5% and 95%. For some series I'...
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132 views

Estimating time-varying tail dependence for Archimedean copulas

Patton (2006) defines the upper tail dependence coefficient for a time-varying bivariate SJC copula as $$\tau^u_t=\Lambda \left(\omega_u + \beta_u \tau^u_{t-1}+\alpha_u \frac{1}{10}\sum^{10}_{i=1}|u_{...
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134 views

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 = mvdc(copula=...
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577 views

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 identify ...
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319 views

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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Gaussian Copulas: My Marginal Distribution Includes Negatives but My Copula is Non-Negative?

Attempting Copula in R for Stock Returns, Bond Returns, and Inflation Rates. This is my first attempt with Copulas but I have looked many places and cannot determine what I'm doing wrong. My Marginal ...
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Hierarchical copula vs. vine copula

Vine copulas are a sequential cascade of bivariate copulas meant to capture the hierarchical structure in the dependence structure of random variables. How does this relate or differ from the concept ...
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Advantage of copula over estimation based on historical data

It seems to me hard to intuitively understand the concept of copulas and their advantages. For example, why would it be better to estimate value at risk of portfolio by modelling its asset returns ...
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Patton Copula model code and significance of parameters

I am trying to implement a copula model using the Patton (2006) Matlab code. I am unable to determine the significance of the parameters. Does anyone know how i can generate the standard errors from ...
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65 views

Gaussian copula: contract price

The hazard rates for A and B are 1% and 2% respectively. A contract pays you $1 if A defaults earlier than B. What is the correlation that minimizes the price of the contract? I have not studied the ...
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161 views

simulating from GARCH model with copula innovations

I have a GARCH model fitted on stock returns as: ...
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119 views

Sampling from conditional copula

Let C be a Gaussian or Student copula and F1,...,Fd the empirical margins. $C(u)=F(F_1(u_1)^{-1},...F_d(u_d)^{-1})$ I know how to draw from C and get $(u_1,...,u_d)$ Imagine that I know $u_1$ and $...
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266 views

How to write time-varying functions in R? Applied example

Let's say I want to use a Gaussian copula $$C_{R_t}(\eta_1, ..., \eta_n) = N_{R_t}(N^{-1}(\eta_1), ...,N^{-1}(\eta_n))$$ with a time-varying correlation matrix $R_t$. Through DCC we model the ...
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128 views

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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97 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 ...
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Help me understand copula

I have been spending dozens of hours trying to understand what copula is and how it works, but still I am not able to get my head straight. I am reading the wiki page https://en.wikipedia.org/wiki/...
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Portfolio VaR using a gaussian copula

I have a portfolio consisting of bonds, stocks, fx and property. I'm using Monte Carlo to estimate the VaR of this portfolio. To generate the forward-looking interest rate risk factor scenarios I use ...
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Value the claim $(X-K)1_{X>K}1_{L<Y<U}$

Consider two correlated assets $X$ and $Y$ with marginals $f_X$ and $f_Y$ and linear correlation coefficient $\rho$. Assume a Gaussian copula, $C_{X,Y}(x,y,\rho)$, can approximate the joint CDF well ...
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Does the $t$-copula or Clayton copula capture the dependence structure of empirical returns better?

Which copula captures the dependence structure of empirical asset returns better? the $t$-copula, which has symmetric tail dependence, or the Clayton copula, which has asymmetric tail dependence, and ...
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How to implement copula portfolio optimization?

This a reference request for any python notebooks, packages or blogs that teach how to do asset allocation using multivariate copulas. How can copula portfolio optimization actually be implemented in ...
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Problem in copula fitting

I have returns of 2 stocks: stock1 and stock2. And I want to fit pair copula. I use this libraries library(VineCopula) library(copula) then I select an ...
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65 views

Using variance reduction on only some models

I am pricing options with some copula based models using Monte Carlo simulation. I was looking up some easily implementable variance reduction methods and decided on antithetic variates. However, ...
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Positive quadrant dependence

Gijbels et. al. Positive quadrant dependence tests for copulas (25 page PDF) What could potentially be application of this concept in economics and finance? From what I read from a couple of papers, ...
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How to fit a skew normal/t copula to data?

I want to use either the skew normal copula or the skew t copula with a time-varying correlation matrix. But so far I haven't found any way to implement this either in R or Matlab. Would anyone be ...