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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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61 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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Does someone share the code about the time-varying copula?

Are there libraries in R for estimating time-varying joint distributions via copulas? Does someone share the code about the time-varying copula?
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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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why we seldom see application of copula-garch model in macroeconomic

I find a lot of reference about copula-garch in finance market,but it seems that articles about copula-garch model in macroeconomic are rare.Is there any instrinc problem when it comes to ...
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Dependence modelling in Finance

we have copula as a function of cdf of random variables to describe how they are related to each other. I have one question in my mind that, how can we generate a new copula function?
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54 views

How to work with vine copula in R?

I have returns of 4 stocks: stock1, stock2, stock3, stock4. And I use R and library(VineCopula) to do: ...
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33 views

Extreme Value Simulation from Copulas with Monte Carlo

I'm trying to simulate the tail values from a multivariate distribution using copulas. I'm using Vine Copula package of R to derive the suitable copula for my data and I generate random samples out of ...
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41 views

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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40 views

Fit a copula model in R

I want to accomplish the task of creating an optimal portfolio of stocks, the yield between which is modeled using kopulas. And I have data: return of 4 stocks: ...
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52 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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88 views

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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1answer
37 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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46 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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139 views

Verifying two properties of the Clayton Copula

So I'm trying to verify the first two properties of a copula for the Clayton model. The first two properties being: $C(u_1,…,u_d)$ is non-decreasing in each component, $u_i$ The $i^{th}$ marginal ...
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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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1answer
85 views

Metric for measuring the “spread” of a copula

I am fitting copula to log returns data for my undergraduate thesis, and comparing the quality of the fit with AIC. One interesting thing that I found is that the Clayton copula, which has negative ...
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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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Any video lecture on copula function, a statistics concept for measuring dependence?

I have read the paper 'Coping with copulas' and it is a bit hard for me to read since it has lots of mathematical equations. So I am looking for any video lecture on this topic, copula function. I ...
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37 views

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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102 views

Verifying that the extreme value copula is indeed a copula

Given the extreme value copula as defined in Schölzel/Friederichs (2008), how does one verify that $\frac{\partial C(u_1, u_2)}{\partial u_1} \geq 0?$ For the LHS, I have $$\exp\left[\log(u_1u_2)A\...
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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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61 views

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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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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1answer
380 views

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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Non stationarity issue on copula estimation procedure

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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1answer
154 views

How to estimate a copula for time series

I want to estimate a copula for the innovations of two dependent time series (A and B). I have found no reference with a step by step on how to do this. I have only found summarized papers from which ...
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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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106 views

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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133 views

simulating from GARCH model with copula innovations

I have a GARCH model fitted on stock returns as: ...
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2answers
458 views

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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1answer
896 views

Gaussian vs Student Copula applied to finance

I would like to get your opinion on the following topic: I am comparing the behaviour of Gaussian and Student-t Copulas. I employ the follwing procedure: Simulate N=100,000 samples from a Student ...
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1answer
103 views

Is there a specific meaning to the word “convoluted” in maths or mathematical finance?

I'm reading about copula estimation in the book Financial Modeling Under Non-Gaussian Distributions by Jondeau, Poon and Rockinger. They say that full maximum likelihood can be difficult because of i) ...
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95 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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639 views

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 ...
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1answer
1k views

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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282 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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64 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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1answer
594 views

Forecasting conditional returns in DCC-GARCH-copula approach in R

anyone who could help me interpreting and modifying this code? I have a dataset and want to reserve the last 100 returns for out-of-sample analysis. After specifying and fitting the garch-spd-copula, ...
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1answer
500 views

(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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'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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1answer
219 views

Copulas and default probability

Assume a basket of 3 credits, each with some unconditional default probability ${q_i}(t) = \Pr [{\tau _i} \le t]$. Consider the joint CDF $H$ of the default times is given by $H(t,t,t) = \Pr [{\tau ...
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128 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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201 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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1answer
264 views

Bivariate Gaussian copula with exponential margins

I got little bit lost in the formulas. Assume to have two random variables distributed exponentially $X_i \sim Exp(\lambda_i)$ and $X_j \sim Exp(\lambda_j)$. Thus, the distribution functions are $...
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924 views

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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0answers
116 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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1answer
87 views

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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115 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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1answer
640 views

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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459 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 ...