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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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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What was the probability distribution used for Mortgage Backed Securities (MBSs) during the subprime crisis?

The probability distribution used for mortgage backed securities divided them into tranches. If tranch#1 was worth 10 million USD, they got paid in full while the rest got paid partially. Most of them ...
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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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how to generate time-varying copulas in r? [duplicate]

i want to generate data from a Time-varying copulas (dynamic coupula) in r, I tried to use D-vine copula
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Price a contingent claim with payoff $(S_T-K)1_{\{S_T>K\}}1_{\{L\leq X_T\leq U\}}$

I'd like to price the following contingent claim using a copula model. $$V_T = (S_T-K)1_{\{S_T>K\}}1_{\{L\leq X_T\leq U\}}$$ where $S$ and $X$ are two stock price processes which follow a non-flat ...
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81 views

Copula analytic formula for $max(S_T^1 - K, 0) 1_{\{L<S_T^2<U\}}$

Consider the payoff function $$ V_T = max(S_T^1 - K, 0) 1_{\{L<S_T^2<U\}} = (S_T^1 - K)1_{\{S_T^1 > K\}}1_{\{L<S_T^2<U\}}$$ where $S_T^1$ and $S_T^2$ are two GBM distributed stocks with ...
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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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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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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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101 views

Does Value-at-Risk have any mathematical equivalence to copulas?

Portfolio Value-at-Risk estimated using the copula approach often just means generating artificial data sampled from a parametric copula('s joint multivariate distribution) as a model fit over the ...
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47 views

Modelling dependance between the two uncorrelated variables using copulas

Are copulas good tool to model the dependence between the two uncorrelated variables. I have X and Y datasets with 260 data points each with Pearson's correlation=-0.06 and Kendall rank correlation=0....
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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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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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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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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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What is the R code for estimating copula parameters of BB1 with dim=2? And what's the code for gof test of BB1?

Kindly assist with R code for BB1 copula. Text books and research articles provide codes for clayton, gumbel, frank, normal and t copulas. However, I can't find code for BB1, the copula family ...
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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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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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765 views

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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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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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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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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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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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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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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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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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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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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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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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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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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163 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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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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simulating from GARCH model with copula innovations

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