13 votes
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Copula Correlations

This may not be a consequence of biased estimators or sampling error. I don't think it is a coincidence that $$\frac{6}{\pi} \arcsin\left(\frac{0.9}{2} \right) = 0.891457\ldots \approx 0.891$$ ...
RRL's user avatar
  • 3,650
8 votes
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How to price this basket option?

No offense but it will be much more complicated than what you think... I'm not even sure that you are familiar with risk-neutral pricing in the first place? I'll try to give you some clues. This ...
Quantuple's user avatar
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5 votes
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Why do we not use copula for forward starting options?

One is exploring forward volatility of a price of a single asset (joint distributions from within a process), the other explores correlation of two prices at the same time for two different ...
ir7's user avatar
  • 5,043
5 votes
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Simulating from a multivariate clayton copula

Since I think this is of interest for other people, I will post the approach I found: First, let $C_n(u_1,\ldots,u_n)$ be a $n$ - dimensional Clayton copula with generator function $F$ and inverse $F^...
simzoor's user avatar
  • 383
4 votes

Copula Correlations

I would guess you are calculating the maximum likelihood estimator: $ \hat{\theta} = \frac{1}{N} \sum (x_i - \bar{x}) (y_i - \bar{y}) $ instead of the unbiased estimator: $ \hat{\theta} = \frac{1}{...
Attack68's user avatar
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4 votes
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Gaussian copula calibration to option price

You did not mention it, but I think you also need to include the discount factor $D$ at the time $T$ of maturity of your option as a third variable. Denote the two interest rates as $r$ and $s$ and ...
g g's user avatar
  • 2,003
4 votes
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Optimal Hedging Ratio using Copula Models

Using a static copula model implies $\rho_{s,f,t}\equiv\rho_{s,f}$. In such case fitting a copula model to obtain $\rho_{s,f}$ is an overkill, since it can be estimated very simply by the empirical ...
Richard Hardy's user avatar
3 votes
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Any video lecture on copula function, a statistics concept for measuring dependence?

It's very difficult to find accessible material on copulas. I'm still struggling to understand them myself. While I haven't come across any videos that explain copulas well, I have found the following ...
Jabbermonkey's user avatar
3 votes
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Verifying that the extreme value copula is indeed a copula

Note that, you only need to show that \begin{align*} A\left(\frac{\log(u_2)}{\log(u_1u_2)}\right)-\frac{\log(u_2)}{\log(u_1u_2)}A'\left(\frac{\log(u_2)}{\log(u_1u_2)}\right) \ge 0, \end{align*} or, ...
Gordon's user avatar
  • 21.1k
3 votes
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How to sample from a copula in matlab

Suppose you have the copula $C(u_1,u_2)$, then you could compute the conditional copula $$c_{u_1}(u_2)=\frac{\partial C(u_1,u_2)}{\partial u_1} \; .$$ Now, you can generate a pair of independent ...
Raskolnikov's user avatar
  • 1,527
3 votes

Copula Correlations

This is an interesting observation that you have. The interesting part is "consistently smaller". The normal copula is based on a multivariate normal distribution. The correlation you get out is the ...
Richi Wa's user avatar
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3 votes
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Copulas and default probability

$$\text{Pr}[\tau_1>t,\tau_2\leq t,\tau_3\leq t]=\text{Pr}[\tau_2\leq t,\tau_3\leq t] - \text{Pr}[\tau_1\leq t,\tau_2\leq t,\tau_3\leq t]$$ $$\text{Pr}[\tau_2\leq t,\tau_3\leq t]=C(1,q_2(t),q_3(t))$...
M. Jeunesse's user avatar
  • 2,422
3 votes
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Bivariate Gaussian copula with exponential margins

$$C(u,v) = \mathbb{P}\left(X\leq N^{(-1)}(u),\quad \rho X + \sqrt{1-\rho^2}X^\perp \leq N^{(-1)}(v)\right)$$
M. Jeunesse's user avatar
  • 2,422
3 votes

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

I think you're asking about the different tranches in a multi-tranch mortgage securitization such as a Collateralized Mortgage Obligation (CMO) was sized, and what the math behind it was. This was ...
Si Chen's user avatar
  • 421
3 votes

How to include heteroscedasticity in copula modelling

I don't know if this will help solve your convergence issue, but a standard way of incorporating conditional heteroskedasticity in copula models is to build a copula-GARCH model. Each time series is ...
Richard Hardy's user avatar
3 votes

Beginner's resources on copulas and impact of correlation on loan defaults?

At the risk of arming you to create the next quant-apocalypse... The statement that the expected loss does not depend on correlation is typically the result of modelling a portfolio as a sum of ...
mike's user avatar
  • 31
2 votes

Fitting Copula and Simulation

You need to estimate or assume a marginal distribution of the (u,v). Lets say you assume normality (don't do this), you would be able to perform a rosenblatt-transformation, to perform the task you ...
dms_quant's user avatar
2 votes
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Relation of survival and non-survival Marshall-Olkin copula

Note that the survival copula $C_{\theta_A, \theta_B}(u, v)$ and the non-survival copula $C(u, v)$ are related by \begin{align*} C_{\theta_A, \theta_B}(\hat{u}, \hat{v}) = \hat{u}+\hat{v}-1 + C(1-\hat{...
Gordon's user avatar
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2 votes
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Clayton-Gumbel (BB1) and Joe-Clayton (BB7) time-varying copulas

You can have a look at Andrew Patton's "Copula toolbox for Matlab". It contains his code for the "Time-varying Symmetrised Joe-Clayton copula".
Peter's user avatar
  • 36
2 votes

Gaussian vs Student Copula applied to finance

The first graph with $\rho=0.1$ is straightforward. The t-copula presents more tail dependence than the gaussian copula. Hence, when you look at the tail, there is more probability mass in the case of ...
Wiles01's user avatar
  • 267
2 votes

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

"convoluted expression" in American usage just means a complicated, big mathematical expression, sometimes also called "hairy" or "messy". It is ugly to work with and to look at, so you prefer not to ...
Alex C's user avatar
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2 votes
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Verifying two properties of the Clayton Copula

Your reasoning for the first property does not look correct or at least I do not understand it. Your arguments for the second property seem sound. But your wording of the second property is a bit ...
g g's user avatar
  • 2,003
2 votes

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

Your confusion stems from you confusing several aspects of VaR and copulas. Note first that Portfolio Value at Risk measures the value at risk of a portfolio. This means the total loss of your ...
g g's user avatar
  • 2,003
2 votes

Simulating from a multivariate clayton copula

Clayton Copula-Matlab Code ...
Frankova T's user avatar
2 votes
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Copula analytic formula for $max(S_T^1 - K, 0) 1_{\{L<S_T^2<U\}}$

For simplicity, we suppose $r = 0$. $$V_t = E^Q((S_T^1 - K)1_{\{S_T^1 > K\}}1_{\{L<S_T^2<U\}}) = E^Q(S_T^11_{\{S_T^1 > K\}}1_{\{L<S_T^2<U\}}) - KE^Q(1_{\{S_T^1 > K\}}1_{\{L<S_T^...
NN2's user avatar
  • 1,008
1 vote

Correlation sensitivity in multivariate $t$-copula for portfolio VaR of electricity futures using Kendall's tau-$b$ correlation matrix

Instead of thinking "at the margin", I've opted to conduct an attribution of sorts, by running the copula with the empirical Kendall's tau-b correlation matrix and again with a zero matrix. ...
CasusBelli's user avatar
1 vote

Modelling dependance between the two uncorrelated variables using copulas

Uncorrelated does not imply independent, hence a copula could capture the dependence for very small correlations if there is any. As an example, the student t copula with a degree of freedom of 0.4 ...
Ben's user avatar
  • 146
1 vote

What is the R code for estimating copula parameters of BB1 with dim=2? And what's the code for gof test of BB1?

I have just found out what the code is. Note that theta and delta come from the copula selected for you through the BiCopSelect() command. ...
user44687's user avatar
1 vote

Verifying two properties of the Clayton Copula

Fix u, obtain derivative of v. And do it again for fixing v. To get marginal density of v, one has to do the integration w.r.t. u
Tak wa Ng's user avatar
1 vote

Any video lecture on copula function, a statistics concept for measuring dependence?

I am sharing what I found most helpful for understanding the concept 'copula'. It is an academic paper written by an undergraduate student in Netherland, for her college graduation in 2007. Copulas: ...
Eiffelbear's user avatar

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