Correlation swap, state of the market

PanzerMeyer · Post by **PanzerMeyer** » Thu Aug 12, 2004 12:06 pm

There seems to be a growing interest in correlation swap, it is still very exotic stuff... My sources (hey Nero) tell me that Socgen again is quite active on that...

do you know how those stuffs are dealt, like if there are standard basket of 20 biggest European shares, or is it only tailor made (with freakin margin) ?

Nonius · Post by **Nonius** » Fri Aug 13, 2004 8:56 am

In terms of papers, I don't see any state of the art. If you look at just sampling errors in correlation (assuming that the time series IS driven by stationary returns), you'll see that the distribution of sampling errors of say, the average value of correlation, is far from normal. It is skewed, depending on what the "real correlation" is, and has fat or thin tails, again, depending on what the average is. So, if you were doing options, you wouldn't just do a stupid bs type of formula. As I have tried to push, one way of looking at fatness and skewness is through the nonlinearity of the situation. That is to say, a 3x3 corr matrix cant be any 3x3 symmetric matrix. I've beat this into the ground I know.

NeroTulip · Post by **NeroTulip** » Fri Aug 13, 2004 9:46 am

[i]If you look at just sampling errors in correlation (assuming that the time series IS driven by stationary returns), you'll see that the distribution of sampling errors of say, the average value of correlation, is far from normal. It is skewed, depending on what the "real correlation" is, and has fat or thin tails, again, depending on what the average is.[/i]

Interesting, do you have a reference for that?

Nonius · Post by **Nonius** » Fri Aug 13, 2004 11:01 am

Nonian brute force simulation. Just do monte carlo, and create distributions of samples of average correlation, then, examine the statistical properties of the sample corr estimate. this approach works with any parameter in a parametric distribution. Think of it this way, suppose I model a distribution as F(C) where C is a pile of parameters. Maybe C lives in a flat space, maybe it is restricted to a nonlinear surface etc etc. Now, you estimate C with historical data. Now, if you estimate C on a smaller set of data, you get a sampling error in measuring C. So, you can just do experimental statistics...just assume a C, then Monte Carlo, then, examine the properties of the distribution of the sampling error of C. If C is constrained in some ways, you will find that the distribution is NOT normal. If you could drum up a parametric distribution in which C lives on the unit sphere in 3 dim, then, suppose you form some value like sum of all components of C, then, the sampling error will not be normal most likely, and part of the issue is that the parameter isn't free to be just any triple of numbers.

PanzerMeyer · Post by **PanzerMeyer** » Fri Aug 13, 2004 11:43 am

so do you know if the big names in Equity DErivatives are trading that easily and with worth to see prices ?

the correlation of stocks, can it be compared to the correlations we find in n-to-default baskets in the Credit derivatives business ?

Nonius · Post by **Nonius** » Fri Aug 13, 2004 1:50 pm

no, in credit derivatives, people talk about correlation products in the sense of Nth to default and CDOs. Though those products have valuations that depend on "dependency" of default, they are not comparable to an equity correlation product.

Johnny · Post by **Johnny** » Fri Aug 13, 2004 2:53 pm

But mathematically, the correlations are related through Merton type models.

NeroTulip · Post by **NeroTulip** » Fri Aug 13, 2004 3:09 pm

[i]Nonian brute force simulation. Just do monte carlo, and create distributions of samples of average correlation, then, examine the statistical properties of the sample corr estimate. this approach works with any parameter in a parametric distribution. [/i]

Me likes Nonian brute force simulation. No banach space bullshit, only the good stuff.

So what's the result? I imagine the distibution of the estimator is symetric for real correlation = 0, negatively skewed if real correlation >0 , positively skewed for real correlation <0. And the tails?

Nonius · Post by **Nonius** » Fri Aug 13, 2004 3:33 pm

you got it dude on all accounts...I need to go back home to get the results on the tails. I did all of these experiements in Nice. By the way, the relationship between confidence and number of observations, interestingly, is like 1/sqrt(N), just like other estimates we are familiar with.

I urge you to just do the simulation yourself. It is easy.

What is interesting is to try to locate a parametric distribution to fit it. YOu could try to fit a normal process to it. You can also try to do a Nonius thing, which is put a process on the orthogonal matrices that diagonaliz and the diagonal matrix. Guess what? Nonius process does in fact fit better than doing the stupid thing. but, it still aint that good.

FDAXHunter · Post by **FDAXHunter** » Fri Aug 13, 2004 3:37 pm

Anybody ever make any headway into pricing by replication? I had started with a covariance swap and then tried to bend the payoff to match that of a correlation swap... without much success.

Ok, truth be told, I spent like 1 hour on it, okay, so I'm not that motivated....