April 27th, 2005, 10:56 pm
QuoteOriginally posted by: JamesMy two:1) is correlation random, 'sticky,' or stationary (we pretty much know it isn't stationary).If it is more than random, and it isn't stationary, then it has some sort of viscosity. What is that? is it mechanical, like fluid dynamics? or is the viscosity also multi-factor? like chemical reactions or sub-atomic physics?If correlation is 'sticky' then it also probably is linearly or polynomially predictable with a positive probablity. (This is what I think Jim Simons is doing at RenTech).Do copula methods help, or are they mearly obscuring fundamental uncertainty, or worse, not uncertainty, but true raw ignorance?The interesting thing about correlation is that even in hindsight our estimation of it tends to not be very good in very many financial cases. My view is that the difference between random and sticky correlation is dwarfed by the standard error of measuring correlation, and defining it on a term structure or instantaneous basis. Even when I use a handful of different estimating techniques to get a correlation estimate for pricing a basket option, what I'm doing is little more helpful than licking my thinb and holding it up to the wind when trying to forecast whether it's a good day to go sailing. The good news is that outside the correlation market, that uncertainty often lets me buy correlation at very low levels and sell it at very high levels.Even if correlation were linearly or polynomial predictable, there would be an intensity process for defining the probability of it collapsing away or going to 1 on a sudden event, and that's one of the fascinating things about working with the future and trying to trade it as a term structure.Copula models help like implied volatility in Black-Scholes helps us: it lets us describe the financial world with a simple variable we can move around to see how something is sensitive to it. In doing so, they simplify our work and let us focus on what's important, and separate out what we hope to work on tomorrow. Correlation is probably subject to some form of the Heisenberg uncertainty principle, which means it is not that we are ignorant but that measurement is funamentally limited, and further limited in finance by the assymetry between the future and the past.Somewhere between random/sticky and curious simplicity, I am playing around with a regime-switching correlation model. Anyone else have experiences with this they would like to share?