Serving the Quantitative Finance Community
joint distribution
outrun, forgive my ignorance, but the usual suspects are no good eg., MCMC, MLE? I've only just started learning about Gibbsian (my futile attempts recorded elsewhere) but the advantage there is of course sampling from the conditionals. If you want I could forward you Casella/George's paper from 1992 on the Gibbs sampler
joint distribution
Now there's an interesting thought - I wonder if it's possible to construct such a distribution. Can you back out the joint distribution from the distribution of the sum & the two marginals?
joint distribution
could you give us a little latex I think I am beginning to visualize the target, and it just sounds like you want to sample with constraintsGibbs is a little easier than strict MCMC (AFAIK) because you don't need a likelihood, though arguably getting the conditionals seems just as difficult in this case. I'll still forward the paper
joint distribution
What you'd like to back out is the conditional distribution for X given Y. Unless X and Y are independent there's no unique solution. There may be a solution, but it's bound to be non-analytical. I'd just go for the usual assumption that everything is joint lognormal, and use existing methods to deal with that.
joint distribution
My gut feeling is that if there is a solution, it will not be as easy as just working with Asian/basket option approximations.Secondly, if you do find such a distribution, you will have ensured that w1*X + w2*Y is lognormal, but what about w3*X + w4*Y ? I.e. the conditional distribution you're using will be different on a per trade basis.
joint distribution
outrun, just a suggestion: why don't you use copula? Use the margins that you want and just sepcify a copula which make sense according to your assumption (tail dependance, etc) and just fit it to data
Last edited by meteor on April 25th, 2007, 10:00 pm, edited 1 time in total.
joint distribution
He's looking for a specific copula that ensures the distribution of the sum of the two random variables is lognormal. Don't think there's a textbook construction algorithm for that