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tibbar
Topic Author
Posts: 554
Joined: November 7th, 2005, 9:21 pm

### correlation swaps

Can anyone suggest a paper that deals with pricing correlation swaps on an arithmetric average realized correlation of a basket of stocks? I was thinking along the lines of modeling each stock using the Heston model and a nice big correlation matrix to specify the correlation between each brownian motion (and price via MC)...but it would be nice to see a paper that deals with these issues...Also need to find some papers on dividend swaps (not seen much from google on this)Thanks
Last edited by tibbar on May 28th, 2007, 10:00 pm, edited 1 time in total.

tibbar
Topic Author
Posts: 554
Joined: November 7th, 2005, 9:21 pm

### correlation swaps

Can anyone confirm if the following approach is sound?- given n stocks in the basket, calibrate a seperate Heston model to each stock- assume the dw_t terms for each stock's volatility process are correlated (i.e. have a nxn correlation matrix for these)- assume all the dw_t terms for dS_t are independent- simulate each stock evoluation via MC and work out correlation swap payoff then discount back to time 0.(this is a generalisation of the approch for valuing correlation swaps given in "Modeling of Variance and Volatility Swaps for Financial Markets with Stochastic Volatilities" by Swishchuk, A.)
Last edited by tibbar on May 28th, 2007, 10:00 pm, edited 1 time in total.

slacker
Posts: 114
Joined: January 14th, 2006, 12:21 am

### correlation swaps

Hi,Not sure between points (2) and (3). Are you saying dw(t,i) and dS(t,i) has a correlation(possibly option implied) for ith stock, dS(t,i) and dS(t,j) has a correlation (maybe historical) and dw(t,i) and dw(t,j) are uncorrelated?.Either ways my naive guess would be that multidim heston would produce a lower expectation. I mean when correlation is being played, I would think you would like a dynamic/time varying correlation matrix. Because you have problems of positive definiteness and bounded values [-1,1] for corr matrix I think people try to take a dynamic covariance matrix.One such type of a covar matrix is one where the matrix is driven by a diffusion process with the probabilities prescribed by a wishart distribution. The dynamics of the corr matrix process are then got from dynamics of the covar matrix through an ito manipuation. This matrix is able to meet the above constraints (under some conditions).Thanks

tibbar
Topic Author
Posts: 554
Joined: November 7th, 2005, 9:21 pm

### correlation swaps

I was intending to follow the approach in the paper I quoted below, but (ahem) I managed to misquote it! Their model is of the following form:dS_i(t) = S_t^i ( mu_i(t) dt + sigma_i(t) dW_i(t) )d(sigma_i)^2(t) = k_i(theta_i^2 - (sigma_i)^2(t) )dt + gamma_i sigma_i(t) dV_i(t)They assume the W_i are correlated, the V_i are uncorrelated and W_i, V_j are uncorrelated (they deal with a 2 stock case, I am generalising here).Do you have a reference for the stochastic correlation matrix approach you suggested? I am keen to keep the model fairly simple as calibration (to 20 stocks in my case) will be difficult enough with the above model.Any views on whether correlation should be implied or historical?

muniangel
Posts: 110
Joined: May 11th, 2005, 9:04 am

### correlation swaps

maybe It's a constructive idea.

rmeenaks
Posts: 186
Joined: May 1st, 2006, 2:31 pm

### correlation swaps

Hi tibbar,Did you get any information, papers, *anything* on these instruments? I am in the same predicament as you are. Basket of stocks and pricing of correlation swaps using an arithmetic average realized correlation. I also need info on dividend swaps as well..Thanks,Ram