Hi,Just wondering if anyone is aware of any clever numerical tricks when solving stochastic vol models of the form:where A and B are sometime referred to as backbone parameters. I could just run a pure Monte Carlo but it would require a lot of numerical effort... can anyone share any numerical tricks that can be used to reduce the problem so that I could use conditional Monte carlo as they do in the Hull-White paper?Many Thanks,

PDE method, perhaps? I still count only two dimensions plus time (assuming r, omega, A and B are not also stochastic), so this should be a pretty easy finite difference exercise...

Yep, you are probably right. I am not quite the PDE guru, any tips on how I would go about evaluating the stability condition (assuming implicit scheme)? I never really understood that Fourier analysis... and what about the boundary conditions?Much appreciated,Sam

QuoteOriginally posted by: samHi,Just wondering if anyone is aware of any clever numerical tricks when solving stochastic vol models of the form:where A and B are sometime referred to as backbone parameters. I could just run a pure Monte Carlo but it would require a lot of numerical effort... can anyone share any numerical tricks that can be used to reduce the problem so that I could use conditional Monte carlo as they do in the Hull-White paper?Many Thanks,Your original idea might very well work if I understand it. You just simulate the volatility process. Eachvolatility sample produces a deterministic, but time-dependent vol.path. You then evaluate the option value for the stock process,conditional on that particular realized volatility path, as you mentioned. Thisrequires solving the CEV model with time dependent volatility -- but, Ibelieve this has been done by Lo, Yuen, and Hui. (google for details).The arguments to pass to the CEV model will reflect the vol. path and an adjusted stockprice if there is a non-zero correlation between your two Brownian motions. (see Romano and Touzi, 1997) Then, just average the Monte Carlo option values in the usual way. The nice thing is that this procedure, when it can be done,reduces everything to just a 1D simulation which can be relatively fast for MC.regards,alanp.s. There's a paper by Willard you shoud look at if you haven't seen it, andI did some work on this general topic (mixing). For details, do a forum search on `Willard' and thethreads will turn up.p.p.s. Upon reflection, if the correlation is non-zero, I'm not sure if this method works. But, I'm pretty confident it works if the Brownian motions are uncorrelated.

Thanks Alan! I am pretty sure the correlation I will use is non-zero, but will take a look at the references nevertheless!regards,sam

Hi,Ok, on a slightly different note but still on the same SDEs below.I am trying to use an antithetic variance reduction in my MC. But I am not so certain whether/how to make it work because I have a 2-D MC and it is not obvious if the payout function (a call on a stock price) is monotonic in both the final stock price and the final volatility. Basically, in 1-D MC integration, if the function is montonic in the simulated variable antithetic variance reduction works well. Any expereiences on whether it works here. I have tried it but the answers that I am getting look wrong. I first tried to apply the anithetic technique (i.e. to set z = -z) to the normal variables for the stock price ONLY. No result. Then I applied it to both normal variables. No luck either. Any help is much appreciated.Sam

the Willard trick doesn't seem to work in the more general CEV Stoc vol hybrid case, because the adjusted Stock Price depends on the S sample path and not just realized vol path.