YomiHave you worked with implied trees? At a certain stage we need to see if FDM for Heston is good by comparing it with established methods such as schemes for STO VOL.Then we can compare on basis of performance, ease of maintenance etc.I cannot visualise a 2-factor trinomial tree. How to model correlation?What do you think?

Does anyone have the Bates paper?Bates is Heston plus an integral term that represents the jump process. In that case we would have the 2-factor Heston + an integral to approximate.Juicy problem?

I might have some code for implied trees on some of my CDs. Will need to search for it.A trinormal tree is a special case of an explicit FD. Must treat correlation in a similar way.George Levy's book(computational finance Numerical Methods for Pricing Financial Instruments ) has an implementation of 2-,3- and 4-factor option pricing models using the binomial tree.QuoteOriginally posted by: CuchulainnYomiHave you worked with implied trees? At a certain stage we need to see if FDM for Heston is good by comparing it with established methods such as schemes for STO VOL.Then we can compare on basis of performance, ease of maintenance etc.I cannot visualise a 2-factor trinomial tree. How to model correlation?What do you think?

Is the bates paper you are looking for?

Yomi,in your opinion it is easier to program a 2-factor tri. than en explict FDM for 2-factor PDE (the latter is quite OK)Would Levy's book be a god buy

> Is the bates paper you are looking forYes, thx. The PIDE is in there but it's a bit camaflauged (I don't know if that is the right spelling) . The integral terms is written as an expectation. So should be OK I think. This eq. is non-linear.

I think a 2-factor explicit FDM is easier to program.In terms of C++ implementation, this book isn't a great book (every is done in c. beginning to realisetheir isn't many good finance books out there for the implementation of pricing models).QuoteOriginally posted by: CuchulainnYomi,in your opinion it is easier to program a 2-factor tri. than en explict FDM for 2-factor PDE (the latter is quite OK)Would Levy's book be a god buy

> In terms of C++ implementation, this book isn't a great book (every is done in c. beginning to realise> their isn't many good finance books out there for the implementation of pricing models).C is not necessarily bad IMO but it does not lead to the most maintainable code. I suppose you are saying that the code is not OO? You want generic and extendible classes that you can customise by just 'plugging in' you own functions/classes?

> I think a 2-factor explicit FDM is easier to program.Think so. With bi/tri you to do lots of tricks (albeit very clever ones) with the mesh, especially with non-const vol.One thing is sure: with explicit FDM there are NO oscillations when S = K!!!

It might be a little late. To solve the compound options numerically, two iterative PDEs are called for in order to price the option-on-option, which could be tedious. Correct me if I was wrong.

> two iterative PDEs You mean a system?

Hi Sammus, I don't think iteration is needed as the coupling of the equations is only 1-way. I think at each time step, it is simply the solution of the underlying option ( 1 eqn ) and then the solution of the compound ( second ). You can include the effects of american exercise, etc at each sub-step. The compound option has terms from the first equation but there are no terms from the second (compound) equation in the first and hence I don't believe iteration is needed. Again, feel free to correct me if I'm wrong as this is pure speculation. Blade

sorry sorry, you are right. There is no need to be iterative. Basically the first PDE gives the underlying option price and the second PDE is to solve for the compound option. BTW, both of the PDEs are two-factor PDEs.

great stuff!

Paper on Heston's stochastic volatility model:http://www.wystup.com/papers/hestonfem.pdf