hi gidss,There a number of issues here, with a few potential pitfalls 1. Van Leer is a robust FVM method and it avoids the oscilllations in the greeks experienced by CN. These days van Leer is rather exotic and my exponential fitting and ADE do the job as well. Here is a detailed analysis we did (see second last article !)van Leer2. Asian PDE: the A term has no diffusion hence only 1 boundary condition is needed in PDE. BUT we need TWO numerical BCs! Centred differencing in A give spurius reflection (same problems as with Cheyette models). Use upwinding.3. Using ADI or Soviet Splitting is ovekill imo; there are easier, better ways these days. Peter Landgraf has a book on Cheyette.Cheyette4. Maybe an idea to examine FD schemes and BCs; here a random searchhttp://www.wpi.edu/Pubs/ETD/Available/etd-0509 ... eray1.pdf5. ADE might be a good candidate, possibly combine with upwinding in A.6. For American option, what technique to use? Front-fixing, penalty.So, to answer: Van Leer is robust but not needed imo; CN (i.e. averaging in time) and centred differences in A to be handled with _extreme_ care.hth

I am also trying to do the same thing - that is, pricing an american asian using finite differences. The approach im using is to reduce the dimenstionality of the governing asian pde according to the following paper:http://www.math.ust.hk/~maykwok/piblica ... uasian.pdf. after reducing the dimensionality i then front fix the free boundary according to a paper by nielsen:http://publications.nr.no/penaltyAmericanOptions.pdf. The problem i encounter is that the boundary conditions do not transform well after so many transformations.Can anyone please help

Hard to say, until you say what the input and output equations are. I don't think dimension reduction is needed; don't be afraid of 2-factor PDE.BTW is Asian PDE with no exercise working?

Thanks Cuchulainn, because i have been dreading the 2D equation...i will attempt the 2D with a geometrical averaging,

QuoteOriginally posted by: kanjuoThanks Cuchulainn, because i have been dreading the 2D equation...i will attempt the 2D with a geometrical averaging,The 2d case is not all that difficult, but mind the boundary conditions for A at the far field (Note: A has no diffusion term). You could use upwinding or even ADE would be a great project.And to use front-fixing or penalty? Does any one know if Brennan Schwartz can be used here? //Another choice is to do front fixing the way Sun does it for convertibles and then Soviet Splitting similar to Roelof Sheppard's thesis; then leg 1 is in S (with the free boundary) and leg 2 in A. Just a suggestion.

hi, I still trying to pricing an american asian option acording to the ZVF(1998) paper using FD, on MATLAB. The PDE is:To have an IMPLICIT DISCRETIZED SCHEME, I used a backward derivative with respect to time, central derivatives with respect to S, upwind derivative with respect to A, where Si=i*dS, i=0,...,N; Aj=j*dA, j=0,...,M; tk=k*dt, k=0,...,Tor My questions and doubts are:1. Is the discretization correct?2. I would like to rewrite the equacion in a trdiagonal matrix form, , where C-tridiagonal matrix and B-boundry condition (like for vanilla option...). If that is possible, what would be the coeficients ai, bi and ci in the diagonal for the matrix C? And are the Boundry condition?3. Since I have two variables, S and A, dimension of C is N*M? 3. this is the pseudo-code I thinking in use:imputs: S, Smax, Amax, N (steps in S) ,M (steps in A),T,sigma,rdefine variables: dt, dS, dA, C 1.Setup the matrix C ; determine the boundry condiction; 2. for k=T0 %backward in time for j=0:M for k=0:N Solve the descretized equation end end end do interpolation if S is not in a point of the gridendWell, that's it!!Please can anybody give me tips, advice, correction... I'll be very glad for that. I'm dealing with this for so long that I just don't know what direction shoulg I take...Thks in advance!!

Your upwinding in A looks Okhttp://en.wikipedia.org/wiki/Upwind_schemeRegarding the 2d system to be solved, one way is to use Craig Sneyd; see this for Cheyette which has the same form as your PDE, slide 32http://www.math.uni-bayreuth.de/~lgruene/diplo ... folien.pdf You can go straight for 2d fdm but then you have to solve a 5-point matrix system.Peter Landgraf also discusses the needed numerical boundary conditions which should not be underestimted.A suggestion would be to do more literature research on pde for Asians. hth

/ /Regarding the 2d system to be solved,/ /Maybe I'm mistaken, why is it regarded as a 2-D equation, because as I understand it, its actually 3-D. And that is my main problem when it comes to developing a scheme for calculating the moving boundary. The 2-D case -(t,S), seems rather straightforward, front fixing works easily. However with a 3-D case - (t, S, A), front fixing is not so clear.

QuoteOriginally posted by: kanjuo/ /Regarding the 2d system to be solved,/ /Maybe I'm mistaken, why is it regarded as a 2-D equation, because as I understand it, its actually 3-D. And that is my main problem when it comes to developing a scheme for calculating the moving boundary. The 2-D case -(t,S), seems rather straightforward, front fixing works easily. However with a 3-D case - (t, S, A), front fixing is not so clear.Front-fixing leads to a nonlinear PDE which is numerically difficult/pain to solve. There are other techniques such as penalty, PSOR which might be easier.How does the smooth pasting condition appear in this case?The only thing I can say that maybe you can use the Vecer technique to reduce the dimension and then solve this as a moving boundary problem in variablle z??http://www.stat.columbia.edu/~vecer/asian-vecer.pdfI have not thought about this problem in this way, so it might not be the solution to the problem.

Can anyone help me find the following article: J.N. Dewynne and P.Wilmott, Asian options as linear complementarity problems: analysis and finite difference solutions. I cant even find it on Google, as in where I can purchase it as an electronic copy.

QuoteOriginally posted by: kanjuoCan anyone help me find the following article: J.N. Dewynne and P.Wilmott, Asian options as linear complementarity problems: analysis and finite difference solutions. I cant even find it on Google, as in where I can purchase it as an electronic copy.Checked if your university library has a copy of this?

yes i did check...my university only has a vol 2 instead of 8. Its is quite expensive for me in the link you gave me