Thanks to other threads on the forum, I've made a program that calculates the price of a standard European option with a PDE. The stuff, however, is pricing the option on a discrete- dividend paying framework.I've been told that Volume Finite Mehtod, in some way, should be well suited for processing PDE computations under jumping diffusion; even though I've tried to investigate various places on the web I still don't quite get it: what would be the real difference (1D option pricing case) between the finite volume method and the finite difference method?I have written a couple of equations. Seems (depending on the mathematical form specified for the space disr.) that the two approaches produce very similar forms on the base problem formulation! At the moment, that confuses me - so the question is: How to distinguish between the two methods? Conceptually, the difference should be pretty clear.- FDM works with the differences in the discrete point values of a continum. - The solution to the pricing problem is derived from a differential form of the underlying equations.- - FVM works with numerical calculations through designated "control volumes". The solution to the problem is derived from an integral form of the underlying equations.Out of these considerations, I can't really get the numerical input of (FVM) such a method! Could someone give me a flavour (sum up) on what would be the practical input of processing a FVM instead of the (usual) FDM?Regards and many thanks.

Hi,It should be no difference between FDM and FVM in 1D because the CV (control volumes) are the same. In 2D (3D), it is another story. FVM is more general and we can play with different CVs to improve the method. You can even use an unstructured mesh in a FVM framework. For higher dimension, you can think to methods based either on sparse grids or on sparse tensor product approximation spacesFarid.

Hello Farid and thank you for the input. "we can play with different CVs to improve themethod." : what are typically, the kind of improvements that are looked forward by running this kind of method? What is it particularly suited to?

HiThese features are well known now in the applied mathematics community working on numerical simulation of hyperbolic problems (at least in an unstructured framework).Have a look to this : http://people.nas.nasa.gov/~barth and have a look to the lecture series described as "VKI Lecture Notes".You find descriptions of CVs in the whole text. Have a look to page 111 in the third file (VKI Lecture Notes: Part 3, master3.ps)Hope that this can help you.F.

This article discusses FVM for Asian options and might be a good startQuoteZvan Robert, Peter Forsyth, Kenneth Vetzal 'Robust Numerical Methods for PDE Models of Asian Options' J.Comp.Finance Winter 98 V.1#2I vaguely remember also approximation of the dividend jumps using nascent delta functions in combination with 'normal' FDM.Is FVM a hard requirement? BAMBIIf you could scope the problem exactly that would be an idea.

Hi,The scope here is basicly to set up options' price under a "cash div." diffusion model.I was told (by ref. to first order space derivative discontinuity and discussion with a physicist)that a nice way to get accurate computation was to try the fv method, instead of fdm. My aim by asking the forum, was firstly to get if FVM was actually considered either a relevant or usual choice in Quantitative Finance, if yes or not, why, ideally. Secondly to know if anyone basically had practical references to a paper addressing PDE option pricing with FV, to get started on it. At the moment I am on the reading of the paper F has dropped to me (tough theoretical stuff!! ) , will then have a look at the references you have given, Cuchulainn. Many thanks.

@Blade is the man for FVM but unfortunately he has not been around here for some time. edit: A good intro to FVM can be founs in the book "Computational Gasdynamics" by Culbert B. Laney

Hi,The best book ever written on FVM is by Jiri Blazek "Computational Fluid Dynamics: Principles and Applications".I read the first edition and it provides a clear and state of art of the finite volume method. This book is an excellent basis to understand (and apply) the FVM.