<t>"Currently we have 1 factor model which work great in VBA, I assume however that 2F HW is much more challanging."With all my respect I a little bit doubt that this would be the case ( the model works great ).Does it calibrate to the whole smile ? Is your volatility/variance stochastic (in some wa...

<t>Hi,although the jemshidian decomposition applies only in one direction, indeed, but you do not need more.1. For multifactor HW you make an SVD to see your axes and scaling factors2. In the direction of the highest eigenvalue you do the Jamshidian decomposition, as follows.2.a. chosing this direct...

<t>The cliquet no, buta. the discretely sampled asian yesb. the Laplace transform yesc. solving PDE's with this laplace transform : yes.d. the calculation of greeks with recursion yes.Peter den Iseger told me, that the joint characteristic function of the Hetson process in Draculescu and Yakovlenko ...

<t>Hi Alan,Ad 1. qua the Iseger method we have ( actually me, under the supervision of Peter ) implemented teh discretely sampled Asian option, and its Greeks as well. It worked quite fine.Ad 2. The method anyway is related on the (weak form of) Poisson summation formula. 1. The domain is split up i...

<t>Use the Moore-Penrose pseudoinverse. ( The pinv command in MatLab ).This has the attribute to give the solution being minimal in a the Eucledian norm.For more detail see Jackel's book. However, I do not understand, why you need to invert a matrix. If I understand well, you want to construct an op...

<t>Hi,1. Of course, the speed of the algorithm depends on the accuracy ( let us consider a normalised [0,1]^{n} hipercube ). A 3D PDE can be solved within some 10 seconds up to an absolute error of 1E-9 ( or higher ) . It is, of sourse, faster for an abs error of 1E-5. 2. 32 bit maqchines are really...

<t>Certainly a good approach.We are working on it. ( since we have a goddamn good algorithm to solve PDE's and a rather good method for MC ).With this you can definitely decrease the variance of the MC : you condition upon the random variables with high variance, solve the conditioned SDE with MC, s...

QuoteDoes the transform work? The mixed derivatives disappaear using Sylvesters law but MD are easy now anyways. Just use 'geschikte afleidingsoperatoren'Yes, with our method up to an absolute accuracy of 1e-10.

And the transformed PDE takes the following form:

<t>Here is a possible solution :If you have a two factor model :, i.e., the two processes are correlated, we may do the following Ansatz :and withas discussed in Lipton's book on page 316.This is one possible way to do this transform.If you have no boundaries (ie, the X plain is infinite ) I prefer ...

<t>What do you do when you distinguish between "dt" and " dW_t" terms ? You sepatare the terms giving non zero expected values ( "dt" terms, trend, etc ) from those with 0 expected values.What is "dW" ? That is a random variable having the (unconditional) density functionf(x) = \frac{1}{\sqrt{2 \pi ...

<t>Gents,we have developed a fast solver algorithm and we plan to write a paper from it.We are going to demonstrate the applicability of the method at different appl. fields.We shall, of course, solve a problem in Finance ( parabolic, linear eqn ), in Wave Propagation ( Helmholtz eqn ). However, we ...

<r>YOu may , I guess be able to use the usual discretisation :The inhomogenity will be caused ( as before ) by the boundary conditions.You should set the determinant to zero, which can result in an instable solution, depending on the shape of f(x). The Fourier transform ( and the 1D Finite Element )...

<t>Just some more points.1. The system of linear algebraic equations takes the following form : 2. Let me advocate, nonetheless for an integral transform solution. ( You know Murphy's rule : If you have a hammer, consider everything as a nail ). Suppose, you have an efficient convolution algorithm, ...

<r>Lectori salutem !I think, you have a set of coupled, first order elliptic equations (ODE's ) , which implies, we should use Variation Calculus ( which is a description of conservation of energy, in this case ). Subseuently we shall use the Euler-Lagrange equation ( <URL url="http://en.wikipedia.o...