<r>Matlab implementations for several methods for pricing options (also American) are compared in the recent paperL. von Sydow, L.J. Höök, E. Larsson, E. Lindström, S. Milovanovic, J. Persson, V. Shcherbakov, Y. Shpolyanskiy,S. Siren, J. Toivanen, J. Walden, M. Wiktorsson, J. Levesley, J. Li, C.W. O...

<t>QuoteOriginally posted by: fantinityHmmm, do you know, where I can find the proof that LCP for Am option, such as Au >= b, x >= g, (x-g)' (Ax - b) = 0 is indeed equivalent to max{A^{-1}b, g} ?For some reason I have second thought about it. Here on p. 72 the equivalence is shown, but step 2 is unc...

<r>The link <URL url="http://eprints.maths.ox.ac.uk/718/1/Sensen_Lin_thesis.pdf"><LINK_TEXT text="http://eprints.maths.ox.ac.uk/718/1/Sen ... thesis.pdf">http://eprints.maths.ox.ac.uk/718/1/Sensen_Lin_thesis.pdf</LINK_TEXT></URL> seems to work.Monraf,Have you tried to the explicit finite difference ...

<t>Without knowing which ADI you refer to, it is difficult to say much. A more precise reference would be helpful.I am not sure how to understand your parameters. Is S = Smax? If so then it migth be a bit small with your S = 2K.To what rho, kappa, eta, sigma, and theta refer to? The notations for th...

<t>Yes the method should work also for problems with a mixed derivative.Although computationally two-way splitting would not be convenientin this case.With a mixed derivative, I would do three-way splitting A = A1 + A2 + A3,where A1 would be the x-direction, A2 would be the y-direction, and A3would ...

The attached write up gives one way to show that Strang symmetrized operatorsplitting method is second-order accurate also for non constant coefficient casewithout assuming commuting operators.

<t>Also space discretization can cause the discretization to be unstable.A sufficient condition for the stability is that the matrix resulting from the discretization has M-matrix property.A matrix has M-matrix property if1) it has positive diagonal,2) it is diagonally dominant (on each row, the dia...

<t>The following gives a sketch how one could try to showthe accuracy of an operator splitting method for variablecoefficient cases.Let A = A1 + A2 be an operator splitting in the matrix level.For example, A1 and A2 can correspond to a(x,y) u_xx andb(x,y) u_yy, respectively.Let an exact time step of...

What would be a good model for stochastic variable dividend?Any good references on this topic?

<t>Taking the maximum of the solved value and exercise value at each time step does give an approximation.It should converge to the right value when the space-time discretization is refined.The projected SOR iteration and many other methods give a more accurate approximation that the aboveprojection...

If I understand correctly then, for example, the front-fixing transformation in the paperis such a transformation. It is probably challenging to solve the resulting nonlinear system analytically.

Is this an issue with ADE/ADI method or the underlyingfinite difference discretization?That is, does the same error appear if the modelproblem is solved with the corresponding fullyimplicit finite difference method?

<t>The smooth pasting condition is not needed witha linear complementarity problem formulation.(With infinite activity jump models the smoothpasting condition does not even hold.)I cannot recommend directly any paper or bookon the relation of smooth pasting condition andlinear complementarity proble...

One way is to first approximatef_X ~= (f(X+dX,Y) - f(X-dX,Y))/(2 dX)and thenf_XY = (f_X)_Y ~= [f_X(X,Y+dY) - f_X(X,Y-dY)]/(2 dY)~= [(f(X+dX,Y+dY) - f(X-dX,Y+dY))/(2 dX) - (f(X+dX,Y-dY) - f(X-dX,Y-dY))/(2 dX)]/(2 dY)= [f(X+dX,Y+dY) - f(X-dX,Y+dY) - f(X+dX,Y-dY) + f(X-dX,Y-dY)]/(4 dX dY).

<t>QuoteOriginally posted by: Cuchulainn Tene,What is the rationale for the relationship between NS and NT (5:1 approx).Smax = 4 * K. edit: had a look at the Bren/Sch algo. Basically, one uses CN(for example) and modified LU to take early exercise constraint. This is almost the same as my scheme exc...