Hi.I am looking for finite difference schemes other than the classical Explicit/ Implicit Euler and Crank Nickholson.Can you suggest some along with some references?

QuoteOriginally posted by: ScroogeMcDuckHi.I am looking for finite difference schemes other than the classical Explicit/ Implicit Euler and Crank Nickholson.Can you suggest some along with some references?Here's a starthttp://www.datasim-component.com/financial.asp ... =resources http://www.datasim-component.com/financ ... tion=books

Thank you. Do any of the books have implementations of higher than CN schemes?

QuoteOriginally posted by: ScroogeMcDuckThank you. Do any of the books have implementations of higher than CN schemes?Do you mean second-order accuracy? Normally is good enough.You can use extrapolation but then round-off errors can creep in.

yes. I am interested in implementing them and compare them with CN.

QuoteOriginally posted by: ScroogeMcDuckyes. I am interested in implementing them and compare them with CN.Here is a thread on all kinds of FDM schemesP.S. CN is not good, it looks good (second order in THEORY only). I wrote a paper on it in best of Wilmott 2).It oscillates like mad at the K and spikes at a barrrier. And the convergence is k^3/5 (deltaT to the power of 3 over 5), not k^2 even for the simple heat equation with a BS type payoff function.Forget CN, it does not work for nonlinear problems. Here are better:. Rannacher. Implicit Euler with extrapolation. Predictor corrector. van Leer (FVM). Runge-Kuttahope this helpsDanielhttp://www.wilmott.com/messageview.cfm?catid=10&threadid=23217

Thank you for the link, the conversation covers exactly what I was looking for.As far as CN is concerned, I have implemented it on a number of different options,the most complex being a double american knockout barrier with discrete dividends. I know about the oscillations in the Greeks, but I have countered that problem by doing an eigenvalue analysis and decreasing the timestep accordingly.I am not aware though about the spike that you mention at the barriers. Can you provide some intuition?Thanx, Leon

> am not aware though about the spike that you mention at the barriers. Can you provide some intuition?Leon,The accuracy of polynomial-based FDM schemes is determined by the truncation errors and these, in their turn are determined by Taylor expansions of the soluition. Of course, solutiion is far from smooth at the barriers. This is why CN does not work there and gives beautiful but incorrect spikes at barrier. Appealing to the famous Lax Equivalence Theorem is fine if the assumptions are true. These days the maximum principle and viscosity solutions (semi-continity) are the way to go.Daniel

> I know about the oscillations in the Greeks, but I have countered that problem by doing an eigenvalue analysis and decreasing the timestep accordingly.CN gives complex eigenvalues (hence oscillations).But I thought this was the situation no matter what the size the deltaT was? I think that delaT = (deltaS) for no OSC?