QuoteOriginally posted by: zetaAt the risk of sending this thread further down the tubes, the book I allude to earlier is "Lie group analysis of differential equations"volume 1, by IbragimovUnfortunately, do anything useful you have to get through volume 3.

your assertion is false, I just squashed a spider with volume I ED:now it serves as a coaster and paperweight

N the non-Newton,QuoteOriginally posted by: NQuoteOriginally posted by: zetaAt the risk of sending this thread further down the tubes, the book I allude to earlier is "Lie group analysis of differential equations"volume 1, by IbragimovUnfortunately, do anything useful you have to get through volume 3.Is it the true Lie or a mere Lie named after the famous mathematician?Tell me the truth, please!Since I am a moron, I cannnot catch your code-using conversations!Please discuss the matters in very plain English or whichsoever language!(One advatage of mine: I have a mutiple-language translator.)Tunito That Non-likes Non-Newton, not A Civl Servant, but a sacred super-hyper clever Ma(s)(themat)i(ci)an

QuoteOriginally posted by: zetaAt the risk of sending this thread further down the tubes, the book I allude to earlier is "Lie group analysis of differential equations"volume 1, by IbragimovWhere to get the book? How come I am not getting that book in the best library here? Is the name correct? Any other book?P.S. - How about requesting Tunito not to post Off topic stuffs here. Please don't spoil this forum's sanctity, Tunito.

This book is a little difficult to get; I think all three volumes go for about 300USD at amazon. Try searching with 'CRC handbook of lie group analysis of differential equations' Volumes I-III edited by N H Ibragimovhere's an article from volume III

QuoteOriginally posted by: zetaThis book is a little difficult to get; I think all three volumes go for about 300USD at amazon. Try searching with 'CRC handbook of lie group analysis of differential equations' Volumes I-III edited by N H Ibragimovhere's an article from volume IIINice zeta thanks for bringing the content back to this haywire thread.

If you are still discussing the use of finite difference for jump+diffusion:I use a standard approach: treat the diffusion and advection terms implicitly and the convolution term explicitly, the method is absolutely stable(the reason is that the norm of convolution is bounded by L^1 of the kernel which is 1 and there is enough stability coming from the implicit part to make the whole scheme stable). It is of 1st order in dt. To make it 2nd order in dt , I use another standard approach: calculate solution with dt and dt/2 and take their linear combination to get dt^2 accuracy. It is also 2nd order in dx (for the convolution I use trapezoids for f but not for the kernel*f, similar to numerical calculation of FT or Fourier coefficients to avoid problems if the distribution of jumps is sharply peaked) and analytically calculate the tails of the convolution outside of range of finite difference (outside Smin and Smax), I use Dirichlet Boundary conditions (consistent with the fact of getting tails for the convolution).As expected it works OK. One can further improve the scheme by speeding up the calculation of the convolution by FFT technique or using certain quadratures, e.g. lagrange quadrature in case of exp(-x^2) kernel and european option (choosing fewer number of nodes for the convolution). Not sure what kind of quadrature technique may help for barrier options. Hermite quadrature may work for part of convolution for exp(-|x|) type of kernel in case of barriers.Some people make the convolution term implicit (in ADI or operator splitting type techniques) and invert it either by FFT technique or by iteration. Iteration maybe useful for american options.

I've implemented the Merto Jump diffusion model with normal distribution for the jump and it happens that even if I don't have a jump, the spot price using Jumpn Diffusion versus GBM are differents due to Lambda*kappa in (dS/dS-)=(mu-Lambda*kappa)dt+sigma*dz+dp.I then have the following question.Shall we really use (mu-Lambda*kappa)*dt even if there is no jump? If yes, do that means the Jump Diffusion solution in the contest of very small values of Lambda or very small time period is exp(-Lambda*kappa *dt) times the the Black-Scholes price with no jump??

For the Implementation, I use the Monte Carlo method.