<r>n-Factor? Uuuuuuuuuuuuuuuuh, I'm currently looking into this, not as easy as one might think. If you're doingstochastic FDM for n-factor, you're running into the problem of simulating integrals like I_(1,2), so an Ito integralwith respect to two (or n) correlated Brownian motions . There are meth...

Regarding the first question: Shreve's book on Brownian Motion has the answer, Oeksendahl isn't as comprehensive as the first one in my opinion. Cuch, what isO in W(s)-W(t)? Still looking at Karhunen Loeve Did you ever have a look atthe Fourier expansion?

<t>My experiments show the following:Its hard to decide, which scheme is better. If you simulate a Call with 2 schemes and say 100.000 simulations, and euler would show a better result (closer to true price), would it be ok to say euler is better? Changing the seed might show different results. I me...

<t>Ok, I had a look at it.A shot: I don't see how it can be more efficient or better than using the Wiener process. Note, that we're using the exact solution, by simulating the increments with normally distributed random variables, so I don't see no point to use an approximation in an approximation....

Did you try Milstein and Euler for dt=1 and different seeds? What are your results, I mean not just one runand two numbers, but many runs with different seeds, which one is better for the parameters you've mentioned?

<t>You're using dW on page 198 correctly, you can use both for PC, I think. For FDM we don't always need pathwise estimates I think. For plain vanilla calls, you're calculating the first moment of the random variable (X_T-K)+. This is exactly what weak schemes are good for, calculate the random vari...

<t>QuoteA scheme is a scheme and has weak and strong convergence, right? There are two types of schemes: weak and strong schemes. Of course, both of the schemes have weak and strong convergence, but they are constructed with a special goal. If you look at the Contents page of Kloedens comp book, you...

Which schemes are you using, weak or strong schemes? I agree with Fingerspitzengefuehl and am impressed, that you have spelled the word without any errors.

<t>Yap, I've used both, poisson and exponential. I don't know how to judge the quality, I haven't done anyspecific tests, except checking if mean and var are ok. You can specify how to generate a rv, there's notjust one way. Basically, you're specifying the underlying algorithm, like Mersenne-Twiste...

<t>I'm using it, everything good. I like the possibility to reset my seed anytime, thus being able to reproducethe same random numbers. I also like, that I can for example use the number series from the MersenneTwister algorithm, which can be used to produce new seeds. The constructors for different...

<t>QuoteWe provide UML framework and the code, nice, yes?? Yes, very nice Quote I just realised that I had never seen any remarks on consistent schemes for SDE, as we have with PDE and ODE.Yes I agree, in the Kloeden, Platen book (not the Computational one), they have a couple of exercises, where yo...

<t>Lapsi,that sounds like a nice setup. Are you guys actually coding the whole class setup for the book? Will the book contain the code? Or will you only provide the UML diagrams for a possible architecture?Cuch, nice theorem. Without having looked into it further I would say, that taking this over ...

Had a quick look, cool. I don't have time to work through it now, but that is definitely something I might look at in october-and the following years . Thanks for sharing

<t>What stands QE for? The Asian thing, I haven't done enough in multifactor stuff. But, why not using the schemes simultaneously for both processes, like in Abe's paper on site 374 for Heston? Throw two correlated brownian motions, evaluate X_n+1 with a scheme and the first brownian motion, than ev...

Yes, I've seen that in the paper of Klaus Schmitz Abe on his homepage. The paper "Measure Order of Convergence Without an Exact Solution Euler vs Milstein", downloadable on his site. Nice paper btw., easy to read. Are you running into problems without an analytical solution? Heston?