<t>How to do Monte Carlo Simulations with Local volatility surface??I have the diffusion process dS/S- =adt + b(S,t)dz (1)What is the good discretization process (1)? I realised that in the case of CEV (b(S,t)=S^(c/2)) for example, by change of variable we have a square root diffusion process and du...

<t>In the previous paper, you don't realy need the index volatility construction. So just the two firs pages of this document are important to you and they will even give you a close form solution to the call option depending to the skewness and kurtosis.The technique is exactly the edgeworth method...

The solution to your problem or a good way to look at it is in the following paperPeter Lee, Limin Wang and Abdelkerim Karim, “Index volatility surface via momentmatchingtechniques”, Risk, December 2003.

<t>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....

<t>In the following paper,L. Andersen and R. Brotherton Ratcliffe, “The equity option volatility smile: an implicitfinite- difference approach”. Journal of Computation Finance, Volume 1, Number 2 (1997).You have a finite difference method to solve European option.It is just like a Binomial tree, and...

For the Implementation, I use the Monte Carlo method.

<t>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....

Sigma(S(t),t) to me stands for the implied volatility surface.IS there any assumption that will make my life easier in valuing the second moment?If Sigma was just a function of t and not S(t), then I'll know how to value the second moment.Thanks

Can any one help me in valuing the first and second moment of an asset with the following Process:dS(t)=mu(t)*S(t)*dt +Sigma(S(t),t)*dWIn fact I'm just trying to value E[S(t)] and E[S(t)^2] Thanks,

I think by using the Monte Carlo approach, I'll only be able to build a volatility surface for the basket depending on time. How can I use such a process to build a volatility surface depending on time and strike?Your other questions are still opened.thanks

<t>Do any one have an idea of how to build the basket implied volatility surface from the implied volatility surface of the underlying equities?I saw the paper of damiano Brigo and Fabio Mercurio et al on Moment-Matching techniques but the volatility only depends on time not on strique or asset valu...