[R] Generating a double-exponential jump diffusion process

[Tamas K Papp]

On Sun, Nov 05, 2006 at 11:13:28AM +0000, Tolga Uzuner wrote:
> Dear R Users,
> 
> Does anyone know of  a package which can generate random realisations of 
> a double-exponential jump diffusion process with a drift ? Something 
> where I can specify the likelihoods of an up or a down jump, the drift 
> rate, and the mean size, and get back a vector of realisation of the 
> process (for purposes of a Monte-Carlo).

Tolga,

I am not really an expert in this field, but AFAIK the likelihood of
Ito/Levy processes does not have closed form solutions apart from a
few well-known exceptions.  People use simulation (Euler method and
variants) to obtain simulated values and likelihoods.  For the latter,
a method called High Frequency Augmentation is used.  Some references
are Jones, C S (1998, 1999), Elerian (1998), Elerian, Chib and
Shephard (1998), Eraker (1997), most of them are about diffusions, but
I guess that they can be adapted to Levy processes too.

HTH,

Tamas