Hi guys!Does anybody know what are the methods for estimating jump-diffusion models?As I understand the standard MLE procedure is invalid in this case.

sorry....this should be in the -General Forum-....you responses are appreciated anyway.

Hi,you can use an approx MLE - start with assuming that there is at max 1 jump between 2 observations, then calculate the transition density p(x_t,x_0) \approx p(x_t,x_0|no jump)*P(no jump)+p(x_t,x_0|1 jump)*P(1 jump) etc.Regards,SurferD

Sorry, I didn't notice your answer. Thanks a lot!However, I dont know why you call it -approx- MLE....as I understand in case when we have at most one jump per day (considering daily data) we can use ordinary MLE. The problem with MLE for continuous tim models is that we may have infinite number of jumps and so we have a mixture of normals, so likelihood function can take infinite values...here we have at most one jump, so we can use MLE.I have another question...How would you model jump size?For the data I examining most positive jumps are larger than negative. So jump model of the form where B is Bernulli and Y is normal is not suitable....because normal distribution is symmetric. So I use the double exponential model for modelling positive and negative jumps separately i.e. positive jumps have exponential distribution with parameted -a- and positive with parameter -b-. This is how jump sizes are modelled in Kou's jump diffusion model. I can't see why I can't use, say, lognormal distribution for jumps.....

By the way....why not model jumps in this case like this where Y is now some distribution which may take positive and negative values but skewed to the right (since positive jumps are larger than negative). We could use Generalized Lambda Distribution and adjust parameters so it fits the data...

I would do as follows: first find out when the jumps happened, then try to estimate its distribution or even better assume some distribution that makes sense and then estimate its parameter, etc.Regards,SurferD

you can find some hints and references in papers by Chernov: http://www-1.gsb.columbia.edu/faculty/m ... rch.htmlin practice, estimating a jump-diffusion model purely on historical data is quite a headache - and the results are not robustCheersmib

thanks guys.Chernov and that company at Columbia (Johannes etc. http://www-1.gsb.columbia.edu/faculty/mjohannes/) use MCMC, particle/practical filtering for estimation...and deal with continuous time models...where simple estimation procedures like MLE doesn't apply.sometimes it's possible to use MLE, like in the case discussed below...honestly, I don't know much about MCMC/particle filtering yet...