Hi,I'm trying to estimate spot volatility, jump frequency and jump volatility of a Mean-Reverting Jump Diffusion process. The likelihood function is (non LaTex, sorry):p = sigma(0 to inf) (exp{-phi*t}*((phi*t)^j)/j) * n(x; kappa*t + j ln(1+kappa); sigma^2*t + j* gamma^2)where n(x;mu;sigma) is the normal distribution, phi is the jump frequency, sigma is the spot vol and gamma is the jump vol. x is the period log return.You'll recognize this as Eq (2.19) from Clewlow and Strickland.The MLE scheme works fine when jump conditions are fairly mild, but for a electricity spot series dies fairly quickly. One prblem I found is the inability to handle very large spikes. So the question is: does any one know of a more stable and/or robust procedure for energy time series. Publications or references would be great. Or should I just stick to numerical methods, which are robust (though not necessarily consistent).Thanks.

Duplicate post, ignore.

As outrun pointed out with an example, you should probably get another model for your series, a model able to capture large jumps. On the other hand, what is the purpose of your work ? If you're only trying to get a good representation of the cdf of the log-returns of your time series, performing a maximum of likelihood estimation is a good idea, since it's very efficient wrt Kolmogorov tests. But if you want to have a fair representation of the path, or th behaviour of your underlying (like for hedging), you should think of getting rid of your model, and maybe try the double exponential one.

Hi,I noticed several times that maximum likelihood (ML) methods don't give very good results whenever large fluctuations occur (such as the spikes you mentionned). I think it comes from the fact that there are several ways to optimize the ML function (if you decrease phi, you can increase sigma for example, or the amplitude of the jumps, etc..). I gave up using ML to calibrate jump-diffusion model. One way to proceed instead is as follow:1) Count off the spikes. Basically any variation such that |dx| > K*sigma is counted as a jump (sigma being the standard deviation of your time series and K a factor that you can adjust). This allows you to get the parameters for the jump process (it will give you the density, the average amplitude as well as the jump vol).2) Once you've "cleaned up" your time series of all the jumps, you can try to apply ML estimation assuming a simple mean reverting model.It's not perfect, but it gives reasonable results (better than ML).

There should be a double sum in that equation (the second over the number of jumps, j).Assuming that you're integrating over the number of jumps correctly, it is well known that these models have a singularity in the likelihood function. This happens because if you double the jump intensity, while making the jump mean and variance half of the reference value, the likelihood in un-altered. If you use a local hill climber, however, I think it is likely that it should converge to some local maximum anyway. Thus, most likely there is a mistake in your code someplace. BE

For this problem I am used to apply the Expectation Maximization technique either.However, I found a nice trick in Honoré, P. (1998) Pitfalls in Estimating Jump-Diffusion Models. The trick helped me to avoid the stability problem by the estimation.Peter

Hi , could someone send me the paper (or a link) of Clewlow and Strickland where they discuss the MLE procedure or they give the desnity of the mean reverting with jumps process? Thanks. V