Damiano Brigo: A Stochastic Process Toolkit for Risk Management

[msinghs]

Hi there, folllowing on from the the tutorial above (google it and you will find the pdf).

I am interested in his calibration of NGARCH and GBM with jumps. When he does the MLE how can he estimate the parameters?

For NGARCH what input do you put for (mu, omega, alpha, beta and gamma)

and for GBM with jumps what input do you put for (mu_star, sigma, lambda, mu_y, sigma_y)?

Please help

 

[msinghs]

Anybody?

 

[BestPhyt]

The author includes MATLAB code to estimate the Gaussian parameters for GBM on page nine, and the starting MLE values are usually the sample mean and variance. The code should return the MLE parameters.

 

[msinghs]

I asked for GBM WITH JUMPS and NGARCH

 

[Aventus]

Hi msinghs, I'm having pretty much the same problems. I am also trying to replicate the estimation procedure for the two processes (NGARCH, Jump Diffusion) and am having trouble finding the right starting points. As the estimation problem might be non-convex, there does not exist a unique local maximum but multiple - and depending on the starting values I chose I get different likelihood values. For the first two moments (mu, sigma) I just calculate the mean and standard deviation and chose those as starting values.

Did you get any further on this? Thanks in advance msinghs (or anyone else).

 

[jcenev]

Hey guys. Did you made any progress on this? I am really stuck with NGARCH and the Jump Diffusion. How do we set the starting params in the calibrating functions?

 

[EtnemelC]

Hi guys. I was studying the same paper of Damiano Brigo, and found the same problem on how to correctly choose the starting values for the parameters vector needed in order to estimate the NGARCH GBM. Does someone knows what is the right way to choose them or where i can find info in order to solve this problem?

By intuition, i guess that a good starting value for the drift parameter 'mu' could be the sample mean, while the asymmetry parameter 'gamma' could be initially set equal to zero (basically it will initially consider a simple GARCH(1,1) model), but i have no idea about the others three parameters.

I would really appreciate any kind of help guys.

 

[CandyOates]

I haven't read the paper, but I know a little bit about optimization...

Try randomly generating several starting points on your domain, or perhaps just local to where you suspect the optimal point to be, and taking the parameters associated with the best value of all the randomly generated points. You could also use a mesh to be more thorough, but it will be more expensive computationally. You won't know if your solution is the global optimizer.

Matlab's global optimization toolbox has implementations of these types of strategies.

http://www.mathworks.com/products/global-optimization/description3.html

 

[diegosanaz]

There is this paper that helped me out in a project. It talks about the MLE estimation (they do it with restrictions). It's easy enough, is just about the transition density.

http://homepages.math.uic.edu/~hanson/pub/ACC02/acc02webcor.pdf

 

[EtnemelC]

Thanks @CandyOates. I was also thinking to use random generation of the starting points in case i don't find anything new related to this problem. My only doubt was, indeed, about how the starting values are actually chosen in the industry to estimate the NGARCH GBM. For example, are there some good theoretical values for the initial parameters, that could be computed from the sample, maximizing the probability to find a global max? If not, obviously, optimization techniques like those you have listed are the only solution to go for.

@diegosanaz, i will certainly study the paper. Hope it will help me with my project too . Thanks.