[R-SIG-Finance] Compound Poisson process

Thomas Steiner finbref.2006 at gmail.com
Wed Aug 27 23:16:32 CEST 2008


Your question is a math-question, not an R-Finance question. So don't
expect too many replies.

Your price process is the sum of a brownian motion and two jump
processes, right?
I'm not sure if the beta distribution is infinitely divisible (Pareto
is). This can put you in big trouble, you will not have stationary
increments anymore.
I'm not totally sure, but the Pareto will give you a simple jump
diffusion (finite activity), which can be sampled easily.


2008/8/27 Zornitsa Luleva <zornitsa.luleva at gmail.com>:
> Dear all,
> i would like to implement two compound Poisson processes that simulate
> upwards and downwards jumps respectively. Thereby, the up jump magnitudes
> are Pareto distributed and the down jump magnitudes are Beta distributed.
> These jump processes as well as a Brownian motion are a part of a model
> describing security prices.
> My goal is to simulate the two processes (independently of each other) with
> known values of the parameters - the Poisson lambdas and the Beta / Pareto
> parameters. Afterwards, I want to take the simulated data and try to
> estimate the parameters using Maximum likelihood estimation (MLE) to see how
> well an estimation algorithm that I implemnted is working.
> My questions:
> 1) Is it right to simulate exponentially distributed waiting times between
> the jumps and then just "jump" with a Beta / Pareto distributed magnitude?
> 2) When I simulate the down jumps and take zero as a starting point, then I
> get negative values. The MLE does not like it, neither do I, because it
> means, that I simulate negative prices. Can I take another starting value
> for the process (for example one) ?
> I am very grateful for a concise answer.
> Cheers,
> Zoe
>        [[alternative HTML version deleted]]
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