[R-SIG-Finance] Compound Poisson process

[Krishna Kumar]

In my little research on this calibrating a symmetric merton type jump 
process (lognormal jump size with poissson jumps) is in itself a little 
difficult.
The likelihood surface tends to have multiple maxima making it a 
stretch. Is there a reason for the assymetric jumps?. {in reality i can 
see why but the calibration is tricky}


Zornitsa Luleva wrote:
> 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
>
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>
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