[R-SIG-Finance] Compound Poisson process

Martin Becker martin.becker at mx.uni-saarland.de
Thu Aug 28 11:06:52 CEST 2008

Dear Zornitsa,

Zornitsa Luleva wrote:
> 1) Is it right to simulate exponentially distributed waiting times between
> the jumps and then just "jump" with a Beta / Pareto distributed magnitude?

to complement what Thomas and Martin already wrote:
Depending on what parts of the process are needed (e.g. final values 
only, discrete approximation of process path,...) different techniques 
(which are mentioned in the monograph by Cont/Tankov) may be favourable:

- final values only: sample the number of jumps from 
Poisson(lambda[i]*T) distribution (when T denotes final time) for Beta 
[1] and Pareto [2] jumps and sum up simulated jump magnitudes 
accordingly (should be especially efficient when implemented in R 
without using C calls). [If jump times are needed: they are distributed 
uniformly on (0,T).]

- discrete approximation: Beta and Pareto distributed jumps may be 
concentrated in one CP process:
  * draw exponential waiting times (rate = lambda[1]+lambda[2])
  * for each jump: with probability lambda[1]/(lambda[1]+lambda[2]) draw 
Beta jump; draw Pareto jump else.

Kind regards,


Dr. Martin Becker
Saarland University
Statistics and Econometrics

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