[R-SIG-Finance] Compound Poisson process

Martin Keller-Ressel mkeller at fam.tuwien.ac.at
Thu Aug 28 10:53:18 CEST 2008

Hi Zornitsa,

On Wed, 27 Aug 2008 16:12:23 -0000, Zornitsa Luleva  
<zornitsa.luleva at gmail.com> wrote:

> 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) ?

The usual approach here would be to model the log-price by a Brownian  
motion plus jumps. This process can of course become negative, but once  
you take the exponential you get a strictly positive price process. Your  
jumps then describe relative change in prices, not absolute change. Such  
models are called exponential Levy models, in 'Financial Modelling with  
jumps' by Rama Cont and Peter Tankov you will find a lot of examples and  
background on this.

best regards,
Martin Keller-Ressel

Martin Keller-Ressel
Research Unit of Financial and Actuarial Mathematics, TU Vienna

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