Brownian Motion using Gamma instead of normal distribution

[MonteCristo]

Hello everybody,

Does someone know why some models use a Gamma instead of a normal distribution to simulate a brownian motion ? what is the aim behind that ?

Thanks

 

[D C]

MonteCristo :: think about what you're saying, look up the definition of Brownian motion. Let's say you were able to construct another scaled symmetric random walk (the way Shreve does in Shreve II) and that you were able to prove that it's increments are independent...would it satisfy all the properties similar to Brownian motion (i.e. martingale, non-zero quadratic variation, etc.)?

What is your motivation for this question? That's probably a better place to start.

 

[D C]

The only way I can make sense of your question is if you meant to let time be distributed by a gamma process. If that's what you meant, here's a white paper on the subject:

http://www.math.nyu.edu/research/carrp/papers/pdf/VGEFRpub.pdf

I assume you are looking for a model that yields access to excess kurtosis? Here Madan, Carr, and Chang (1998) argue that their VG process construct is superior to the BS models used to price options.

 

[MonteCristo]

MonteCristo :: think about what you're saying, look up the definition of Brownian motion. Let's say you were able to construct another scaled symmetric random walk (the way Shreve does in Shreve II) and that you were able to prove that it's increments are independent...would it satisfy all the properties similar to Brownian motion (i.e. martingale, non-zero quadratic variation, etc.)?

What is your motivation for this question? That's probably a better place to start.

Hi, it about replacing normal random generator by the difference between two gammas so as we could have 1/2 times down, 1/2 up. Thank you very mush !