# Tag Info

0

Try the VG model by Madan, Carr & Chang.

1

I think this question might be asking for the central limit theorem. If we consider a process W which varies as a series of independent random steps, then the Central Limit Theorem tells us that after many steps, the value of W will be normally distributed.

2

The question is not 100% clear. If you set $X = W_t-W_s$ where $t-s = 1$ then this is equal in distribution to $W_1-W_0$ and the defining property of Brownian motion is that increments are normally distributed. In the general case $W_t-W_s$ is $N(0,t-s)$, where the second parameter is variance. If you set $dW_t = W_{t+dt}-W_t = Z \sqrt{dt}$, where ...

3

This is a good shorter reference: http://www.impan.pl/CZM/tankov.pdf. Cont and Tankov have also written a longer book about modelling with Levy processes that I think is really good. There's going to be a strong connection between the sequence of jump times and the Levy measure $\nu$. In a single unit of time, $\nu(dx)$ is a measure (not necessarily a ...

Top 50 recent answers are included