# Mix of Arithmetic and Geometric Brownian Motion

Talking with some traders the other day, I found out that they were using a pricing model based on a mix between a geometric brownian motion and an arithmetic brownian motion to price certain derivatives.

Would anyone know if this is actually a well known model? Or is this actually one of these "secret" solutions that certain quant teams develop?

Practitioners' take on the matter would be particularly helpful.

$$dx(t)=\ldots\ dt+[x(t)]^\gamma\ dW(t)$$
If $\gamma$ is zero then you've got BM, if it's one you get GBM, inbetween you have a 'mix'.
• thanks, I suppose I would be looking at something like: $dx(t) = r [x(t)]^{\gamma} + \sigma [x(t)]^{\gamma}dW(t)$. Does this model have a well-used name? – Iliana Jul 24 '16 at 10:43