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.


1 Answer 1


Are you talking about something like this?

$$dx(t)=\ldots\ dt+[x(t)]^\gamma\ dW(t)$$

If $\gamma$ is zero then you've got BM, if it's one you get GBM, inbetween you have a 'mix'.

  • $\begingroup$ 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? $\endgroup$
    – Iliana
    Commented Jul 24, 2016 at 10:43
  • 1
    $\begingroup$ I would put it under (Generalized) Constant Elasticity of Variance models. $\endgroup$
    – Kiwiakos
    Commented Jul 24, 2016 at 14:14

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