# binomial option pricing model - problem with risk-neutral probability

I have a little problem: in the binomial option pricing model, the price of a european derivative security $V_{n}$ satisfies: $V_{n}=[1/(1+r)]*[\tilde{p}*optionUp +\tilde{q}*optionDown]$ where: $\tilde{p}=\frac{e^{r*\Delta T} -d}{u-d}$ But when I read the article "option pricing model" on Wikipedia(http://en.wikipedia.org/wiki/Binomial_options_pricing_model), the $\tilde{p}$ of Wikipedia's $\textbf{algorithm}$ is slightly different: $\tilde{p}=\frac{(ue^{-r*\Delta T} -1)*u}{u^2-1}$ (I take q=0) I try to compare these 2 forms but they are not equal... why ??? Thanks ! :)

In the link you provided, by noting the construction of array p[], p0 and p1 are respectively the discounted $\texttt{down}$ and $\texttt{up}$ probabilities. Since $d=\frac{1}{u}$, then \begin{align*} p0 &= e^{-r \Delta T}\, \frac{u-e^{(r-q)\Delta T}}{u-d}\\ &= \frac{\big(u\,e^{-r \Delta T} -e^{-q\Delta T}\big)u }{u^2-1}, \end{align*} and \begin{align*} p1 &= e^{-r \Delta T}\,\big(1-p0\, e^{r \Delta T}\big)\\ &=e^{-r \Delta T} - p0. \end{align*} Note that $p1\, e^{r \Delta T}$ and $p0\, e^{r \Delta T}$ are respectively the $\texttt{up}$ and $\texttt{down}$ probabilities.