Tag Info

Note that, for small $\delta$, $e^{\delta}= 1+ \delta + O(\delta^2)$ and $\sqrt{x+\delta} = \sqrt{x} + O(\delta)$. Then, \begin{align*} u &= e^{r\Delta t} + e^{r\Delta t}\sqrt{e^{\sigma^2\Delta t} - 1}\\ &= 1+ r\Delta t + O(\Delta t^2) + [1+ r\Delta t + O(\Delta t^2)] \sqrt{ \sigma^2\Delta t +O(\Delta t^2)}\\ &=1+ r\Delta t + O(\Delta t^2) + [1+ ...