abbreviations

: current price of the underlying
$\tau\stackrel{\Delta}{=}T-t$
$f\stackrel{\Delta}{=}I\!\!E[S_T\vert S_t=x]= xe^{(r_d-r_f)\tau}$ : forward price of the underlying
$\theta_{\pm}\stackrel{\Delta}{=}\frac{r_d-r_f}{\sigma}\pm\frac{\sigma}{2}$
$d_{\pm}\stackrel{\Delta}{=}\frac{\ln\frac{x}{K}+\sigma\theta_{\pm}\tau}{\sigma\sqrt{\tau}}=\frac{\ln\frac{f}{K}\pm\frac{\sigma^2}{2}\tau}{\sigma\sqrt{\tau}}$
$n(t)\stackrel{\Delta}{=}\frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}t^2}=n(-t)$
${\cal N}(x)\stackrel{\Delta}{=}\int_{-\infty}^xn(t)\,dt=1-{\cal N}(-x)$

2000-06-11

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