identities

$\displaystyle \frac{\partial d_{\pm}}{\partial\sigma}$	$\textstyle =$	$\displaystyle -\frac{d_{\mp}}{\sigma}$	(19)
$\displaystyle \frac{\partial d_{\pm}}{\partial r_d}$	$\textstyle =$	$\displaystyle \frac{\sqrt{\tau}}{\sigma}$	(20)
$\displaystyle \frac{\partial d_{\pm}}{\partial r_f}$	$\textstyle =$	$\displaystyle -\frac{\sqrt{\tau}}{\sigma}$	(21)
$\displaystyle xe^{-r_f\tau}n(d_+)$	$\textstyle =$	$\displaystyle Ke^{-r_d\tau}n(d_-).$	(22)
$\displaystyle {\cal N}(\phi d_-)$	$\textstyle =$	$\displaystyle I\!\!P[\phi S_T\geq\phi K]$	(23)
$\displaystyle {\cal N}(\phi d_+)$	$\textstyle =$	$\displaystyle I\!\!P\left[\phi S_T\leq\phi \frac{f^2}{K}\right]$	(24)

2000-06-11

Ads