Composite asset - necessary adjustments

Submitted by loner on 17 January, 2008 - 3:11pm

Derivatives
Finance

Assume $S_t$ in $FX_t^{h}$ follows $dS_t=\mu_{h}S_tdt+\sigma_{s}S_tdW_t$ and we have a foreign currency, $FX_t^{a}$ , with the corresponding $\mu_{a}$ , $\sigma_{fx_{h}fx_{a}}$ and $\rho_{s,fx_{h}fx_{a}}$ .

A composite asset of $S_t$ into $FX_t^{a}$ , $S_t^{a}$ , is then

$<br /> dS_t^{a}=\mu_{a}S_t^{a}dt+\sqrt{\sigma_{s}^2+\sigma_{fx_{h}fx_{a}}^2+2\sigma_{s}\sigma_{fx_{h}fx_{a}}\rho_{s,fx_{h}fx_{a}}}S_t^{a}d\acute{W}_t$