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Composite asset - necessary adjustments

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

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

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