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A stock in foreign market with the fx dynamic (in foreign measure) as the followings:

$\begin{align} dS_t &= r_f S_tdt + \sigma_s S_tdW_t^s \\ dF_t& = (r_d-r_f)F_tdt + \sigma_F F_tdW_t^F \\ dW_t^sdW_t^F &= \rho dt \end{align}$

$1$ unit of foreign currency equals to $F_t$ unit of domestic currency. $\tilde{\mathbb{E}}$ is in domestic measure.

Please correct me if I am wrong:

  1. Physically settled: The price in domestic currency of an instrument that will physically delivery the holder a share of the stock at time $T$ is $e^{-r_dT}\tilde{\mathbb{E}}(S_T)$
  2. Cash settled: The price in domestic currency of an instrument that will give the holder domestic dollar equivalent to the value of the share at time $T$ is $e^{-r_dT}\tilde{\mathbb{E}}(F_TS_T)$
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  • $\begingroup$ $\tilde{\mathbb{E}}(S_T)$ looks weird or wrong to me: you would be taking the domestic expectation of a foreign variable $\endgroup$
    – nbbo2
    Jun 17, 2022 at 12:06
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    $\begingroup$ Agree. 1. Looks like a quanto contract. Physical vs cash settle should not change the payout. If you get physical delivery you still have to sell the stock into foreign currency and then do a FX trade $\endgroup$
    – dm63
    Jun 17, 2022 at 15:20

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