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In there, I expressed interest in how well the usual strategy of replicating an underlying stock would work in this case. This strategy would consist of investing Delta (derivative of the option's price wrt stock price) in the foreign stock, and borrowing domestically.

Are there some market conditions under which that strategy actually would work? An idea of one such condition could be that the exchange rate remains constant over the relevant period?

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    $\begingroup$ Of course if the exchange rate stays unchanged it would work. But now think if the price of the stock (in terms of foreign currency, say 100 Quanzas per share) stays constant and the FX rate fluctuates. At time T you will have lost/made some money when you settle the contract in domestic currency. $\endgroup$ – noob2 Mar 3 '17 at 16:51

You can borrow domestically. However, we note the following:

  • You can not use your domestic cash to buy foreign stock directly, instead, you also need a foreign cash account.

  • Moreover, for the replicating portfolio to be self-financing, the capital gain from the foreign stock and the cash account need to properly adjusted, that is, the foreign cash account is necessary.

  • Since you are replicating a domestic payoff, all the foreign asset values need to be converted to domestic currency.

In summary, you need instruments $XS$, $XB^f$, and $B^d$. By missing any of them, you won't be able to have a self-financing replicating portfolio.

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  • $\begingroup$ Could you re-explain the foreign cash account? Since we can convert currencies back and forth, and we need to borrow in order to keep the portfolio self-financing, why not borrow from the domestic account, and just convert it to the foreign currency as we please? If we gained something in the foreign market and needed to store that somewhere, we could convert it back and store it in the domestic cash account? So do I really need a foreign cash account? $\endgroup$ – Jaood Mar 3 '17 at 22:28
  • $\begingroup$ That foreign cash account does not have to be a real account, it can be the amount that you converted. But you need to have that amount there. $\endgroup$ – Gordon Mar 3 '17 at 23:01

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