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I have 2 questions.

In the Black Scholes formula for currency options, where does forward premium come in? Volatility will be a historic parameter, so which component considers fwd premia.

Typically, is OIS used to fix overnight rate? and the overnight rate would be the Fed Funds rate, right? USDIRS is used to hedge LIBOR.

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  • $\begingroup$ If you found my answer helpful, please consider accepting it as the correct answer. $\endgroup$ – AdB Apr 8 at 6:32
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When you say the Black Scholes formula for currency options, I assume you are referring to the Garman-Kohlhagen formula described here. Note that this formula is based on the interest rate differential $r_d - r_f$, which essentially captures the forward premium.

An even more explicit way to see this is to use the Black Model described here. Using this formula with $F_{t,T} = S_t e^{(r_d - r_f)(T-t)}$ being the forward FX rate will yield exactly the same formula as Garman-Kohlhagen (try to verify this algebraically), so it is clear that the option is actually written on the forward exchange rate - hence, it natually captures the forward premium.

I am a little unsure what you are asking in your second paragraph. It is true that OIS (Overnight Indexed Swap) captures the overnight rate. However, the OIS is not the same as the Fed Funds Rate (see this question).

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