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With reference to the forward exchange rate definition, let be:

  • $S$: the spot rate

  • $F$: the forward rate

  • $r_d$ and $r_f$: respectively the domestic and foreign interest rates

  • $DF_d$ and $DF_f$: respectively the domestic and foreign discount factors

Then, by no arbitrage assumption it holds true that:

1) $S = (1 + r_d)/ (1 + r_f) * F$ in the discrete case;

2) $1 + r_d = (1 + r_f) * F/S$ in the discrete case;

3) $F = DF_f/ DF_d * S$ in the continuous case;

4)For the investor who owns in domestic currency a sum X and decides to invest it in the foreign denominated currency, the foreign interest rate $r_f$ is perceived as a premium which has to be discounted;

5) All the rest being fixed, $F$ is expected to increase as $r_d$ decreases

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By definition, the FX spot rate is the number of units of domestic currency (also referred to as numéraire) needed to buy one unit of foreign currency at a given time. The FX forward rate is a contract leading to an exchange of notionals in a future time at a pre-specified (forward) rate. The outright forward is related to the FX spot rate via the spot-rates parity: $$f(t,T)=S_te^{(r_d-r_f)(T-t)}$$ By no-arbitrage, any forward value has zero value at inception. At any time $\tau\in(t,T]$, for a given exchange rate known as strike rate, the forward value is given by the payoff: $$V_f (t,T)=e^{-r_d (T-t)} (f(t,T)-K)=S_t e^{-r_f (T-t) }-Ke^{-r_d (T-t) }$$

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  • $\begingroup$ thank you very much. Which answer do you think is correct, given the information you provided me? $\endgroup$ – Pietro Scaglione Feb 25 at 9:54
  • $\begingroup$ It should be pretty immediate from my answer! All are true, but 1). $\endgroup$ – FunnyBuzer Feb 25 at 13:24

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