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Given money market rates such as USD LIBOR and EURIBOR and in the context of FX options valuation, I have been reading about the importance to include a so called basis adjustment to one of the respective mm rates.

  1. Since interest rate parity seems to break down, what is the economical foundation of such an adjustment?

  2. With reference to my previous question, if I use the Black model (in a GBM world) to value, say a one month call option on the EURUSD spot (priced on the forward), is it true that the basis adjustment is already included in the one month forward? So I can simply use the (unadjusted) one month EURIBOR for the domestic interest rate r (the discount factor)?

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If the forward fx price is available, it already includes any basis adjustment and you may use the Black model (in a GBM world) to value the option. In that case the only usage of the interest rate input is to discount the payoff.

The reason that the fx forward may not be consistent with the two risk-free interest rates (i.e. appearing to violate interest rate parity) is that in practice, you cannot actually borrow and lend at those two interest rates. That's certainly true for individuals, but it's also true for banks. A bank can't easily borrow dollars at Fed Funds (unsecured) and invest Euros at Eonia separately. What it can do is simultaneously borrow dollars and invest in Euros, in the so called currency basis swap market.

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