Converting an FX Option Premium Between Currencies

Summary

The document addresses how to express an FX option premium in a different currency after pricing it with a Black-style formula. The answer is to convert the already calculated premium using the spot exchange rate, just as one would convert the value of another asset denominated in the original currency. This avoids repricing the option when the request is only to restate its premium in the other currency.

The guidance is concise and assumes the spot quote is interpreted in the correct direction for the desired conversion. It does not discuss alternative settlement conventions, collateral currencies, discounting, or the effect of changing pricing assumptions. The explanation is a currency-unit conversion, not a new valuation of the option under a different market or numeraire.

Key ideas

• An option premium calculated in domestic currency can be converted using the spot FX rate.
• The exchange-rate quote direction determines whether to multiply or divide.
• Currency conversion restates the premium and does not require repricing when valuation assumptions are unchanged.
• The brief answer does not address settlement conventions or collateral effects.

Tags

# FX option premium conversion from one currency to another


# FX option premium conversion from one currency to another












Suppose we have an FX option with the underlying FX rate $X^{FOR/DOM}$ and suppose we used a Black like formula to get the price, which is given in domestic currency. How can one simply convert the premium in the domestic currency to a premium in the foreign currency without having to reprice the option?

Thanks

## Answer by Kurt G. (score 2, accepted)

https://quant.stackexchange.com/a/66595

You simply take the spot fx rate and convert the domestic premium into the foreign currency. It works with the option price exactly the same way as with the price of any other asset.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.