FX Option Delta and the Effect of Reporting Currency

Summary

The document raises a currency-convention question about the delta of a USD-denominated USDJPY option when the holder measures value in another currency. It distinguishes the option’s sensitivity to USDJPY spot, expressed as the derivative of its dollar value, from converting the resulting exposure into the holder’s reporting currency.

For a JPY-based holder, the question is whether delta should instead be computed from the option value after conversion into yen, which would include the spot conversion itself, or whether the usual spot delta should be reported and then converted. No answer or derivation is included, so the document does not resolve how desks should define or report conversion delta. The distinction matters because a translated value can have an additional sensitivity to the exchange rate used for conversion.

Key ideas

• The usual USDJPY option delta is the derivative of the USD option value with respect to USDJPY spot.
• A holder’s reporting currency can change how the option’s value and exposure are expressed.
• The document poses, but does not answer, whether JPY conversion belongs inside the delta calculation.

Tags

# Should the delta of fx options include conversion delta?


# Should the delta of fx options include conversion delta?












Imagine you are based in EUR and trade a USDJPY FX option, worth $f(s)$ where $s$ is the USDJPY exchange rate and $f$ is the USD value of the option.

Then the delta is simply the usual delta, $f'(s)$, the derivative with respect to the USDJPY spot, and you can convert this to EUR using the EURUSD rate.

But if you were based in JPY, would the delta be the derivative of $f(s)s$? Or would one still report $f'(s)$ but converted to JPY as $f'(s)s$?

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