FX Option Delta in a Different Accounting Currency

Summary

The document raises a question about how to express an FX option’s delta when the trading book uses an accounting currency different from either currency in the option. Its example is a one-year at-the-money EUR call and USD put, with option and rate inputs specified, while the book is accounted for in JPY. The question asks how a move in EUR/USD should affect the option’s JPY delta and whether converting a USD delta is sufficient.

No answer or calculation is included, so the treatment remains unresolved. In particular, the text speculates that EUR/USD and USD/JPY movements may be correlated, but it does not establish a correlation model or explain how cross-currency exposure should be incorporated. The example is useful for identifying a valuation and risk-reporting issue, but it does not provide a method or evidence for resolving it; the result would depend on delta convention, currency conversion, and assumptions about joint exchange-rate moves.

Key ideas

• An FX option’s delta depends on the currency in which the exposure is measured.
• The example asks how to report a EUR/USD option’s exposure in a JPY-denominated book.
• Converting a delta between currencies may not alone address the effect of cross-rate movements.
• The document does not provide a solution or specify a correlation model.

Tags

# Delta of FX Options, Different Currency in Trading Book - Trading Interview Question


# Delta of FX Options, Different Currency in Trading Book - Trading Interview Question












Having done stochastic analysis in university, together with tons of other math courses, do never prepare you for an actual interview in trading. Stumbled on what I believe might be an easy question, but do not see it at the moment.

Imagine a $1$ year ATM $EUR$ call $USD$ put strike $K=0.9090$, $S = 0.9090$, volatility $\sigma = 12\% $, $r_{EUR} = 3.96 \%$ and $r_{USD} = 3.57 \%$. Depending on the perspective we have, the delta will be difference as follows:

However, say that we are using a different currency on the trading book as our accounting currency. Take $JPY$ as an example with the current rate at $USDJPY = 100$. How would the delta in $JPY$ be affected if spot $EURUSD$ starts moving, say $+1\%$ move.

First, I would convert the delta in $USD$ to $JPY$, does it make sense? Then, instinctively the correlation between the currencies will have an effect. Since a fair assumption, is that an appreciation is $USD$ versus $JPY$ would depreciate $EURUSD$, negatively correlated. Hence, an even higher delta in the end?!

Got lost pretty fast, so would be much appreciated if someone can clarify and what assumptions you would add (take a simple $\Gamma$ if needed, but felt like there was something else to the question).

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.