Lets suppose a G10 FX vol market-maker starts out with a flat book. During the day, the market-maker bought a EURUSD 1 week ATM straddle from one client while sold USDJPY 1 week ATM straddle from another client, with same USD notional.
So the entire book looks like this:
- long EURUSD 1 week ATM straddle (same USD notional)
- short USDJPY 1 week ATM straddle (same USD notional)
Also, lets suppose the EURUSD 1 week smile is downward-sloping, and USDJPY 1 week smile is downward-sloping (or JPYUSD 1 week smile is upward-sloping).
Then, another client comes in RFQing a two-way price on EURJPY 1 week ATM straddles, coincidently for the same USD-equivalent notional.
If the market-maker does not have any views in the next 1 week and wants to be flat (maybe needs to go on vacation), is the market-maker axed a certain way on EURJPY 1 Week straddles? For simplicity, assume everything is done simultaneously, so no market moves would impact the decision.
My guess would be that if the market-maker is sitting in a US domiciled desk, then the market-maker would be axed to sell EURJPY 1 week ATM straddles. Given no market move, being able to sell EURJPY will not only flatten out the delta/gamma risk but also roughly flatten out the vanna risk
Or would the preference be to trade out of each of the EURUSD option and the USDJPY option separately, since these vols trade differently? And quote the EURJPY option without any axe, so all three 1 week options would be managed separately?
Look forward to your thoughts.