Alright so in this example an American investor wants to own an Australian equity and get paid the return that equity experiences in the local market, but in USD. The trader who prices and sells this option will only have the ability to hedge with shares of the local stock (call it AEQ for Australian equity), AUDUSD spot/forwards, and AUDUSD FX options. So the first thing he obviously would have to do after selling this product to an investor is buy AEQ for himself, which he pays AUD currency for, and then buy AUDUSD to convert the premium and current PV of the option into USD. If AEQ goes up, the trader accumulates AUD P&L, which gives him long AUD delta exposure, while the investor's position only accumulates USD P&L. That means the trader will have to sell AUDUSD as AEQ goes up, and of course buy back AUDUSD as AEQ goes down, i.e. the trader finds himself long the correlation between AEQ and AUDUSD, which of course makes the quanto option itself short that correlation. How the trader hedges the optionality of the position depends on what his assumption about what the fair value of the implied correlation between AEQ and AUDUSD is. If the fair value is +100%, then he will sell an AUDUSD FX option as his position will show a long AUDUSD gamma position (given he gets long AUDUSD as AEQ goes up, and vice versa, and the two things move perfectly in sync). If the correlation is -100%, he will see a short FX gamma position and buy an AUDUSD option. If it's zero, he won't deal any FX option and just hedge out the FX exposure with forwards as it develops. And then there will be a relatively smooth gradient of gamma between the zero gamma at 0% correlation and the amounts he is long or short at +100% and -100% correlation respectively. Once he marks his correlation at what he think it will actually realize until maturity of the quant0 and then hedges his FX option exposure according to that correlation, his unhedged risk becomes purely being wrong about his correlation assumption (as that will have him mis-hedged on his gamma). There's not really a way to hedge this exposure, so traders will price the quanto option using a conservative assumption for what the correlation could be, and then risk manage according to fair value, hoping to earn the difference in price between where they bid or offered the correlation and where they actually believe it will realize. That's how they earn their bid/offer spread.
