Before starting implementing a quanto pricer, I'd like one to confirm my algorithm. Even though there are several topics on it it's still not clear on my side.
Say I can price a stock under Heston model, and that now I'd like to introduce the quanto feature, my reasoning is the following:
- Compute implied strikes from quoted RR and BF in the FX market
- Calibrate FX and stock under Heston
- Compute the historical correlation between FX/Equity (Question, how long should be the observation window given that most of the options will be between 1 and 2 years ?)
- Generate under Heston my correlated dynamics between FX/Equity, while adjusting my asset dynamic by the quanto adjustment rho.volHestonEq.volHestonFx (Question, should I also adjust the volatility term ? If so what's the adjustment ?)
- compute the expectations under Q of my stock and then apply the forward exchange rate to get things quantoed.