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Interview question: Hybrid modelling for cross-asset class

An interview question for a hybrid strategy quant position today:
If you need to a long-dated FX option, and not only the FX spot but also the interest rate itself is stochastic, how are you going to build the model to price this product?
(The direction is to build a hybrid model which involves rate and FX volatility. I like to hear what model you guys will implement in practice)

His follow-up question: how are you going to calibrate this cross-asset model?
(My answer was to calibrate the rate and FX model dynamics separately, and then calibrate their correlation. But this is a wrong answer.)