I have an "exotic" option that is a function of two interest rates (say 3m Libor at 1y maturity and 2y maturity). I assume both the rates follow sabr model (already calibrated to vanillas), so I have both the marginals fully defined. Price of this option is observable in the market. I assume Gaussian copula to model the dependence of two rates. So only parameter left to estimate is the correlation.
How do I calibrate this copula to market prices i.e. how do I estimate the correlation? I vaguely know it will involve iteratively solving the double integral of gaussian copula to match market price but I don't know how to get the limits of the integral and also how to go from copula to option price.
Please feel free to assume a reasonable payoff of option in case it helps explain. Thanks for any pointers for this copula beginner.