Calibrating Local Volatility Models with Stochastic Drift and Diffusion

We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, deterministic and finally rates. For each model, we include detailed derivations of the corresponding SDE systems, list required input data steps calibration. give conditions under which a can exist given European option prices, rate model parameters, correlations. The models are posed in foreign exchange setting. drift term is as difference two short domestic foreign, modeled by G1++ process. volatility, variance CIR tests to show convergence accuracy proposed algorithms.