The article extends the Dupire formula to handle cases with stochastic interest rates and local volatility. It provides formulas for scenarios with two stochastic short rates, such as in foreign exchange or commodity markets. The researchers also developed a more general formula that can handle multiple stochastic factors in the drift and diffusion terms, allowing for the computation and calibration of leverage functions in stochastic local volatility models. The formulas can be used numerically to calculate implied volatilities efficiently.