Before revision:  Our approach is based on stochastic differential equations (SDEs)  like the HJM-equation or the Black-Scholes equation  governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs.
After revision:  Our approach is based on stochastic differential equations (SDEs) like the HJM-equation or the Black-Scholes equation governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical evaluation of the respective SDEs.