Schemes can be Explicit (fast but unstable if steps are too large), Implicit (stable but computationally intensive per step), or Crank-Nicolson (a highly accurate, numerically stable hybrid approach).
These are used to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables. By running millions of simulations, firms can estimate the price of exotic derivatives. mathematical modeling and computation in finance pdf
These treat volatility as a random process governed by its own stochastic differential equation, allowing it to vary continuously over time. Schemes can be Explicit (fast but unstable if