Explain finite-difference method in finance

Question

Explain finite-difference method in finance.

Answer 1

Financial problems starting from stochastic differential equations as models for quantities developing randomly, like equity prices or interest rates, are using the language of calculus. We refer, in calculus to gradients, slopes, rates of change and sensitivities. Such mathematical ‘derivatives’ explain how fast a dependent variable, changes as one of the independent variables, as an option value, as an equity price and changes. These sensitivities are technically explained as the ratio of the infinitesimal change in the dependent variable to the infinitesimal change into the independent.

And we need an infinite number of such infinitesimals to explain an entire curve. Nonetheless, when trying to compute these slopes numerically, on a computer, for illustration, we cannot deal along with infinites and infinitesimals, and have to resort to estimates.