Determine the efficiency of finite differences

Question

Determine the efficiency of finite differences?

Answer 1

Finite differences are extremely good at coping with low dimensions, and that are the method of choice when you have a contract with embedded decisions. They are excellent for non-linear differential equations.

The time taken to price an option and compute the sensitivities to underlying(s) and time using the explicit finite-difference method will be

O(M ε^-1-d/2),

Here M is the no. of different options in the portfolio and we need an accuracy of ε, and d is the no. of dimensions except time. So when we have a non-path-dependent option upon a single underlying so d = 1. Note there that we may require one piece of code per option, therefore M in the above.