This post is part 3 of a series of Reading Lists for Beginner Quants. Other posts in the series concentrate on Derivative Pricing, C++ Programming and Python Programming.

This post is part 3 of a series of Reading Lists for Beginner Quants. Other posts in the series concentrate on Derivative Pricing, C++ Programming and Python Programming:

In the previous article the core C++ books required for a good grounding in quantitative programming were outlined. Now it is time to discuss the books useful for learning numerical methods, in particular Finite Difference Methods (FDM) and Monte Carlo Methods (MCM).

### Finite Difference Methods

Finite Difference Methods are a class of numerical methods used to provide an approximate, discrete solution to various partial differential equations, in particular the Black-Scholes PDE. Finite Difference Methods work by discretising the derivative terms in the PDE, such that they can be implemented algorithmically. An explicit finite difference method has the quantities at the next time step calculated in terms of the values at the previous step. An implict finite difference method has the quantities at the next time step calculated in terms of both the values of the next time step and the previous time step. Stability of the scheme is an important concept.

The following articles discuss FDM in more detail:

The following are some of the more well known (and recommended!) text books on Finite Difference Methods:

### Monte Carlo Methods

Monte Carlo Methods rely on the concept of risk neutral valuation in order to price derivatives. In essence, many underlying random asset price paths are calculated and the associated derivative payoff is calculated for each path. The mean of the payoffs are taken and then the price is discounted to today's price. This will give an approximation of the the option price. Further accuracy can be obtained by increasing the number of random trials.

The following Wikipedia articles discuss MCM in more detail:

Here are some of the top financial modelling Monte Carlo Method books: