Quant Reading List Numerical Methods

This post is part three of a series of reading lists for beginning quantitative analysts. Other posts in the series concentrate on Derivative Pricing, C++ Programming and Python Programming.

Reading Lists for Beginning Quantitative Analysts

This post is part of a series of reading lists for beginner quantitative analysts. Other posts in the series concentrate on Derivatives Pricing, C++ Programming and Python Programming:

In the previous article we outlined a range of C++ books to help learn the syntax necessary for implementing derivatives pricing models. Such models often require the use of numerical methods to provide solutions in an approximate fashion. Two methods in particular are well-used for derivatives pricing: Finite Difference Methods (FDM) and Monte Carlo (MC) methods.

Finite Difference Methods

Finite difference methods are a class of numerical methods used to provide approximate solutions to various Partial Differential Equations that arise in derivatives pricing models. Perhaps the most famous is the Black-Scholes PDE used to price a European call or put.

Finite difference methods work by discretising the derivative terms in the PDE, leading to a series of algebraic equations that can be solved algorithmically. An explicit finite difference method calculates the quantities at the next time solely in terms of the values at the previous step. An implict finite difference method calculates the quantities at the next time step in terms of both the values of the next time step and the previous time step.

An important concept in finite difference methods is whether a particular solution scheme is stable.

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. The first two are easier to obtain, while the latter two are generally harder to find:

Monte Carlo Methods

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

The following Wikipedia articles discuss MCM in more detail:

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

Suggested Reading

The best books to start with from a C++/numerical point of view are Daniel Duffy's Financial Instrument Pricing Using C++ and Mark Joshi's C++ Design Patterns and Derivatives Pricing books. Mark Joshi's C++ text should be read in conjunction with his Concepts and Practice of Mathematical Finance that was discussed in the previous article.

They will provide a strong beginner to intermediate usage of C++, with detailed insights into both FDM and MCM. Depending on which method is preferred—FDM or MCM—a subsequent choice might include Paul Wilmott's Option Pricing or Paul Glasserman's Monte Carlo Methods in Financial Engineering.

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