Financial Instrument Pricing Using C++, 2nd Edition

CHAPTER 32Monte Carlo Simulation, Part II

32.1 Introduction and Objectives

In this chapter we continue with the analysis of the Monte Carlo method already discussed in Chapter 31, in which we designed a software framework for one-factor plain options. We discovered a number of new features that we would like to address here:

• R1: More general SDEs, for example support for corrected drift functions and the derivative of the diffusion term.
• R2: Support for a range of finite difference schemes, for example the predictor–corrector and Milstein methods.
• R3: More support for random number generation based on the C++ <random> and Boost Random libraries.
• R4: Improving speedup by using multithreading and multitasking code (for example, C++ Concurrency and PPL).
• R5: Creating a mediator class that prices several option types in a seamless manner (using events that are supported by Agents Library and the Boost signals2 library).
• R6: Developing flexible modules (for example, builders and factories) to configure the software framework while keeping the code maintainable.

We address these requirements by creating C++ code to realise them.

32.2 Parallel Processing and Monte Carlo Simulation

In this section we discuss feature R4. In general, the Monte Carlo method has a reputation for being slow, especially when we simulate many paths (Glasserman, 2004). (Incidentally, it is a good idea to run your Monte Carlo application in release mode.) We can start thinking about how to improve the speedup ...