Chapter 17. Derivatives Valuation

Derivatives are a huge, complex issue.

— Judd Gregg

Options and derivatives valuation has long been the domain of so-called rocket scientists

on Wall Street — i.e., people with a Ph.D. in physics or a similarly demanding discipline

when it comes to the mathematics involved. However, the application of the models by the

means of numerical methods like Monte Carlo simulation is generally a little less involved

than the theoretical models themselves.

This is particularly true for the valuation of options and derivatives with European

exercise — i.e., where exercise is only possible at a certain, predetermined date. It is a bit

less true for options and derivatives with American exercise, where exercise is allowed at

any point over a prespecified period of time. This chapter introduces and uses the Least-

Squares Monte Carlo (LSM) algorithm, which has become a benchmark algorithm when it

comes to American options valuation based on Monte Carlo simulation.

The current chapter is similar in structure to Chapter 16 in that it first introduces a generic

valuation class and then provides two specialized valuation classes, one for European

exercise and another one for American exercise.

The generic valuation class contains methods to numerically estimate the most important

Greeks of an option: the Delta and the Vega. Therefore, the valuation classes are important

not only for valuation purposes, but also for risk management purposes.