Chapter

Numerical Techniques

Claus Munk

in Fixed Income Modelling

Published in print June 2011 | ISBN: 9780199575084
Published online September 2011 | e-ISBN: 9780191728648 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199575084.003.0016
Numerical Techniques

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Numerical procedures — computer-implemented algorithms — have to be applied in order to price assets with early exercise features and assets with complicated payoff structures. This chapter introduces the three main types of numerical procedures used in fixed income modelling. The finite difference approach offers a numerical solution of the partial differential equations that prices have to satisfy in diffusion models. Monte Carlo simulation gives an approximation of the expected value of a random variable, which is useful since prices are linked to expected payoffs (appropriately risk-adjusted and discounted). Approximating trees provide an approximation of the stochastic process of the relevant state variables in a given model and assets are typically easy to price by backwards recursion through the tree. For all three procedures, the chapter presents examples, explains how to apply the procedures to American-style options, and discusses the computation of appropriate risk measures. The procedures are compared and strengths and weaknesses of the different procedures are explained

Keywords: finite difference; explicit; implicit; Crank-Nicolson; Monte Carlo simulation; variance reduction techniques; Longstaff-Schwartz least squares method; approximating tree; trinomial tree; American option

Chapter.  33838 words.  Illustrated.

Subjects: Financial Markets

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