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Fixed Income Modelling$
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Claus Munk

Print publication date: 2011

Print ISBN-13: 9780199575084

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199575084.001.0001

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Numerical Techniques

Numerical Techniques

Chapter:
(p.472) 16 Numerical Techniques
Source:
Fixed Income Modelling
Author(s):

Claus Munk

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199575084.003.0016

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

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