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Financial Derivative and Energy Market Valuation: Theory and Implementation in MATLAB
book

Financial Derivative and Energy Market Valuation: Theory and Implementation in MATLAB

by Michael Mastro PhD
March 2013
Intermediate to advanced content levelIntermediate to advanced
664 pages
15h 11m
English
Wiley
Content preview from Financial Derivative and Energy Market Valuation: Theory and Implementation in MATLAB

Chapter 14: Application of Characteristic Functions

14.1 Introduction

This chapter commences by providing the mathematical link between a characteristic function and its corresponding probability density function (PDF) and cumulative distribution function (CDF). These relationships are used in the generation of a PDF or CDF for any reasonable characteristic function. Proper formatting of the numerical procedure allows the use of efficient fast Fourier transform (FFT) or fractional fast Fourier transform (FrFFT) routines. Similar numerical techniques can be used to fit the parameters of a particular characteristic function to a set of asset prices.

14.2 Levy Theorem

The Fourier transform of the real-space PDF, , is the characteristic function, , as given by

equation

By symmetry, the PDF can be recovered by the inverse Fourier transform of the characteristic function as given by

equation

The probability of finding at random variable in the interval (−∞,x) drawn from an arbitrary distribution is the CDF as ...

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Publisher Resources

ISBN: 9781118501818Purchase book