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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 18: Affine Jump-Diffusion Processes

18.1 Introduction

A major advancement in the study of quantitative finance occurred when a number of disparate areas of modeling were consolidated into the affine jump-diffusion transform formalism (Duffie et al., 2000). The term affine simply denotes a constant term plus a linear term. Affine asset pricing generally involves defining state prices with the drift, diffusion, interest rate and jump process coefficients, which are affine functions. This structure ensures that the derivation of the model arrives at two unique Ricatti ordinary differential equations (ODEs). Often, a solution to the Ricatti equations is available, which gives the valuation equation in a closed form. This chapter will derive several affine models—of increasing complexity—that are relevant in commodity pricing.

18.2 Affine Mean Reversion Process

In the affine mean reversion model, the logarithm of the spot is described by only one factor, a short-term variation , as given by

equation

The short-term variation is described under a real-world measure as

equation

This Ornstein–Uhlenbeck ...

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Publisher Resources

ISBN: 9781118501818Purchase book