Some Properties of CIR Processes

This article derives some properties of variants of squared Bessel processes known as CIR processes in the finance literature. We derive the transition probability density function of a square-root process and compute the resolvent density of CIR processes. As a consequence, we derive the density of...

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Bibliographic Details
Published inStochastic analysis and applications Vol. 24; no. 4; pp. 901 - 912
Main Authors Chou, Ching-Sung, Lin, Hsien-Jen
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Taylor & Francis Group 01.08.2006
Taylor & Francis
Subjects
Applications
Barrier options
CIR processes
Exact sciences and technology
Hitting times
Insurance, economics, finance
Mathematics
Probability and statistics
Probability theory and stochastic processes
Resolvent
Sciences and techniques of general use
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
Statistics
Stochastic processes
Density estimation
CIR process
Stochastic analysis
Resolvent
Finance
Square root process
Martingale
Probability density function
Transition probability
Laplace transformation
Hitting probability
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Summary:This article derives some properties of variants of squared Bessel processes known as CIR processes in the finance literature. We derive the transition probability density function of a square-root process and compute the resolvent density of CIR processes. As a consequence, we derive the density of CIR processes sampled at an independent exponential time. Moreover, we derive explicit expressions of the Laplace transforms (LTs) of first hitting times by martingale methods.
ISSN:0736-2994
1532-9356
DOI:10.1080/07362990600753643