The integrated square-root process
University of Melbourne Author/sDufresne, Daniel
AffiliationEconomics and Commerce: Centre for Actuarial Studies
CitationsDufresne, Daniel (2001) The integrated square-root process.
Access StatusOpen Access
ISBN 0734021348 research paper no. 90.
The square-root process has been used to model interest rates and stochastic volatility. This paper studies some of its properties, particularly those of the integral of the process over time. After summarizing the properties of the square-root process, the Laplace transform of the integral of the square-root process is derived. Three methods for the computation of the moments of this integral are given, as well as some properties of the density of the integral. The last section studies the relationship between the Laplace transforms of a variable and of its reciprocal, a topic which arises in the previous analysis and elsewhere. An application to the generalized inverse Gaussian distribution is given
Keywordssquare-root process; stochastic volatility; volatility swaps; Asian options; interest rate models; generalized inverse Gaussian distribution.
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