On the distribution of a discrete sample path of a square-root diffusion
AbstractWe derive the multivariate moment generating function (mgf) for the stationary distribution of a discrete sample path of n observations of a square-root diffusion (CIR) process, X(t). The form of the mgf establishes that the stationary joint distribution of (X(t(1)),...,X(t(n))) for any fixed vector of observation times (t(1),...,t(n)) is a Krishnamoorthy-Parthasarathy multivariate gamma distribution. As a corollary, we obtain the mgf for the increment X(t+dt)-X(t), and show that the increment is equivalent in distribution to a scaled difference of two independent draws from a gamma distribution. Simple closed-form solutions for the moments of the increments are given.
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Bibliographic InfoPaper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2012-12.
Date of creation: 2012
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-15 (All new papers)
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