A Stochastically Correlated Bivariate Square-Root Model

Allan Jonathan da Silva (), Jack Baczynski and José Valentim Machado Vicente
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Allan Jonathan da Silva: Coordination of Mathematical and Computational Methods, National Laboratory for Scientific Computing (LNCC), Petrópolis 25651-075, RJ, Brazil
Jack Baczynski: Coordination of Mathematical and Computational Methods, National Laboratory for Scientific Computing (LNCC), Petrópolis 25651-075, RJ, Brazil
José Valentim Machado Vicente: Institute of Mathematics and Statistics, Rio de Janeiro State University (UERJ), Rio de Janeiro 20550-900, RJ, Brazil

IJFS, 2024, vol. 12, issue 2, 1-24

Abstract: We introduce a novel stochastically correlated two-factor (i.e., bivariate) diffusion process under the square-root format, for which we analytically obtain the corresponding solutions for the conditional moment-generating functions and conditional characteristic functions. Such solutions recover verbatim those of the uncorrelated case which encompasses a range of processes similar to those produced by a bivariate square-root process in which entries are correlated in the standard way, that is, via a constant correlation coefficient. Note that closed-form solutions for the conditional characteristic and moment-generating functions are not available for the latter. We focus on the financial scenario of obtaining closed-form expressions for the exact price of a zero-coupon bond and Asian option prices using a Fourier cosine series method.

Keywords: stochastic correlation; CIR model; conditional characteristic functions; stochastic differential equation; financial modeling; option pricing; COS method (search for similar items in EconPapers)
JEL-codes: F2 F3 F41 F42 G1 G2 G3 (search for similar items in EconPapers)
Date: 2024
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