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A Stochastically Correlated Bivariate Square-Root Model

Author

Listed:
  • Allan Jonathan da Silva

    (Coordination of Mathematical and Computational Methods, National Laboratory for Scientific Computing (LNCC), Petrópolis 25651-075, RJ, Brazil
    Department of Production Engineering, Federal Center for Technological Education (CEFET/RJ), Itaguaí 23812-101, 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)

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.

Suggested Citation

  • Allan Jonathan da Silva & Jack Baczynski & José Valentim Machado Vicente, 2024. "A Stochastically Correlated Bivariate Square-Root Model," IJFS, MDPI, vol. 12(2), pages 1-24, March.
    • Handle: RePEc:gam:jijfss:v:12:y:2024:i:2:p:31-:d:1363241
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    References listed on IDEAS

    as
    1. Almeida, Caio & Vicente, José, 2009. "Are interest rate options important for the assessment of interest rate risk?," Journal of Banking & Finance, Elsevier, vol. 33(8), pages 1376-1387, August.
    2. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    3. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
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