IDEAS home Printed from https://ideas.repec.org/a/gam/jijfss/v12y2024i2p31-d1363241.html

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7072/12/2/31/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7072/12/2/31/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Damir Filipovi'c & Martin Larsson, 2017. "Polynomial Jump-Diffusion Models," Papers 1711.08043, arXiv.org, revised Jul 2019.
    2. Allan Jonathan da Silva & Jack Baczynski, 2024. "Exploring non-analytical affine jump-diffusion models for path-dependent interest rate derivatives," Computational Management Science, Springer, vol. 21(1), pages 1-32, June.
    3. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2020. "Early exercise boundaries for American-style knock-out options," European Journal of Operational Research, Elsevier, vol. 285(2), pages 753-766.
    4. Alan Beggs, 2021. "Afriat and arbitrage," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 167-176, October.
    5. Duy-Minh Dang & Volter Entoma, 2026. "A data-driven Fourier-mixture neural-network method for density estimation," Papers 2605.18019, arXiv.org.
    6. Jean-Yves Datey & Genevieve Gauthier & Jean-Guy Simonato, 2003. "The Performance of Analytical Approximations for the Computation of Asian Quanto-Basket Option Prices," Multinational Finance Journal, Multinational Finance Journal, vol. 7(1-2), pages 55-82, March-Jun.
    7. Marcelo F. Perillo, 2021. "Valuación de Títulos de Deuda Indexados al Comportamiento de un Índice Accionario: Un Modelo sin Riesgo de Crédito," CEMA Working Papers: Serie Documentos de Trabajo. 784, Universidad del CEMA.
    8. Chris Kenyon & Andrew Green, 2015. "Self-Financing Trading and the Ito-Doeblin Lemma," Papers 1501.02750, arXiv.org.
    9. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
    10. Enrico Biffis & Beniamin Goldys & Cecilia Prosdocimi & Margherita Zanella, 2015. "A pricing formula for delayed claims: Appreciating the past to value the future," Papers 1505.04914, arXiv.org, revised Jul 2022.
    11. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    12. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    13. Anlong Li, 1992. "Binomial approximation in financial models: computational simplicity and convergence," Working Papers (Old Series) 9201, Federal Reserve Bank of Cleveland.
    14. Boswijk, H. Peter & Laeven, Roger J.A. & Vladimirov, Evgenii, 2024. "Estimating option pricing models using a characteristic function-based linear state space representation," Journal of Econometrics, Elsevier, vol. 244(1).
    15. Timothy Johnson, 2015. "Reciprocity as a Foundation of Financial Economics," Journal of Business Ethics, Springer, vol. 131(1), pages 43-67, September.
    16. Ivan Peñaloza & Pablo Padilla, 2022. "A Pricing Method in a Constrained Market with Differential Informational Frameworks," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 1055-1100, October.
    17. Pascal Franc{c}ois & Genevi`eve Gauthier & Fr'ed'eric Godin & Carlos Octavio P'erez Mendoza, 2024. "Enhancing Deep Hedging of Options with Implied Volatility Surface Feedback Information," Papers 2407.21138, arXiv.org, revised Aug 2025.
    18. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    19. Das, Sanjiv Ranjan, 1998. "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 333-369, November.
    20. Jamshidian, Farshid, 2008. "Numeraire Invariance and application to Option Pricing and Hedging," MPRA Paper 7167, University Library of Munich, Germany.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jijfss:v:12:y:2024:i:2:p:31-:d:1363241. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.