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On the Analysis of a Generalised Mean-Reverting Stochastic Model with Two Uncorrelated Brownian Motions

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  • Emmanuel Coffie

    (University of Liverpool)

Abstract

We introduce a highly sensitive mean-reverting stochastic model under the influence of two uncorrelated Brownian motions. However, due to its structural complexity and analytical intractability, we develop new mathematical techniques to investigate into the properties of the true and numerical solutions. Moreover, we show that, for a sufficiently small step size, the numerical solutions converge to the true solution in probability. Finally, we provide numerical demonstrations to support the theoretical findings.

Suggested Citation

  • Emmanuel Coffie, 2025. "On the Analysis of a Generalised Mean-Reverting Stochastic Model with Two Uncorrelated Brownian Motions," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-20, March.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:1:d:10.1007_s11009-025-10149-7
    DOI: 10.1007/s11009-025-10149-7
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    References listed on IDEAS

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    1. Adrian Dragulescu & Victor Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 443-453.
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    3. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    4. Nowman, K B, 1997. "Gaussian Estimation of Single-Factor Continuous Time Models of the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 52(4), pages 1695-1706, September.
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