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Convergence in probability of numerical solutions of a highly non-linear delayed stochastic interest rate model

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  • Emmanuel Coffie

Abstract

We examine a delayed stochastic interest rate model with super-linearly growing coefficients and develop several new mathematical tools to establish the properties of its true and truncated EM solutions. Moreover, we show that the true solution converges to the truncated EM solutions in probability as the step size tends to zero. Further, we support the convergence result with some illustrative numerical examples and justify the convergence result for the Monte Carlo evaluation of some financial quantities.

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  • Emmanuel Coffie, 2025. "Convergence in probability of numerical solutions of a highly non-linear delayed stochastic interest rate model," Papers 2510.04092, arXiv.org.
    • Handle: RePEc:arx:papers:2510.04092
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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. 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.
    3. 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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