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Convergence of a exponential tamed method for a general interest rate model

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  • Lord, Gabriel
  • Wang, Mengchao

Abstract

We prove mean-square convergence of a exponential tamed method, for a generalized Ait-Sahalia interest rate model. The method is based on a Lamperti transform, splitting and applying a tamed numerical method for the nonlinearity. The main difficulty in the analysis is caused by the non-globally Lipschitz drift coefficients of the model. We consider the existence, uniqueness of the solution and boundedness of moments for the transformed SDE before proving bounded moments and inverse moment bounds for the numerical approximation. The exponential tamed method is a hybrid method in the sense that a backstop method is invoked to prevent solutions from overshooting zero and becoming negative. We successfully recover the strong convergence rate of order one for the exponential tamed method. In addition we prove that the probability of ever needing the backstop method to prevent a negative value can be made arbitrarily small. In our numerical experiments we compare to other numerical methods in the literature for realistic parameter values.

Suggested Citation

  • Lord, Gabriel & Wang, Mengchao, 2024. "Convergence of a exponential tamed method for a general interest rate model," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    • Handle: RePEc:eee:apmaco:v:467:y:2024:i:c:s0096300323006720
    DOI: 10.1016/j.amc.2023.128503
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