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Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model

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Abstract

We are interested in the strong convergence of Euler-Maruyama type approximations to the solution of a class of stochastic differential equations models with highly nonlinear coefficients, arising in mathematical finance. Results in this area can be used to justify Monte Carlo simulations for calibration and valuation. The equations that we study include the Ait-Sahalia type model of the spot interest rate, which has a polynomial drift term that blows up at the origin and a diffusion term with superlinear growth. After establishing existence and uniqueness for the solution, we show that an appropriate implicit numerical method preserves positivity and boundedness of moments, and converges strongly to the true solution.

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Author notes

  1. Lukasz Szpruch

    Present address: Mathematical Institute, 24-29 St. Giles’, Oxford, OX1 3LB, UK

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, UK

    Lukasz Szpruch, Xuerong Mao, Desmond J. Higham & Jiazhu Pan

Authors
  1. Lukasz Szpruch
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  2. Xuerong Mao
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  3. Desmond J. Higham
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  4. Jiazhu Pan
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Corresponding author

Correspondence to Desmond J. Higham.

Additional information

Communicated by Anders Szepessy.

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Szpruch, L., Mao, X., Higham, D.J. et al. Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model. Bit Numer Math 51, 405–425 (2011). https://doi.org/10.1007/s10543-010-0288-y

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  • DOI: https://doi.org/10.1007/s10543-010-0288-y

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