Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model |
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Authors: | Lukasz Szpruch Xuerong Mao Desmond J Higham Jiazhu Pan |
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Institution: | 1.Department of Mathematics and Statistics,University of Strathclyde,Glasgow,UK;2.Mathematical Institute,Oxford,UK |
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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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Keywords: | |
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