Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model
Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model
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DOI：
10.1007/s10543-010-0288-y
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发表时间：
2011-06
影响因子：
1.5
通讯作者：
L. Szpruch;X. Mao;D. Higham;Jiazhu Pan
中科院分区：
文献类型：
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作者：
L. Szpruch;X. Mao;D. Higham;Jiazhu Pan
我们感兴趣的是Euler-Maruyama型逼近的强收敛性的一类随机微分方程模型的高度非线性系数的解决方案，出现在数学金融。在这方面的结果可以用来证明蒙特卡罗模拟校准和估价。我们研究的方程包括Ait-Sahalia类型的即期利率模型，该模型具有在原点爆炸的多项式漂移项和超线性增长的扩散项。在建立解的存在性和唯一性之后，我们证明了适当的隐式数值方法保持了矩的正性和有界性，并且强收敛到真解。
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.