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Structure preserving stochastic integration schemes in interest rate derivative modeling

机译:利率导数建模中的结构保全随机积分方案

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In many applications, differential equation models require geometric integration, i.e., the application of structure-preserving integration schemes. In computational finance, for example, the numerical simulation of extended Libor market models used to value structured interest rate derivatives has to preserve positivity or boundedness of the underlying stochastic processes used to model mean-reverting volatility or forward rates. This paper discusses how stochastic integration schemes can be constructed in order to maintain these properties of the analytical solution. Milstein-type methods prove to be the method-of-choice with respect to both efficiency and preservation of structural properties, as they turn out to dominate the increments of Brownian motions. These theoretical results are confirmed by numerical tests.
机译:在许多应用中,微分方程模型需要几何积分,即保留结构的积分方案的应用。例如,在计算金融中,用于对结构化利率衍生工具进行估值的扩展Libor市场模型的数值模拟必须保留用于建模均值回复波动率或远期利率的基础随机过程的积极性或有界性。本文讨论了如何构建随机积分方案以保持分析解决方案的这些属性。事实证明,Milstein型方法是效率和结构特性保留方面的首选方法,因为它们最终支配了布朗运动的增量。这些理论结果通过数值测试得到证实。

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