《Chebyshev Methods for Ultra-efficient Risk Calculations》
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作者:
Mariano Zeron Medina Laris, Ignacio Ruiz
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最新提交年份:
2018
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英文摘要:
Financial institutions now face the important challenge of having to do multiple portfolio revaluations for their risk computation. The list is almost endless: from XVAs to FRTB, stress testing programs, etc. These computations require from several hundred up to a few million revaluations. The cost of implementing these calculations via a \"brute-force\" full revaluation is enormous. There is now a strong demand in the industry for algorithmic solutions to the challenge. In this paper we show a solution based on Chebyshev interpolation techniques. It is based on the demonstrated fact that those interpolants show exponential convergence for the vast majority of pricing functions that an institution has. In this paper we elaborate on the theory behind it and extend those techniques to any dimensionality. We then approach the problem from a practical standpoint, illustrating how it can be applied to many of the challenges the industry is currently facing. We show that the computational effort of many current risk calculations can be decreased orders of magnitude with the proposed techniques, without compromising accuracy. Illustrative examples include XVAs and IMM on exotics, XVA sensitivities, Initial Margin Simulations, IMA-FRTB and AAD.
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中文摘要:
金融机构现在面临的一个重要挑战是,必须对其风险计算进行多次投资组合重估。清单几乎无穷无尽:从XVAs到FRTB,压力测试程序等等。这些计算需要数百到数百万次的重新评估。通过“强力”全面重估来实施这些计算的成本是巨大的。目前,业界对这一挑战的算法解决方案有着强烈的需求。本文给出了一种基于切比雪夫插值技术的求解方法。这是基于一个已证明的事实,即对于一个机构拥有的绝大多数定价函数,这些插值函数都表现出指数收敛。在本文中,我们详细阐述了它背后的理论,并将这些技术扩展到任何维度。然后,我们从实际的角度来处理这个问题,说明如何将其应用于该行业目前面临的许多挑战。我们表明,在不影响准确性的情况下,使用所提出的技术,许多当前风险计算的计算工作量可以减少几个数量级。示例包括XVAs和IMM关于exotics、XVA敏感性、初始保证金模拟、IMA-FRTB和AAD。
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分类信息:
一级分类:Quantitative Finance 数量金融学
二级分类:Risk Management 风险管理
分类描述:Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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