英文标题：
《Pricing and Risk Management with High-Dimensional Quasi Monte Carlo and
Global Sensitivity Analysis》
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作者：
Marco Bianchetti, Sergei Kucherenko, Stefano Scoleri
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最新提交年份：
2015
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英文摘要：
We review and apply Quasi Monte Carlo (QMC) and Global Sensitivity Analysis (GSA) techniques to pricing and risk management (greeks) of representative financial instruments of increasing complexity. We compare QMC vs standard Monte Carlo (MC) results in great detail, using high-dimensional Sobol\' low discrepancy sequences, different discretization methods, and specific analyses of convergence, performance, speed up, stability, and error optimization for finite differences greeks. We find that our QMC outperforms MC in most cases, including the highest-dimensional simulations and greeks calculations, showing faster and more stable convergence to exact or almost exact results. Using GSA, we are able to fully explain our findings in terms of reduced effective dimension of our QMC simulation, allowed in most cases, but not always, by Brownian bridge discretization. We conclude that, beyond pricing, QMC is a very promising technique also for computing risk figures, greeks in particular, as it allows to reduce the computational effort of high-dimensional Monte Carlo simulations typical of modern risk management.
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中文摘要：
我们回顾并应用准蒙特卡罗（QMC）和全球敏感性分析（GSA）技术，对日益复杂的代表性金融工具进行定价和风险管理。我们使用高维Sobol低差异序列、不同的离散化方法，以及对有限差分的收敛性、性能、速度、稳定性和误差优化的具体分析，详细比较了QMC和标准蒙特卡罗（MC）结果。我们发现，我们的QMC在大多数情况下都优于MC，包括最高维的模拟和计算，显示出更快、更稳定地收敛到精确或几乎精确的结果。使用GSA，我们能够从QMC模拟的有效维数降低的角度充分解释我们的发现，这在大多数情况下是允许的，但并不总是通过布朗桥离散化。我们的结论是，除了定价，QMC是一种非常有前途的技术，也适用于计算风险数据，尤其是希腊人，因为它可以减少现代风险管理中典型的高维蒙特卡罗模拟的计算工作量。
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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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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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