Global hedging in incomplete markets

不完全市场中的全球对冲

• 批准号: RGPIN-2017-06837
• 负责人: Godin, Frédéric
• 金额: $ 1.38万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758976
• 关键词: Global; hedging; incomplete; markets

The recent financial crisis highlighted the importance of sound risk management practices for financial institutions to avoid financial hardship and bankruptcy. The hedging of financial derivatives is a prime concern for financial institutions; these products entail complex risks which can lead to extreme losses in a short amount of time. My research program focuses on hedging procedures which apply in realistic incomplete market frameworks where risk cannot be completely eliminated. More precisely, my program aims at contributing to the development of a specific category of hedging schemes referred to as global hedging. Global hedging schemes minimize risk up to the maturity of the hedge. This represents a conceptual advantage over traditional myopic methods such as delta-hedging and local risk-minimization which only consider risk up to the next time period. This explains why global hedging methods were shown to exhibit a higher performance than their local counterparts, see François et al. (2012), Godin (2015) and Augustiniak et al. (2016).Although global hedging schemes are more efficient, their use is currently hindered by their higher complexity. Indeed, global hedging models involve optimal stochastic control to optimize hedging policies. The numerical implementation of such procedures is non-trivial because of the associated heavy numerical burden. The main long term objective of my research program is to contribute to the development of global hedging models to allow their application in a wider number of practical setups and to facilitate their implementation. This objective will be realized through three main research avenues: (i) Developing more efficient numerical algorithms which can accelerate the running time of global hedging. Examples of schemes that will be investigated include spectral interpolation, simulation and regression and post-decision state variables dynamic programming. (ii) Quantifying the outperformance of global hedging over traditional local methods and assessing the magnitude of residual risk in various market contexts. (iii) Developing hedging schemes in broader contexts considering additional risks that are not currently taken into account by existing methods. Such risks include liquidity risk and volatility surface risk.The development of efficient hedging procedures should benefit sophisticated investors and financial institutions by allowing them to significantly reduce their risk profile, thus decreasing the probability they become insolvent.

最近的金融危机凸显了金融机构健全的风险管理实践对于避免财务困难和破产的重要性。金融衍生品的对冲是金融机构最关心的问题；这些产品涉及复杂的风险，可能会在短时间内导致巨大的损失。我的研究项目侧重于对冲程序，该程序适用于无法完全消除风险的现实不完整市场框架。更准确地说，我的计划旨在促进特定类别的对冲计划（称为全球对冲）的发展。全球对冲计划可最大限度地降低对冲到期前的风险。这代表了相对于传统短视方法（例如德尔塔对冲和局部风险最小化）的概念优势，这些方法仅考虑下一时间段的风险。这解释了为什么全球对冲方法比本地对冲方法表现出更高的性能，请参阅 François 等人。 (2012)、Godin (2015) 和 Augustiniak 等人。 (2016)。尽管全球对冲方案更有效，但其使用目前因其较高的复杂性而受到阻碍。事实上，全球对冲模型涉及最优随机控制来优化对冲政策。由于相关的繁重的数字负担，此类过程的数字实现并非易事。我的研究计划的主要长期目标是促进全球对冲模型的发展，使其能够在更广泛的实际设置中应用并促进其实施。这一目标将通过三个主要研究途径来实现：（i）开发更有效的数值算法，可以加快全局对冲的运行时间。将研究的方案示例包括谱插值、模拟和回归以及决策后状态变量动态规划。 (ii) 量化全球对冲相对于传统本地方法的优异表现，并评估不同市场环境下剩余风险的大小。 (iii) 在更广泛的背景下制定对冲计划，考虑目前现有方法未考虑到的额外风险。这些风险包括流动性风险和波动性表面风险。开发有效的对冲程序应该有利于经验丰富的投资者和金融机构，使他们能够显着降低风险状况，从而降低他们资不抵债的可能性。