Global hedging in incomplete markets

最近的金融危机突显了健全的风险管理做法对金融机构避免财务困难和破产的重要性。金融衍生品的套期保值是金融机构最关心的问题；这些产品涉及复杂的风险，可能在短时间内导致极端损失。我的研究项目专注于套期保值程序，这些程序适用于现实的不完全市场框架，在那里风险不能完全消除。更准确地说，我的计划旨在促进一种特定类别的对冲计划的发展，称为全球对冲。全球对冲计划在对冲到期前将风险降至最低。与增量对冲和局部风险最小化等传统的短视方法相比，这代表了一种概念上的优势，后者只考虑下一时间段之前的风险。这解释了为什么全球对冲方法表现出比当地对冲方法更高的表现，见François等人。(2012)、Godin(2015)和Augustiniak等人。(2016)。 尽管全球对冲计划效率更高，但它们的复杂性目前阻碍了它们的使用。事实上，全球套期保值模型包括最优随机控制，以优化对冲政策。由于相关的沉重的数值负担，这种程序的数值实施不是微不足道的。我的研究计划的主要长期目标是为全球对冲模型的发展做出贡献，使它们能够在更广泛的实际设置中应用，并促进它们的实施。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，以加快全球套期保值的运行时间。将被研究的方案的例子包括谱内插、模拟和回归以及决策后状态变量动态规划。(2)量化全球套期保值的表现优于传统的本地方法，并评估各种市场环境下剩余风险的大小。(3)考虑到现有方法目前没有考虑到的额外风险，在更广泛的背景下制定套期保值计划。此类风险包括流动性风险和波动面风险。 开发有效的对冲程序应该会让老练的投资者和金融机构受益，因为它们可以大幅降低风险状况，从而降低它们破产的可能性。

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.