Global hedging in incomplete markets

最近的金融危机突出表明，金融机构必须采取健全的风险管理做法，以避免陷入财务困境和破产。金融衍生工具的套期保值是金融机构的主要关注点;这些产品涉及复杂的风险，可能在短时间内导致极端损失。我的研究项目主要集中在套期保值程序，适用于现实的不完全市场框架，风险不能完全消除。更确切地说，我的计划旨在促进一个特定类别的对冲计划的发展，称为全球对冲。全球对冲计划可将风险降至最低，直至对冲到期。这代表了一个概念上的优势，传统的短视的方法，如三角对冲和局部风险最小化，只考虑到下一个时间段的风险。这就解释了为什么全球对冲方法表现出比本地对冲方法更高的性能，见François et al.（2012），Godin（2015）和Augustiniak et al.（2016）。 虽然全球套期保值计划更有效，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，以优化对冲政策。由于相关的沉重的数值负担，此类过程的数值实现并不是微不足道的。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，使其在更广泛的实际设置中的应用，并促进其实施。这一目标将通过三个主要的研究途径来实现：（i）开发更有效的数值算法，可以加快全球套期保值的运行时间。将被调查的计划的例子包括光谱插值，模拟和回归和决策后的状态变量动态规划。(ii)量化全球套期保值优于传统本地方法的表现，并评估各种市场环境下的剩余风险大小。(iii)在更广泛的背景下制定套期保值计划，考虑现有方法目前未考虑的额外风险。该等风险包括流动性风险及波动面风险。 制定有效的套期保值程序应使老练的投资者和金融机构受益，使他们能够大大降低风险，从而降低破产的可能性。

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.