Global hedging in incomplete markets

最近的金融危机凸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。金融衍生品的对冲是金融机构最关心的问题；这些产品具有复杂的风险，可以在短时间内导致极端损失。我的研究计划侧重于套期保值程序，适用于现实的不完全市场框架，其中风险不能完全消除。更准确地说，我的计划旨在促进一种被称为全球对冲的特定类别对冲计划的发展。全球对冲计划最大限度地降低风险，直至对冲到期。这代表了传统短视方法的概念优势，如delta对冲和局部风险最小化，这些方法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比本地对冲方法表现出更高的绩效，参见franois等人（2012）、Godin（2015）和Augustiniak等人（2016）。

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.