论文标题
Horizon内部预期有跳跃模型中的不足和风险结构
Intra-Horizon Expected Shortfall and Risk Structure in Models with Jumps
论文作者
论文摘要
本文涉及跳高模型中的Horizon风险。我们对Horizon内部风险的一般理解是按照Boudoukh，Richardson，Stanton和Whitelaw（2004），Rossello（2008），Bhattacharyya，Misra和Kodase（2009），Bakshi和Panayotov（2010）以及Leippold and Leippold and Vasiljevi（2019年）的方法。特别是，我们认为，严格依靠时间点措施来量化市场风险不能被认为是一种令人满意的方法。取而代之的是，我们认为，在处理（M）任何财务状况时，必须在交易范围内的任何时候捕获可能在交易范围内的任何时间捕获损失的幅度来补充这种方法。为了解决这个问题，我们提出了预期的一般利润和损失过程中预期不足的摩托内类似物，并讨论其关键特性。如Cheridito，Delbaen和Kupper（2004）所引入的那样，我们的Horizon内部预期缺口已明确定义（m）（m）在建模市场动态和构成一致的风险衡量时，遇到的任何流行级别的莱维过程的（ES）都很好地定义了。在计算方面，我们提供了一种简单的方法来推导流行的莱维动力学固有的Horizon内风险。我们的一般技术依赖于成熟度的第一步概率的结果，并允许扩散和单一跳跃风险贡献。这些理论结果与经验分析相辅相成，其中流行的Lévy动力学被校准为标准普尔500指数数据，并对所得的Horizon内部风险进行了分析。
The present article deals with intra-horizon risk in models with jumps. Our general understanding of intra-horizon risk is along the lines of the approach taken in Boudoukh, Richardson, Stanton and Whitelaw (2004), Rossello (2008), Bhattacharyya, Misra and Kodase (2009), Bakshi and Panayotov (2010), and Leippold and Vasiljević (2019). In particular, we believe that quantifying market risk by strictly relying on point-in-time measures cannot be deemed a satisfactory approach in general. Instead, we argue that complementing this approach by studying measures of risk that capture the magnitude of losses potentially incurred at any time of a trading horizon is necessary when dealing with (m)any financial position(s). To address this issue, we propose an intra-horizon analogue of the expected shortfall for general profit and loss processes and discuss its key properties. Our intra-horizon expected shortfall is well-defined for (m)any popular class(es) of Lévy processes encountered when modeling market dynamics and constitutes a coherent measure of risk, as introduced in Cheridito, Delbaen and Kupper (2004). On the computational side, we provide a simple method to derive the intra-horizon risk inherent to popular Lévy dynamics. Our general technique relies on results for maturity-randomized first-passage probabilities and allows for a derivation of diffusion and single jump risk contributions. These theoretical results are complemented with an empirical analysis, where popular Lévy dynamics are calibrated to S&P 500 index data and an analysis of the resulting intra-horizon risk is presented.
