Market Expectations, Long Term Risk, and Stochastic Spectral Theory

市场预期、长期风险和随机谱理论

• 批准号: 1536503
• 负责人: Vadim Linetsky
• 金额: $ 29.36万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1536503&HistoricalAwards=false
• 关键词: Market; Expectations; Long; Term; Risk

This project focuses on learning expectations of market participants about probability distributions of future asset returns from the current prices of options on those assets combined with assumptions and historical data about the underlying risk-return trade-offs in the economy. Risk assessments are based on historical data. The limitation of the historical approach is in potentially underestimating the probability of events that did not occur in the historical data under consideration. The goal of this research is to improve probability models of markets by developing theory and methods for calibrating them to additional sources of information in addition to historical data. This will help put risk management and investment decision making on a more solid foundation and will aid the financial services industry and market regulators in extracting implied probability distributions from market prices of options to improve risk management. The project is interdisciplinary, drawing on the fields of operations research, economics, probability theory and mathematical analysis and will have a positive impact on education and human resources development.The methodology is based on far-reaching extensions of the recent Recovery Theorem of Ross that shows that when all uncertainty (risk) in the economy is modeled as a discrete-time irreducible finite-state Markov chain and the stochastic discount factor is transition independent, then there exists a unique recovery of the Markov chain's transition probability matrix from options prices. We aim to extend the recovery methodology to general classes of continuous-time Markov processes, including diffusions and jump-diffusions. On the other hand, we aim to relax the transition independence assumption by building on the fundamental work of Hansen and Scheinkman on long term risk. Our approach aims to combine structural assumptions on the stochastic discount factor drawn from the macro-finance literature with the joint calibration of the resulting models to currently observed market options prices together with historical time series data on the underlying asset returns. This will involve analytical development of the spectral theory for Markov processes and computational implementations of recoveries in specific classes of models.

该项目的重点是根据这些资产的期权当前价格，结合有关经济中潜在风险回报权衡的假设和历史数据，了解市场参与者对未来资产回报概率分布的预期。风险评估基于历史数据。 历史方法的局限性在于可能低估历史数据中未发生事件的概率。 这项研究的目标是通过开发理论和方法来根据历史数据之外的其他信息源来校准市场的概率模型，从而改进市场的概率模型。 这将有助于为风险管理和投资决策奠定更坚实的基础，并将帮助金融服务业和市场监管机构从期权市场价格中提取隐含概率分布，以改善风险管理。该项目是跨学科的，借鉴了运筹学、经济学、概率论和数学分析领域，将对教育和人力资源开发产生积极影响。该项目基于罗斯最近的恢复定理的深远扩展，即表明当经济中的所有不确定性（风险）被建模为离散时间不可约有限状态马尔可夫链并且随机贴现因子与转移无关时，则存在从期权价格中马尔可夫链转移概率矩阵的唯一恢复。我们的目标是将恢复方法扩展到一般类别的连续时间马尔可夫过程，包括扩散和跳跃扩散。另一方面，我们的目标是通过汉森和谢克曼关于长期风险的基础工作来放宽转型独立性假设。 我们的方法旨在将从宏观金融文献中提取的随机贴现因子的结构假设与对当前观察到的市场期权价格以及基础资产回报的历史时间序列数据的结果模型进行联合校准结合起来。这将涉及马尔可夫过程的谱理论的分析发展以及特定类别模型中回收率的计算实现。