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.

该项目的重点是学习市场参与者对这些资产期权当前资产价格的概率分布的学习期望，并结合了有关经济中潜在的风险回收权衡的假设和历史数据。风险评估基于历史数据。 历史方法的局限性在于可能低估所考虑的历史数据中未发生事件的可能性。 这项研究的目的是通过开发理论和方法来改善市场的概率模型，除历史数据外，还将其校准为其他信息来源。 这将有助于将风险管理和投资决策置于更坚实的基础上，并将帮助金融服务行业和市场监管机构从期权市场价格中提取隐含的概率分配以改善风险管理。 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马尔可夫链的过渡概率矩阵来自期权价格。我们旨在将恢复方法扩展到连续时间马尔可夫流程的一般类别，包括扩散和跳膨胀。另一方面，我们旨在通过建立汉森和Scheinkman对长期风险的基本工作来放松过渡独立性假设。 我们的方法旨在将宏观金融文献中随机折现因子的结构性假设与最终观察到的市场期权价格的联合校准以及有关基础资产回报的历史时间序列数据以及有关型模型的联合校准结合起来。这将涉及对马尔可夫过程的频谱理论的分析发展，以及在特定类别类别中的恢复性的计算实现。