Stochastic Modeling of Risk Aversion and its Implications for Derivative Pricing and Risk Management

风险规避的随机模型及其对衍生品定价和风险管理的影响

• 批准号: 1156888
• 负责人: Siu-Tang Leung
• 金额: $ 6.58万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1156888&HistoricalAwards=false
• 关键词: Stochastic; Modeling; Risk; Aversion; its

In many financial applications, investors are inevitably exposed to unhedgeable risks due to, for example, hedging constraints or other market frictions. The value of derivative securities naturally depends on how risks are managed, as well as the investor?s preferences between risk and return. This project will systematically investigate some recent problems that involve incorporating the investor's risk preferences into the valuation of derivatives, with a focus on employee stock options (ESOs) and credit derivatives. The project objective is to design efficient and robust valuation models that can be calibrated given market data and applied to construct the optimal risk management strategies consistent with the investor?s risk preferences. The research involves developing applicable mathematical tools to model, estimate, and analyze the complex risk structures of these derivatives, which have a significant bearing on their values. Moreover, the project includes the analytical and numerical studies of a number of stochastic control and optimal stopping problems that naturally arise in these valuation problems. By quantifying their risks and returns, the research will also shed light on some optimal contract design problems for these derivatives.Employee stock options are an important component of compensation in the US. Concerned about their cost to shareholders, the US Financial Accounting Standards Board since 2004 has required firms to estimate and report the granting cost of ESOs. The central challenge of ESO valuation lies in the uncertain timing of option exercises, which depends on the employee's risk aversion and various contractual restrictions of the options. On the other hand, credit derivatives are financial instruments whose payoffs are contingent on the occurrence of default event(s), such as the bankruptcy of a firm. The trading volume of credit derivatives has grown dramatically in the past decade, but the valuation and risk management technologies have not kept up. The recent crisis in the credit markets reflects ineffective risk management of complex credit derivatives by major financial institutions. Hence, this research aims to develop a valuation framework that explicitly accounts for the investor's risk preferences, contractual features and market conditions, so as to accurately quantify the risks of these derivatives. These valuation problems are important not only for individual or institutional investors, but also for regulators.

在许多金融应用中，由于对冲限制或其他市场摩擦等原因，投资者不可避免地面临不可对冲的风险。衍生证券的价值自然取决于风险管理方式以及投资者对风险与回报的偏好。该项目将系统地研究近期一些涉及将投资者的风险偏好纳入衍生品估值的问题，重点关注员工股票期权（ESO）和信用衍生品。该项目的目标是设计高效、稳健的估值模型，该模型可以根据市场数据进行校准，并应用于构建符合投资者风险偏好的最佳风险管理策略。该研究涉及开发适用的数学工具来建模、估计和分析这些衍生品的复杂风险结构，这对其价值有重大影响。此外，该项目还包括对这些估值问题中自然出现的许多随机控制和最优停止问题的分析和数值研究。通过量化其风险和回报，该研究还将揭示这些衍生品的一些最优合约设计问题。在美国，员工股票期权是薪酬的重要组成部分。考虑到股东的成本，美国财务会计准则委员会自 2004 年以来一直要求公司估算并报告 ESO 的授予成本。 ESO估值的核心挑战在于期权行权时间的不确定性，这取决于员工的风险厌恶程度和期权的各种合同限制。另一方面，信用衍生品是一种金融工具，其收益取决于违约事件（例如公司破产）的发生。过去十年，信用衍生品的交易量急剧增长，但估值和风险管理技术却没有跟上。最近的信贷市场危机反映出主要金融机构对复杂信贷衍生品的风险管理不力。因此，本研究旨在建立一个明确考虑投资者风险偏好、合约特征和市场条件的估值框架，从而准确量化这些衍生品的风险。这些估值问题不仅对个人或机构投资者很重要，对监管机构也很重要。