Stochastic Models of Asset Valuation in Markets with Frictions

有摩擦市场中资产估值的随机模型

• 批准号: 9971415
• 负责人: Thaleia Zariphopoulou
• 金额: $ 10.2万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2002-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971415&HistoricalAwards=false
• 关键词: Stochastic; Models; Asset; Valuation; Markets

ABSTRACT: The PI proposes to continue her program to develop methods to study abroad range of valuation problems in portfolio management and assetpricing. More precisely, using techniques from the theories of stochasticcontrol and nonlinear partial differential equations, the PI proposes tocontinue her research program in the following two general areas:A. Models with transaction costs: The goal is to investigate (i) thevaluation of early exercise instruments and exotic derivatives in amulti-security framework, (ii) the estimation of hedging probabilities ina relaxed super replication setting, (iii) the impact of a finite horizonto trading policies, and (iv) the asset valuation with transaction costsand alternative price processes.B. Models with stochastic volatility: The goals are (i) the completecharacterization and calibration of stochastic volatility functions and(ii) the analysis of delta hedging and value at risk in the presence ofstochastic volatility and unhedgable risks. Financial markets are not "perfect" due to the presence of variousfrictions like transaction costs, asymmetric information, stochasticvolatility, trading constraints, irreversibilities and liquidity. Thesemarket imperfections generate unhedgable risks which cannot be priced viathe existing classical valuation principles. This project proposes to introduce novel valuation methodologies and to analyze the relevantstochastic optimization problems. In addition to the areas of derivativepricing and portfolio management, it is expected that the new results willbe applied to other valuation systems arising in corporate finance, creditrisk, insurance theory, electronic commerce and optimal environmentalmanagement.

摘要：PI建议继续她的计划，以开发方法来研究海外投资组合管理和资产定价中的一系列估值问题。更准确地说，使用随机控制理论和非线性偏微分方程的技术，PI建议在以下两个一般领域继续她的研究计划：A。有交易成本的模型：目的是研究（i）多证券框架下提前执行工具和奇异衍生品的定价，（ii）宽松超复制环境下套期保值概率的估计，（iii）有限风险对交易策略的影响，（iv）考虑交易成本和替代价格过程的资产定价。随机波动率模型：目标是（i）随机波动函数的完整表征和校准;（ii）在存在随机波动和不可对冲风险的情况下分析Delta对冲和风险价值。 金融市场并不是“完美的”，因为存在着交易成本、信息不对称、随机波动、交易约束、不可逆性和流动性等各种摩擦。这些市场的不完善性产生了无法对冲的风险，而这些风险不能用现有的经典估值原则来定价。本计画提出引进新的评估方法，并分析相关的随机最佳化问题。除了衍生品定价和投资组合管理领域外，预计新的结果将应用于公司融资，信用风险，保险理论，电子商务和最佳环境管理中出现的其他估值系统。