Asymptotic and Statistical Analysis of Volitility and its Implications for Derivative Pricing and Risk Management

波动性的渐近统计分析及其对衍生品定价和风险管理的影响

• 批准号: 0090067
• 负责人: K. Ronnie Sircar
• 金额: $ 8.1万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2003-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0090067&HistoricalAwards=false
• 关键词: Asymptotic; Statistical; Analysis; Volitility; its

Dear Professor Pang, Here is the abstract in text form.Ronnie Sircar.------------------------------------------------------------------Asymptotic and Statistical Analysis of Volatility and its Implicationsfor Derivative Pricing and Risk ManagementProposal Number: 0090067PI: K. Ronnie Sircar Department of Operations Research & Financial Engineering Princeton University.In modern financial markets, investors are increasingly faced withexposure to changing and uncertain volatility. This project concernsmathematical models in which volatility is a stochastic process, andtheir use in derivative pricing and risk management. The main aim isto develop an efficient and robust framework in which models arecalibrated from observable market data and then used to designrisk-minimizing strategies that hedge a portfolio against thepotentially serious consequences of changing volatility. This problemis important for investors from large trading institutions toindividuals with pension funds.The spectacular growth in the size of the derivatives market over thelast twenty-five years (currently it has a turnover of trillions ofdollars in the US) plus recent infamous (and equally spectacular) risk(mis)management disasters, such as the Barings, Orange County and LongTerm Capital Management fiascos, have created an urgent need for smartmathematical and computational models to quantify the respective risksand rewards of such investments. This project aims to build on themethodology introduced by Black, Scholes and Merton, to take intoaccount the fluctuating nature of market volatility. Mathematicaltools are combined with statistical analysis of past prices to produceformulas and software that accurately capture the potential losses andgains in today's vast derivative market.

尊敬的彭教授，这里是文本形式的摘要。Ronnie Sircar.------------------------------------------------------------------Asymptotic和统计分析波动率及其对衍生品定价和风险管理的影响建议编号：0090067PI：K.Ronnie Sircar普林斯顿大学运筹学和金融工程系。在现代金融市场，投资者越来越多地面临不断变化和不确定的波动性的风险敞口。本项目涉及波动率是随机过程的数学模型，以及它们在衍生品定价和风险管理中的应用。其主要目标是开发一个高效而稳健的框架，其中的模型从可观察的市场数据中重新校准，然后用于设计风险最小化策略，以对冲投资组合免受波动性变化的潜在严重后果的影响。这个问题对从大型交易机构到拥有养老基金的个人投资者来说都很重要。过去25年里，衍生品市场规模的惊人增长(目前它在美国的营业额高达数万亿美元)，加上最近臭名昭著(同样引人注目)的风险(MIS)管理灾难，如霸菱、奥兰治县和长期资本管理公司(Long Term Capital Management)的惨败，产生了对智能数学和计算模型的迫切需求，以量化此类投资的各自风险和回报。这个项目旨在建立在布莱克、斯科尔斯和默顿引入的方法论的基础上，以考虑到市场波动的波动性质。数学工具与对过去价格的统计分析相结合，以产生公式和软件，准确地捕捉当今巨大的衍生品市场的潜在损失和收益。