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

尊敬的庞教授，这是本文的摘要。波动率的渐近和统计分析及其对衍生品定价和风险管理的启示罗尼·瑟卡尔 在现代金融市场中，投资者越来越多地面临着不断变化和不确定的波动性。这个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。 其主要目的是开发一个有效的和强大的框架，其中模型是从可观察的市场数据重新校准，然后用于设计风险最小化的策略，对冲投资组合对潜在的严重后果的变化波动。这个问题对从大型交易机构到拥有养老基金的个人的投资者都很重要。在过去的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为数万亿美元）加上最近臭名昭著的（同样壮观的）风险管理灾难，如巴林银行、橙子县银行和长期资本管理公司的惨败，已经创造了一个智能的数学和计算模型来量化各自的风险和回报的投资的迫切需要。这个项目的目的是建立在themethodology介绍了布莱克，斯科尔斯和默顿，考虑到波动性质的市场波动。数学工具与过去价格的统计分析相结合，产生了公式和软件，可以准确地捕捉当今庞大的衍生品市场的潜在损失和收益。

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.