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

波动率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: 9803169
• 负责人: K. Ronnie Sircar
• 金额: $ 5万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-01 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803169&HistoricalAwards=false
• 关键词: Asymptotic; Statistical; Analysis; Volatility; its

DMS-9803169 Asymptotic and Statistical Analysis of Volatility and its Implications for Derivative Pricing and Risk Management K. Ronnie Sircar In financial mathematics, a methodology (due to Black and Scholes) exists for pricing and hedging against the risk of derivative securities (eg. options) on stocks when the volatility of the stock is constant. However, it is widely believed that volatility has a random component and must be described by a suitable stochastic model. This project aims to produce a statistical description of stock volatility dynamics using historical price data, and to combine it with an asymptotic analysis of the partial differential equation for derivative prices to infer the market's view of probable future stock movements, and in particular, whether this view has become more pessimistic since the 1987 crash. The analysis will exploit the discrepancy in time-scales of fluctuation between the Brownian motion driving the stock price process and the volatility stochastic process. The spectacular growth in the size of the derivatives market over the last twenty years (currently it has a turnover of trillions of dollars in the US) plus recent infamous (and equally spectacular) risk (mis)management disasters such as the Barings and Orange County fiascos, have created an urgent need for good mathematical and computational models to quantify the respective risks and rewards of such investments. This project aims to build on the Nobel Prize winning methodology of Black, Scholes and Merton, to take into account the fluctuating nature of market volatility. Mathematical tools are combined with statistical analysis of past prices to produce formulas and software that accurately capture the potential losses and gains in today's vast derivative market.

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影响在金融数学中，存在一种定价和对冲衍生品证券风险的方法（由于Black和Scholes）。当股票的波动是恒定时，股票的期权。然而，人们普遍认为波动率具有随机成分，必须用合适的随机模型来描述。本项目旨在利用历史价格数据对股票波动动态进行统计描述，并将其与衍生品价格偏微分方程的渐近分析相结合，以推断市场对未来可能的股票走势的看法，特别是，自1987年崩盘以来，这种观点是否变得更加悲观。分析将利用驱动股价过程的布朗运动与波动随机过程在波动时间尺度上的差异。过去二十年来，衍生品市场规模的惊人增长（目前在美国有数万亿美元的营业额），加上最近臭名昭著的（同样惊人的）风险（管理不善）灾难，如巴林银行（Barings）和奥兰治县（Orange County）的惨败，迫切需要良好的数学和计算模型来量化这类投资的各自风险和回报。该项目旨在建立诺贝尔奖得主布莱克、斯科尔斯和默顿的方法，以考虑市场波动的波动性。数学工具与过去价格的统计分析相结合，生成公式和软件，准确捕捉当今庞大衍生品市场的潜在损失和收益。