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

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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.