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

Princeton University, Princeton NJ

Investigators

Abstract

Dear Professor Pang, Here is the abstract in text form. Ronnie Sircar. ------------------------------------------------------------------ Asymptotic and Statistical Analysis of Volatility and its Implications for Derivative Pricing and Risk Management Proposal Number: 0090067 PI: K. Ronnie Sircar Department of Operations Research & Financial Engineering Princeton University. In modern financial markets, investors are increasingly faced with exposure to changing and uncertain volatility. This project concerns mathematical models in which volatility is a stochastic process, and their use in derivative pricing and risk management. The main aim is to develop an efficient and robust framework in which models are calibrated from observable market data and then used to design risk-minimizing strategies that hedge a portfolio against the potentially serious consequences of changing volatility. This problem is important for investors from large trading institutions to individuals with pension funds. The spectacular growth in the size of the derivatives market over the last twenty-five 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, Orange County and Long Term Capital Management fiascos, have created an urgent need for smart mathematical and computational models to quantify the respective risks and rewards of such investments. This project aims to build on the methodology introduced by 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.