The main objectives of the proposed research are to develop, analyze, and implement new, fast, and accurate numerical methods for valuation of path-dependent options with regime switching and calibration of interest rate models. The fast growth in financial derivative markets provides natural needs and great challenges in computational mathematics. According to the quarterly report of Office of the Comptroller of the Currency, commercial banks held a record $119.2 trillion in derivatives contracts in the second quarter of 2006. Financial products are utilized as instruments of risk reduction by organizations and individual investors who have sizable assets and are exposed to moves in the world markets. The proposed research will focus on two specific topics of computational finance (financial engineering): (1) pricing of American options with regime switching; (2) fitting the quadratic model of short interest rates to current market data.
This project will produce reliable tools for economists and practitioners in the financial industry to understand and evaluate the studied financial derivatives, and thus they can make better financial decisions about the risk management of their portfolios. Also, Ph.D. students will be involved in the project through working on some problems of the project for their dissertations and will also be trained in C++ programming by implementing the proposed numerical algorithms. These students will most likely work for a bank or a financial services firm and can make these U.S. financial institutions more competitive in world markets.
