This proposed research requests funding for the development of high performance computational tools for the fast and accurate calibration of pricing models for financial and energy option contracts using available market data. The results of this research will be used to determine the parameters of various option pricing models that relax the restrictive assumptions of the widely used Black-Scholes-Merton model. For options of the European type, we investigate algorithms for solving optimization problem constrained by discretized partial integro-differential equations. For options of the American type with early exercise features, we develop efficient solution techniques for mathematical programs with complementarity constraints. We also investigate various methods for solving linear complementarity systems arising from the semi-discretization of parabolic variational inequalities for the valuation of American type options.
If successful, the results of the proposed research will lead to the accurate calibration of financial and energy option pricing models, a practical problem that is of fundamental importance to many industrial constituents, including financial firms, pension and mutual fund managers, market participants, energy generators, and commodity producers, who use option contracts as hedging tools to safeguard against large price fluctuations in interest rates, currency exchange rates, equity prices, energy and commodity prices. Improved pricing models in which risks associated with the underlying financial variables are modeled in more appropriate ways will yield better investment decisions and will help reduce arbitrage opportunities and stabilize the financial markets. The results of our research will also benefit the mathematical programming field and other service industries where similar model calibration problems are important.
