FINANZIA: Computational Methods and Software for Financial Derivatives

Principal Investigators: Elias N. Houstis

Research Assistant: Kostas Pantazopoulos

Support: Purdue Research Foundation

Computational finance has already been established as a new discipline of finance. Financial institutions are hiring numerical analysts, engineers, and computer scientists to apply computational techniques to a multitude of every day problems. The option valuation problem is among the most important applications in need of mathematical and computational support. Option valuation mandates the use of advanced mathematical models. Furthermore it requires an integrated computational support that will address the multitude, diversity and dynamics of contemporary option products. The difficulty with the underlying approximate numerical models is their extrapolating nature. This characteristic leads usually to multidimensional free boundary value problems that are difficult to approximate and analyze. Moreover, their real time solution makes the study of their parallel processing necessary. There are five technical thrusts in the FINANZIA project:

  1. The development and analysis of numerical methods for non-linear parabolic initial/boundary value problems with free boundaries and their application to the option valuation problem.
  2. The development of the FINANZIA option valuation library and its integration with existing problem solving environments such as //ELLPACK, Excel and Matlab.
  3. The development of parallelization methodologies to support the mapping of option valuation models on parallel machines including networks of workstations.
  4. The benchmarking and performance evaluation of option valuation algorithms in a parametric framework following an object oriented characterization of the option products universe.
  5. The development of intelligent techniques for computational finance problems including optimal algorithm selection for the option valuation problem, neuro-fuzzy prediction techniques for implied parameters and secure outsourcing of financial computations.