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Stock Market: Using Mathematics in Finance







Everyone has a clear notion of financial risk. When the stock market drops, when interest rates rise, when oil prices rise, some lose money. Financial options were designed a few decades ago to offer insurance against such occurrences. These are more or less complicated financial instruments, which offer the investor protection from evil. Unlike fire insurance for a home, they cannot be easily priced by looking at history and making statistics; in fact, pricing them is a complex problem whose solution won the Nobel prize for Myron Scholes and Robert Merton last year. This is the realm of financial engineering.

Recent advances in the pricing of derivative securities, risk management, and information technology are forcing the rapid adoption of mathematical methodologies of an increasing degree of sophistication. The financial services industry (FSI) is currently in the midst of massive restructuring brought about by globalization and the introduction of new information technologies. Acquisitions and mergers are changing its face, while internal overhauls are changing the way in which financial institutions do business.

The series of losses that recently shook institutions such as Barings, Sumitomo, Orange County, and Long-Term Capital Management (LTCM) was but one consequence of the enormous changes which are reshaping the FSI. The collapse of Barings points out that all companies are at risk. The general public might say that these occurrences are an indictment of the new methodologies; however, one of the most remarkable facts is the minimal damage suffered by LTCM during the catastrophic events which rattled the global financial markets during the summer of 1998. This can be viewed as a success of the emerging methodologies.

It is no longer possible to reverse this process of adopting increasingly sophisticated mathematical methodologies. Regulatory agencies and central banks demand it, and the aggressive competition of the most sophisticated players in the global marketplace drive it. The acquisition of the most advanced financial and risk-management technologies translates into a competitive advantage for those financial institutions which are able to rely on the expertise of highly quantitative personnel in a wide range of key technical positions. What is needed in this environment is a larger pool of personnel with a fundamental understanding of the new mathematical technologies, and an increasing amount of R&D in the understanding and management of risk at all levels.

This new environment requires personnel with advanced training in a new combination of knowledge and skills: a solid understanding of the behavior of the driving forces of financial markets; the quantitative skills to develop pricing models, risk management techniques, and utilize emerging technologies; and the personal skills to work and communicate effectively within their corporate structure and with clients. This combination of skills implies a need for new, targeted graduate-level programs.

One such program is the recently developed Master's program in mathematical finance at the University of Toronto. An interdisciplinary program involving three faculties and seven departments, this program has been designed to mimic the workplace. Students move through the program as a cohort, spending their days working in the newly constructed computational laboratory and their evenings attending lectures specifically geared to their needs. In this intense and demanding work environment, students learn to do pricing model design and verification, parameter estimation, and learn to analyze and manage risk in their state-of-the-art computational facilities, gaining hands on practical experience. In the evening lectures, they learn the theoretical underpinnings of the area and the theory and practice of the main tools and techniques which are necessary for solving their problems. The lectures and evening seminars are given by a mix of university faculty members and industrial personnel. A 4-month internship in the middle of this intense 12 month professional program further ensures that students understand the marketplace and are able to integrate their academic knowledge with a workplace functionality.

This program is targeted at mathematical scientists and other students with outstanding quantitative skills and provides them with a solid background in finance while further developing the specific analytic skills required for quantitative analysis and risk management. Graduates of this program will have learned to successfully combine the high level mathematical sophistication normally associated with quantitative analysts and risk managers with the communication skills associated with higher management and trading functions. By merging the academic strengths of the university with the applied expertise within the local financial community, this program is another example of how the university community is working to produce graduates who are ready to drive the changes in the financial services industry and to propel the industry firmly into the next millennium. For more information about this program, visit their Web site.