Juan Cardenas is a financial engineer for Summit Systems Inc., a software company based in New York City. Its product is a front to back office risk-management system, mainly focused on interest rate derivatives and primarily used by investment banks. Juan has been with the Financial Engineering Group at Summit since obtaining his Ph.D. in 1993.
Juan's group is responsible for developing, implementing, and documenting pricing models, algorithms for yield curve construction, hedging, and in general, analytics that require more sophisticated mathematics. "Frequently this involves interacting with clients, be they traders, risk managers, or quantitative analysts," says Juan. "The organization relies on the FE Group to verify that the numbers that are produced by the different analyses are correct."
He has worked with a variety of applications that require mathematical solutions. Under certain models, stochastic differential equations are used to describe interest rates. Parabolic partial differential equations arise when one wants to find the theoretical price of derivative products (e.g. options). Various matrix decompositions from numerical linear algebra are used to find optimal hedge ratios. These ratios are developed to protect against possible market movements by calculating the positions that should be taken in selected financial instruments. "Understanding and implementing correctly the above models, algorithms, etc. requires higher mathematics," says Juan. "Justifying the outputs of the analyses requires knowing the theory behind the problems and understanding the solution methods -- quite mathematical many times."
Juan has a B.S. in mathematics from Stanford University, and a M.S., and Ph.D. in mathematics from New York University, Courant Institute. He interned two summers at Morgan Stanley Co., Inc., a Wall Street firm, while in graduate school. He obtained his current position through an executive recruiter or "headhunter" he contacted after being given the name by a fellow student. Part of his attraction to working in business was the desire to get a permanent job, as opposed to a temporary academic position, and to work on applied problems. "It is rewarding to see one's work being applicable and of use to others," Juan says. "There is also quick feedback to let you know if your work is useful or not."
Among the courses he finds useful in his work are numerical analysis (covering linear algebra and differential equations), probability and statistics, and partial differential equations. He mentions that other courses of interest to a mathematician going into finance are corporate finance and operations research, as well as a programming language such as C or C++. "Do not ignore areas of mathematics different from your area of concentration," notes Juan. "The nature of problems you will be faced with will vary, and breadth of knowledge in mathematics will be very useful. Having some teaching experience will not hurt because one needs to be able to explain concepts clearly and concisely."
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