The financial mathematics master’s program at Johns Hopkins is offered through the Department of Applied Mathematics and Statistics as a Master’s of Science in Engineering (MSE) degree. The program takes three semesters to complete, with students starting in the later summer and finishing in mid-December. Students with a strong quantitative undergraduate background are encouraged to apply for admission to the program.
The Master’s program in Financial Mathematics will provide a solid foundation in applied mathematics, providing the basis for an understanding and appreciation of existing models commonly used in financial applications and inferential and computational tools for developing their solution. The program will also furnish the appropriate insights in Finance where quantitative skills are most germane. The combination of these elements will create a springboard for addressing today’s quantitative challenges in finance as well as provide the preparation to meet the challenges of the future.
In order to be consistent with our aim of producing the next generation of leaders in financial mathematics, while we focus on the enhancement of students’ already considerable quantitative abilities, the program will also emphasize mastery of the abilities to translate real-world problems into mathematical ones and to communicate the solutions obtained to specialists and non-specialists alike. Accordingly there are two complementary skills that the program will ensure.
First, there is no question that mastery of computing is essential to Financial Mathematics. Thus, every graduate must have a working knowledge of the utilization of computers in Financial Mathematics. This includes such topics as: computer programming (in C/C++), use of numerical software packages, symbolic computations, and the implementation of interfaces between algorithms and data.
As important as computing, so also is the need for effective communication. We will require that students refine their communication skills by frequently making presentations in a seminar setting or similar forum, and acquire the critical technical and oral presentation skills through coursework and from the expertise available in Johns Hopkins’ Professional Communications program.
Financial mathematics is a relatively new discipline, rooted in modern economic thought yet steeped in the classical intellectual disciplines of chance and uncertainty. Tracing its origins to the early 1970s, and maybe more so to the introduction of the personal computer, financial engineering’s early triumphs include the development of structured mortgage-backed securities (now the biggest bond market) and a rationale for option pricing – the consequences of which are totally pervasive in modern investing, the markets, and finance.
Like much of engineering, financial mathematics constructively uses fundamental mathematical and scientific principles with professional practices to yield products and processes. Rather than trying to understand the social-economic interplay of wealth and well-being, financial mathematics considers a flow of cash (the cash-flow): its exchange, its contingency, and its value both in a relative and an absolute sense. These could be from the standpoint of the investor (a central bank, insurance company, or mutual fund, for example), a Wall Street dealer, a global bank, or a hedge fund. The flow of cash could be packaged as a stock, bond, option, swap, or exchange of currency. This cash flow is rarely tangible, but it is very real in the memory and storage components of computers world-wide, and certainly to the owners of its rights.
So much of financial Mathematics rests upon the mathematics that models data and uncertainty, provides for optimal allocations, and serves the construction of numerical and computational solutions. Such mathematical techniques are well practiced in engineering disciplines. For example, in option analysis we find techniques identical to those used in modeling heat transfer and molecular diffusion; risk measurement and hedging use concepts like those used in designing flight controls or audio amplifiers; and in structuring an investment portfolio or a collateralized bond the very same algorithms are used as for allocating resources for a supply chain or specifying the path of the traveling salesman.
The unifying premise for financial mathematics is more than just a collection of techniques applied to a common problem area, but rather must incorporate the interplay among companies, investors, and global dealers. The global dealers on Wall Street, in London and Hong Kong, and elsewhere act as the factories for the (re-)packaging of capital products into instruments that are vital to the course of world-wide capital allocation, deployment, and risk transfer. That interplay, through the global markets, is the mechanism for the flow of capital among the economies of the world, and for the individuals in those economies.
The financial mathematics Master’s program aims to equip graduates with the engineering-driven approaches widely used to construct and deploy the financial transactions and processes that, in their context, function as the international financial system and capital markers. These are the mechanisms enabling the creation/employment of wealth and for the worldwide distribution of well-being within the constraints and intent of global financial policy.
Admissions for AMS PhD Students
Students in the Applied Mathematics and Statistics PhD program may apply to the Financial Mathematics Master’s program. However, a student cannot be admitted to this program and cannot take any of the three required semesters of the 553.847 Financial Mathematics Seminar until they have passed the Introductory Exam.