Proposal for the Center for Mathematical and Empirical Finance at UCSB

  • Introduction

  • Summary

  • Statement of Purpose

  • Background Information

  • Research Plan

  • Contribution Plan

  • Collaboration

  • Links with Financial Institutions

  • Graduate Emphasis in Mathematical and Empirical Finance

  • Budget

  • Relation of Proposal to Goals, Objectives and Priorities of UCSB

  • Introduction

    The proposal for the Center for Mathematical and Empirical Finance Mathematics (CMEF) and graduate-program-emphasis in Financial Mathematics contains outlines for two levels of program development.

    The graduate program, designated as an emphasis in Financial Mathematics for graduate students in Statistics and Applied Probability, is designed to train students for work in the field of finance. The current proposal outlines a two-year course of study that includes courses from the graduate curriculum of the Statistics and Applied Probability, Economics and Mathematics departments. In addition, an alternative two-year program is presented, which includes a much heavier emphasis on mathematical finan ce. It is our intention that as additional resources become available to the CMEF, these new courses in finance will be developed and included in the two-year course of study. Although the courses will be staffed by the Center, they will be administered as graduate courses on the Department of Statistics and Applied Probability. These courses are in addition to the existing department offerings, so additional resources (which are described in detail in the section titled Budget Request) are needed to compensate faculty for the teaching overload. The proposal describes objectives for international cooperation with the Institute of Statistics and Econometrics at the University of Kiel, Germany and Laboratoire d'Econometrie, Ecole Polytechnique, Paris, France.

    The program for external funding of research activities is the most ambitious part of the proposal. Briefly, the proposal contains the benefits from corporate membership with the CMEF and discusses the focus of research that will be funded. New resources are required to implement the third level of program. Development of corporate members has already begun, but may not bear fruit for some time.

    This draft-proposal is largely written by Zari Rachev in collaboration with Doug Steigerwald (Economics, UCSB), Jon Sonstelie (Chairman, Economics, UCSB), Stamatis Dostouglou (Mathematics, UCSB), Bill Ziemba (Faculty of Commerce, University of British Columbia, Vancouver, Canada), Stefan Mittnik (Director of the Institute of Statistics and Econometrics, University of Kiel), Michel Balinski (Director, Laboratoire d'Econometrie, Ecole Polytechnique, Paris), Eckhard Platen (Australian National University and Banker Trust, Canberra) and Paul Embrechts (Chair Department of Mathematics, ETH, Zurich). Supplementary materials were provided by Raisa Feldman (Statistics and Applied Probability, UCSB) and Glen Swindle (Statistics and Applied Probability, UCSB).

    All documents have informal character and are only intended to help the discussion on a possible future collaboration between Department of Statistics and Applied Probability and Department of Economics in the area of Mathematical and Empirical Finance.


    The proposal seeks resources for establishment of a Center for Mathematical and Empirical Finance (CMEF) at UCSB that will be aimed at bridging the gap between leading academic work in Mathematical and Empirical Finance and the needs of practitioners, particularly those concerned with derivative instruments and risk management. The Center will contain a highly focused research program that will be an important resource for industry. Further, the Center will stimulate interdisciplinary links between different research groups at UCSB and attract external funding.

    While this proposal is for a research unit that is not formally constituted as an ORU, it is planned as an interdisciplinary unit with international and corporate affiliate components that together exceed the parameters and scope f some of the more informal "centers" on campus. Therefore, and in anticipation of new requirements governing the use of the term "Center" in the revised "Administrative Policies and Procedures Concerning Organized Research Units," the proposal is being presented for formal campus review, including consultation with the Academic Senate and final approval by the Chancellor. This proposal (for the Center) is paired with the proposal for an emphasis at the graduate level that is integral to the purpose and scope of the Center, and which will receive Center support. The proposed participating faculty are presenting these two proposals as a "package" for review and approval.

    Statement of Purpose

    The Center for Mathematical and Empirical Finance will allow UCSB to provide quality national leader ship in the important and rapidly evolving area, Mathematical Finance. The competitive and mathematically sophisticated area of modern finance requires fundamental research to be conducted at the highest level and standard. The Center will concentrate on interdisciplinary research both within the university and with other universities and financial institutions. Because many of the research problems in the field arise within financial institutions or involve proprietary data that is costly to acquire close contacts with financial institutions are vital. The structure of the departments of economics and statistics are such that close contacts with financial institutions are difficult to develop and maintain. The primary purpose of the center is to develop these contacts through corporate membership.

    The center will also support graduate and postdoctoral training in the new research field that arises from the application of modern stochastics in Mathematical and Empirical Finance, and by teaching both students and other scientists the new methodology. To support graduate training, the center will provide funding for the creation and staffing of new courses in both the departments of economics and statistics. The Center will provide an outstanding postdoctoral and graduate training area with excellent job opportunities.

    Background Information

    During the last two decades modern probabilistic, statistical and numerical methods have become essential tools in modeling and managing a wide range of financial instruments on stocks and exchange rates including options, bonds, other security derivative and large portfolios. Challenging mathematical and econometric problems have emerged hand those have initiated intensive research in Mathematical and Empirical Finance. These problems have stimulated new developments in identification and stability of stochastic models (Mandelbrot's Paretian stable and fractal models for asset returns and stable portfolios), time series analysis (ARCH and GARCH models), stochastic analysis and control theory (Continuous Time Finance).

    The international significance of the research at UCSB is clearly evidence by faculty's research record and recognition. This will provide the necessary background for this new research direction, in which the Statistics and Applied Probability, Departments of Economics, and Mathematics at UCSB should have a leading position and should attract increasing interest worldwide from academics and practitioners.

    Research Plan

    With this proposal the center seeks resources to support the following research plan

    Contribution to Educational Programs

    The director of the Center would oversee the development of courses in the departments of economics and statistics that relate directly to the Center's activities. The principle goal of the education component is the development of an emphasis in mathematical finance for graduate students in statistics. In addition, the Center would fund the creation and staffing of additional courses in the economics department that would enhance the finance field designation.
    For students who have completed the emphasis in mathematical finance, one component of which is an internship with a corporate sponsor, there would be formal placement opportunities with the corporate sponsors.


    International Collaboration with University of California at Santa Barbara in cooperation with Institute of Statistics and Econometrics Christian-Albrechts-University of Kiel, Germany Laboratoire d'Econometrie Ecole Polytechnique, France.

    The proposal describes the objectives, significance, and resource requirements for an International Center for Mathematical and Empirical Finance to be established at the University of California at Santa Barbara in cooperation with the Insatiate of Statistics and Econometrics, Christian-Albrechts-University of Kiel, Germany (Director: Stefan Mittnik) and Loboratoire d'Econometrie, Ecole Polytechnique, France (Director: Michel Balinski).
    The main objective of the Center is to become an international research and training center for the study of mathematical and empirical finance. It will stimulate international research and educational activities, bridging the gap between leading academic work in mathematical and empirical finance and the needs of the financial sector. The Center's activities will increase the university's national and international visibility, help foster the university's interactions with the financial service community and the business sector at large, and attract external funding.

    Links with Financial Institutions

    The Center for Mathematical and Empirical Finance (CMEF) would produce applied research on financial instruments of direct benefit to the financial institutions that fund it. Both theoretical and empirical work is involved. The Center would produce research preprints and a regular newsletter. It would run research seminars and conferences. CMEF also would act as a resource center in the financial field and maintain an extensive bibliographic library and database.
    Close contact would be maintained between CMEF's researchers and the Cooperate Members. We are currently working in an area where there is the closest of relationships between leading academic research and the work of practitioners. The Corporate Members will directly influence the choice of research program. While one of the main research functions is to produce research for publication in journals and books, the Center can also facilitate constancy arrangements with staff or work for companies on a confidential basis. CMEF should employ a small staff of highly qualified researchers plus a secretary/administrator.

    Corporate Members :

    Most of Chef's funding should be provided by its Corporate Members. This is augmented from time to time by sources of research funding. Our members should be representative of the leading financial institutions in USA, Germany and France. They should have a strong involvement in the activities of the Center. Most Members should make a three year commitment which will be renewed annually. This provides CMEF with a sensible planning horizon, and enables it to recruit the highest caliber staff. One year memberships are also available at a rather higher membership fee.

    Membership Arrangements : The CMEF will be mainly funded by its Corporate Members who will enjoy a close relationship with the work of the Center and participate in shaping its research directions. The Corporate Members form a key group of financial institutions with major interests in financial instruments and risk management. The Center undertakes academic studies of direct relevance to its Corporate Members.

    Corporate Members receive the following benefits:


    Research Resources Prospective Corporate Members should note that important though these benefits are, they are independent of the main function of CMEF, which is to undertake applied research on financial instruments and related topics for publication. All our Corporate Members would receive identical privileges.

    Organization of the Center:

    Director: Professor S.T. Rachev - Ph.D. 1979, D.Sc. 1986 -- Department of Statistics and Applied Probability, University of California, Santa Barbara. His current research interest lies in mathematical finance. Four of his Ph.D. students work in academic institutions with interest in finance and actuarial science. At present he has two Ph.D. students and two post-doctoral students (Matthias Gelbrich, Humboldt University, and Bertrand Gamrowski, Laboratoire de Econometrie, Ecole Polytechnique and Direction de la Recherce et de l'Innovation, Credit Commercial de France) working on mathematical finance. His joint monograph with Stefan Mittnik (Institute of Statistics and Econometrics, University of Kiel) on stable models for asset returns and option pricing is about to appear in Wiley. The entire issue of Econometrics review (1993) (12(3)) is devoted on his paper with S. Mittnik on alternative stable models for stock price changes. Rachev is author of 120 papers in refereed journals and 4 monographs.

    He has done considerable amount of consulting on modeling asset returns, portfolio analysis and option pricing in Japan for Quick Institute (Tokyo), Paris (Laboratoire de Econometrie, Ecole Polytechnique), and security firms Kepler (SUNY, Stony Brook, NY) and AXCOM (Berkeley, California).

    Research Coordinator: Professor Doug Steigerwald Ph.D. 1989. Department of Economics at University of California, Santa Barbara. Current research interests: Empirical finance with special emphasis on nonparametric time-series methods. Former Ph.D. student Steve Fox works in a financial consulting firm (The Frank Russell Company, Tacoma, Washington). Two current Ph.D. students are studying empirical finance: Suzana Velicovic-Brown is studying the effects of dividend policy on stock prices and Collin Crownover is studying exchange rate behavior as it relates to purchasing power parity. Published work includes articles in the Journal of Empirical Finance and the Journal of Econometrics on empirical finance and nonparametric time-series methods. Participant in the National Bureau of Economic Research Asset Pricing group.

    Additional Members of the Center:

    Statistics and Applied Probability

    1.Raisa Feldman - Ph.D. 1987. Technion-IIT. Current research interest stochastic processes; Gaussian and stable random fields; Monte Carlo methods. Dr. Feldman has been studying various problems in random fields. Her joint work with Robert Adler(Technion, Israel) deals with intersection local times for a Gaussian measure-valued process, called the Brownian density process. This work explains how the intersection local time of this particular measure-valued process arises naturally in a motion of interacting particles and gives its evolution equation in terms of integrals over Gaussian white noises. Another direction of her research was the systematic study of intersection local times for continuous semi-martingales and related questions. She also studies the first hit probabilities for random walks.

    2.Jacek Leskow - Ph.D. 1987. Current research interests: analysis of stationary of time series with application to financial data, risk analysis for social and financial phenomena. Leskow's research on stationarity is supported by a NATO grant. He has also obtained a fellowship of a US Census Bureau for this research on stochastic models of poverty in the US. Currently, he is working on numerical methods for stationarity testing. Published work includes articles in Stochastic Processes an Applications, Statistics and Probability Letters, and Statistics and Decisions. Leskow also owns a consulting firm in Wroclaw, Poland that runs projects for financial, public and academic institutions there.

    3.Glen Swindle - Ph.D. 1988. Current research interests: Pricing and hedging of derivatives in the presence of transaction costs, the study of adaptive systems which model the behavior of interacting economic agents. He is: Participant in "The Global Economy as a Complex Adaptive System" at the Santa Fe Institute (Sept. 1993). Speaker at: National Academy of Science Colloquium - The Opening to Complexity (Irvine, CA, June 1994). Co-organizer: Workshop on the Behavior of Financial Markets, University of Chicago, May, 1995.


    1.Henning Bohn - Ph.D. 1986, Stanford Business School. Before joining UCSB in 1992, Dr. Bohn was on the Finance Faculty of the Wharton School, University of Pennsylvania. He was named exceptional speaker at the 1992 Securities Industry Institute. His current research interests are macro-economics, fiscal and monetary policy, and international finance. His published work includes articles in the American Economic Review, the Journal of Monetary Economics, and the Journal of Money, Credit, and Banking.

    2.Joon-Ho Hahm - Ph.D. in Economics and Finance (1993), Graduate School of Business, Columbia University. Current research includes various topics in the empirical macro-finance area; the effects of time-varying conditional variances in macro aggregates and asset returns on the optimal consumption portfolio, behavior of changing financial market volatility's, differential risk premia across countries, and information in the term structure of interest rates on future exchange rates.

    3.John (Jack) M. Marshall - Ph.D. 1969, MIT. Current research interests are insurance economics, economics of uncertainty, and economic theory. He has recently written papers on optimum health insurance and optimum property insurance. His thesis advisee, Steven Slezak, (now at University of Michigan Business School) wrote his dissertation on Wednesday effects and weekend effects in stock market returns. Current advisee Y.Y. Chen is writing on the theory and empirical implications of insolvency of insurance companies Previously Professor Marshall has had research interests in insider trading in financial markets and index of output and input prices for financial intermediaries.

    Advisory Committee :

    We wish to also establish an advisory committee that involves Professor:

    Available Research Facilities

    1.Statistical Consulting Laboratory at Department of Statistics and Applied Probability
    2.Social Science Computing Facility

    Proposal for Graduate Emphasis in Mathematical and Empirical Finance

    MA/Ph.D. in Statistics and Applied Probability Emphasis in Mathematical and Empirical Finance

    Preparation :
    Because the two year course of study requires a broad range of skills in economics, mathematics, and statistics, many prospective students will not be prepared for first year courses. Training for the two year course is contained in a single preparatory year. All courses are not required for all students, the program merely summarizes the requirements for entering graduate students.

    Zero Year (preparatory year) - First Quarter
    Economics 104A (Microeconomics Theory)
    Mathematics 118A (Real Analysis)
    Statistics 120A (Probability Theory)
    Statistics 130A (Statistical Computing)

    Zero Year - Second Quarter
    Economics 104B (Microeconomics Theory)
    Mathematics 118B (Real Analysis)
    Statistics 120B (Probability and Statistics)
    Statistics 130B (Statistical Computing)
    Zero Year - Third Quarter
    Computer Science 12 (Introduction to C and Unix)
    Economics 105 (Macroeconomic Theory)
    Mathematics 118C (Real Analysis)
    Statistics 120C (Statistical Theory)

    Graduate Coursework - Program Based on Current Course Offerings The graduate program is designed to train students for technical work in finance. By emphasizing the technical aspects of modern financial analysis, the program is distinguished from more traditional courses of study offered at business schools. In particular, the program is unique in that it combines mathematically sophisticated courses in finance (Statistics ***) available in only a few mathematics graduate programs, which is found in only a few graduate economics programs. The economics courses in the first year provide the basic background in empirical and international economics program.
    The course of study for the graduate program is one year. The course schedule is
    First Year - First Quarter
    Economics 235A (Finance)
    Statistics 235A, (262) (Deterministic and Probabilistic Methods in Finance)

    First Year - Second Quarter
    Statistics 235A, (262) (Deterministic and Probabilistic Methods in Finance)
    Economics 245B (Time-Series Econometrics)

    First Year - Third Quarter
    Statistics 235C (262) (Dynamics Asset Pricing)
    Statistics 262 (Portfolio Analysis and Risk Management)

    Graduate Coursework - Program Based on Additional Finance Course Offerings If more resources are available, additional finance courses will be offered. The additional resources will provide for development and staffing of the additional courses as outlined in the funding request. Additional courses are listed as Statistics 262. Below, each course for which a textbook is appropriate is a suggested textbook. The course schedule for the more finance focused graduate program is

    First Year - First Quarter
    Economics 235A (Asset Pricing) Huang, C. and R. Litzenberger, Foundations for Financial Economics
    Statistics 235A (262) (Deterministic and Probabilistic Methods in Finance) Duffie, D. Security Markets: Stochastic Models Krouse, C. Capital Markets and Prices Valuing Uncertain Income Streams
    Economics 210B (Microeconomic Theory) Kreps, D. A course in Microeconomic Theory
    Statistics 213A (Probability Theory)

    First Year - Second Quarter
    Economics 210C (Microeconomic Theory)
    Statistics 213B (Stochastic Processes)
    Statistics 235B (262) (Deterministic and Probabilistic Methods n Finance)
    First Year - Third Quarter
    Statistics 235C (Dynamic Asset Pricing) Merton R.C. Continuous Time Finance
    Statistics 213C (Stochastic Calculus and Control Theory)

    Summer Internship with banking/investment financial institutions after the first year
    Second Year - First Quarter
    Statistics 245A (262) (Risk Theory I) Grandel, J. Risk Analysis
    Statistics 230A (Market Microstructure)
    Economics (Time-Series Econometrics)
    Second Year - Second Quarter
    Statistics 245B 1262 (Risk Theory II)
    Statistics 246 1262 (Futures Markets) Duffie, D. Future Markets
    Economics 245B (Time-Series Econometrics) Elective Second Year - Third Quarter
    Statistics 247 (262) (Fixed Income Securities and Derivatives)
    Statistics 599 (Portfolio Analysis and Risk Management)
    Elective Electives:
    Mathematics 246A-C (Partial Differential Equations)
    Statistics 208B (Stochastic Operations Research)
    Statistics 221A (Advanced Probability and
    Stochastic Processes)

    Budget Requests:

    The proposal is aimed at securing funding from financial institutions for research personnel within the departments of Statistics and Applied Probability, Economics, and Mathematics. The funding would assist the center in its goal of making leading academic research available. It is our intention that any University support for the Center would be in addition to existing commitments to the Statistics and Applied Probability and Economics departments. Although external support is to the Statistics and Applied Probability and Economics departments. Although external support is vital to the long-run success of the Center, complete reliance on external funding could compromise the integrity of the Center's research. Therefore, we envision that approximately half of the Center's long-run funding will come from the University.

    Funding Requests:

    Below are specific funding requests with estimated annual costs in bold face. Zari Rachev is the proposed director of the center. As director he will be responsible for development of the center's programs and disbursement of the center's funds.
    1) Summer support for affiliated faculty to compensate for additional teaching and course development responsibilities required for the more finance focused graduate program (listed with the heading "When more resources become available". We request the summer support for a period of three years, after which enough information will have been gathered to seek more permanent sources of funding. The money is needed because affiliated faculty are already fully committed within their departments, and the graduate program requires additional courses. Our proposal is to offer the following additional courses to complete the required first year curriculum beginning in Fall 1995 (Note-the proposed staffing is preliminary):

    Deterministic and Probabilistic Methods in Finance - Rachev Micro Theory Prep - Marshall

    Deterministic II - Swindle/Leskow Empirical Finance - Steigerwald

    International Financial Management - Bohn Dynamic Asset Pricing - Rachev

    Amount: Six FTE per year for first year course development. Note that summer support does not provide a permanent solution to the problem of attracting and keeping high quality finance faculty. For a more permanent solution, we envision the following. Development of the Center would lead to joint appointments within the Center and member departments, the Center would provide funding for visitors, data collection, research assistance, and run executive education programs. The affiliated faculty would be able to receive payment either directly from corporate sponsors or through executive education programs. Without this request to compensate faculty for the additional work, it will be necessary to hire additional researchers in mathematical finance at a salary in the range of $120,000.

    We believe that with a modest initial investment, a successful program can be started. The demand for graduates from the program is likely to be high; already are placing their graduate students at financial consulting firms. We are not alone in our belief that demand for graduates is likely to be high.
    2) Support for an annual research conference. The conference would highlight the research of the Center's faculty and emphasize the application of the research to corporate members. Amount: $2000.
    3) Support for an industry workshop. The workshop would bring in members of the financial industry for a day to explain their problems. They would meet with faculty and graduate students over lunch, during scheduled appointments in the afternoon, and after the presentation. Faculty and students would provide help in problem solving and tutorials (e.g. in estimation methods). The seminar would also assist job placement of our students. Amount: $2000.

    4) Support for a working paper series to disseminate research of the Center's faculty. Amount: $500.

    5) Location: One office on campus.

    Relation of Proposal to Goals, Objectives and Priorities of UCSB