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Financial
Mathematics

Mathematical models for financial transactions have proven useful to better understand the nature of the risk involved as well as to provide a unified platform from where to analyze markets. The mathematical tools can be used, among other things, to calibrate models in order to better reflect market conditions as well as to look for investment opportunities. Presently, there is a well developed financial industry that requires highly trained personal to assist in complex financial decisions involving sophisticated mathematical models.

The Financial Mathematics Research Group

The Financial Mathematics Research Group at Ryerson University is composed by Dr. Marcos Escobar, Dr. Sebastian Ferrando and Dr. Pablo Olivares. The group is based in the Department of Mathematics and has academic collaborations with the Department of Mathematics at the University of Toronto, the Department of Mathematics at UNICAMP, Brazil, Technical University of Munich, Germany, and Mar del Plata National University, Argentina. It also conducts industrial research collaborations, currently the group assists Sigma Analysis and Management on their research needs.

Research Group Funding

  • MITACS

  • NSERC DISCOVERY

  • NSERC USRA

  • NSERC CRD

  • Industry: Sigma Analysis and Management

Industry Projects

Sigma Analysis and Management: Analysis and Modeling of Hedge Funds.

MSc Program in Applied Mathematics

The MSc in Applied Mathematics at Ryerson University is a research based program that provides students with a solid training in foundational and technical aspects of applied computational mathematics. Interested students can specialize in financial mathematics by taking the required foundational courses as well as the specialized financial courses. These students also have the possibility of conducting hands-on projects for the financial industry. Besides the normal funding through teaching assistantships and awards, students in financial mathematics have the opportunity to access industry based funding. More details about the program structure and entrance requirements can be found in the above link.

Seminars, Research Activities and Students

The Departmental Seminar Series houses the financial mathematics seminars where financial practitioners are regularly invited to speak. Technical reports written by members of the group and collaborators can be obtained from the web page of RAMLab (Ryerson Applied Mathematics Laboratory). This laboratory offers students access to powerful computers needed during their research activities. Some of the research areas available to students are:

  • Arbitrage and hedging in financial mathematics.

  • Analytical approaches to stochastic calculus.

  • Multidimensional modeling, derivative pricing.

  • Hedge funds and investment allocations.

  • Stochastic modeling and statistical inference.

  • Models with jumps and calibration.



Students, research assistants and post doctoral fellows who are currently being supervised or have been supervised by members of the Mathematics Finance Group can be found here.

Students interested in applying to the MSc program who want to pursue studies in financial mathematics are encouraged to contact any member of our research group for information about admissions and financial support.

Announcements

The following is a list of upcoming and past seminars organized by the Mathematical Finance group:


  • February 13 2013,1:00 p.m.( Room:Eng-210)
    Dr. Sebastian Ferrando
    Title: Constrained Estimator for Conditional Expectations
    Abstract: We describe work in progress with collaborators that propose an estimator for a conditional expectation based on partial information.
    The data is assumed to be available in the form of lower dimensional conditional expectations along with a joint probability.
    This estimator was recently introduced in the literature in order to estimate the risk of a portfolio in terms of risk factors
    $X_1, \ldots, X_N$ with joint probability $P_X$. We describe several ways to evaluate this estimator for arbitrary data and
    provide extensions of the original estimator.
Past seminars:
  • 2)October 26th, 1:30 p.m.( Room:Eng-210)
    "Dr. Pablo Olivares
    Title: "Problems in Modelling Hedge Funds" Abstract: We consider the modelling of Hedge Fund indices from daily data by using several discrete time types of switching Markov models as regression with stochastic coeffcients depending on the business cycles and financial variables with normal noises, switching between stable Levy processes and regressions with option- like unit root coefficients and GARCH coeffcients. We discuss fitting problems and state identifcation.

  • 1)September 28th, 1:30 p.m.( Room:Eng-210)
    Dr. Sebastian Ferrando
    Title: "Trajectory Based Pricing and Arbitrage Opportunities" Abstract: Assuming as given a trajectory/path space, we dene an associated market model and a notion of pricing interval. Brie y, we go over some of the theoretical properties of the model, describe a general example and take the oppor- tunity to make some technical comments. We then present a simpler, but practical, model that allow us to compute the pricing interval and to compare to market data. We report on preliminary numerical findings related to realizable arbitrage opportunities (as seen from our model) even when transaction costs are taken into consideration.