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Ph.D. in Financial Mathematics

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  • Program tanımları
    Financial Mathematics Program

    The last decades witnessed the projection of sophisticated mathematical techniques to the center of the finance industry. In the 80's the main investment banks hired mathematicians, physicists and engineers to become financial engineers. Gradually, the main skills defining this professional category are being clarified and today many universities all over the world are designing programs to develop modeling and mathematical expertise in financial applications.

    In our country, the financial sector has enjoyed unparalleled expansion in the last decades and more and more sophisticated financial instruments are expected to be introduced into the sector in the forthcoming ones. Already there are serious attempts to integrate derivative securities and markets into the Turkish financial system. These developments will lead to a demand for talented people trained in the field of financial mathematics.

    The Institute of Applied Mathematics is responding to this new trend in the Turkish finance industry by developing an interdisciplinary program that will introduce students to models and mathematical techniques used in option pricing, pricing of other complex financial products, and to some aspects of financial econometrics. The program combines the strengths of the departments of Mathematics, Business Administration, Economics, Statistics and Industrial Engineering of the Middle East Technical University.

    Admission of Requirements

    The admission procedure of these programs will be implemented according to the “Academic Rules and Regulations Concerning Graduate Studies of METU”. However, some programs might have additional admission requirements. University graduates of any discipline willing to acquire expertise in financial mathematics are natural candidates for these programs. These programs are also open to graduates working in financial and insurance industries. In general, the applicants will be evaluated based on their success in their graduation fields, their LES (Graduate Education Examination) scores, English Proficiency, and the result of a possible examination/interview given by the Institute.

    The program is equally suitable for students who have just finished their undergraduate education or for practitioners in financial industry holding a Bachelor degree. Applicants must have a strong academic background showing good analytical skills. The applicants are expected to have working knowledge of calculus (including partial differentiation, Taylor series, Riemann-Stieltjes integrals), linear algebra (systems of equations, determinants, diagonalization of symmetric matrices, eigenvalues, etc.), elementary theory of ordinary and partial differential equations, in addition to some basic knowledge of computer programming. Course work or job experience in probability is also recommended. A promising student lacking prerequisites may be admitted but required to take the summer Mathematics Preparatory Course (MPC) before beginning the program.

    Ph.D. Program
    • 7 elective courses
    • Ph.D. Thesis(non-credit)
    Total : 21 credits

    Ph.D. Program on B.Sc.
    • 5 core courses
    • 9 elective courses
    • 1 seminar course(non-credit)
    • Ph.D. Thesis(non-credit)
    Total : 42 credits

    Core Courses for Ph.D. on B.Sc.

    1. IAM 520 Financial Derivatives (3-0)3
    This course is designed to provide a solid foundation in the principles of financial derivatives and risk management. It attempts to strike a balance between institutional details, theoretical foundations, and practical applications. The course equally emphasizes pricing and investment strategies in order to motivate students to start thinking about risk management in financial markets. Parallel to the already increasing attempts to integrate derivative securities and markets into the Turkish financial system, it is believed that this course will fill a gap and students will be exposed to a rather comprehensive coverage of theory and application in the derivatives area. This course is expected to give the students a “competitive advantage” when they enter the job market since “derivatives” is a “hot topic” nowadays and BA4825/5825/IAM520 is one of the very few courses offered on this topic in Turkey!

    2. IAM 522 Stochastic Calculus for Finance (3-0)3
    Discrete-time models: trading strategies, self-financing strategies, admissible strategies, arbitrage, martingales and viable markets, complete markets and option pricing. Optimal stopping problem and American options : Stopping time, Snell envelope, American options, European options. Brownian motion and stochastic differential equations: Brownian motion, martingales, stochastic integral and Itô calculus, Ornstein-Uhlenbeck process, stochastic differential equations. The Black-Scholes model: the behavior of prices, self-financing strategies, the Girsanov theorem, pricing and hedging of options, hedging of calls and puts, American options, perpetual puts. Option pricing and partial differential equations: European option pricing and diffusions, partial differential equations and computation of expectations, numerical solutions, application to American options. Interest rate models: modelling principles, some classical models. Asset models with jumps: Poisson process, dynamics of risky assets, pricing and hedging of options. Simulation and algorithms for financial models.

    3. IAM 524 Financial Economics (3-0)3
    Competitive Models with Symmetric Information : Arbitrage and Martingales, Pricing and Hedging Contingent Claims, Consumption and Portfolio Decisions, Walrasian Equilibrium Theory and Term Structure of Interest Rates. Strategic Models with Asymmetric Information: Market Microstructure : A Critique of the Walrasian Equilibrium : The Informational Role of Prices, The Rational Expectations Equilibrium (REE) Concept and Problems, Noisy REE: Aggregation and Transmission of Information, Trading contraints and New Problems, Market Structure and Regulation, Asymmetric Information Models of Market Making, Homogeneous Information Models of Market Making, Intraday transaction Prices and Volumes.

    4. IAM 526 Time Series Applied to Finance (3-0)3
    This course is concerned with recent developments in the time series techniques for the analysis of financial markets. It provides a rigorous account of the time series techniques dealing with univariate and multivariate time series models. The techniques will be illustrated by a number of applications.

    5. IAM 541 Probability Theory (3-0)3
    The objective of this course is to initiate students to Probability Theory in which the main tools are those of Measure Theory. The proposed outline constitutes the prerequisites for Stochastic Calculus and other studies in the domain of stochastic processes.

    The content of the course covers probability spaces, independence, conditional probability, product probability spaces, random variables and their distributions, distribution functions, mathematical expectation ( integration with respect to a probability measure), Lp-spaces, moments and generating functions, conditional expectation, linear estimation, Gaussian vectors, various convergence concepts, central limit theorem and laws of large numbers.

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