## Curriculum

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### Integrated PhD in Financial Mathematics

**Compulsory Courses****Credit:**3(3-0);**ECTS:**8.0See the course in IAM Catalogue or METU Catalogue

**Credit:**3(3-0);**ECTS:**8.0See the course in IAM Catalogue or METU Catalogue

**Credit:**3(3-0);**ECTS:**8.0See the course in IAM Catalogue or METU Catalogue

**Credit:**3(3-0);**ECTS:**8.0See the course in IAM Catalogue or METU Catalogue

**Credit:**0(0-2);**ECTS:**10.0See the course in IAM Catalogue or METU Catalogue

**Credit:**0(0-0);**ECTS:**130.0See the course in IAM Catalogue or METU Catalogue

**Credit:**3(3-0);**ECTS:**8.0**Numerical Methods for Discrete Time Models:**binomial method for options; discrete time optimal control problems.**Reminders on Continuous Models:**Ito process and its applications in stock market, Black-Scholes equation and its solution; Hedging, Volatility smile.**Monte Carlo Method for Options:**generating random numbers, transformation of random variables and generating normal variates; Monte Carlo integration; pricing by Monte Carlo integration; variance reduction techniques, quasi-random numbers and quasi-Monte Carlo method.**Finite Difference Methods for Options:**explicit and implicit finite difference schemes, Crank-Nicolson method; Free-Boundary Problems for American options.**Finite Difference Methods for Control Problems:**Markov Chain approximation method, elliptic Hamiltion-Jacobi-Bellman equations, computational methods.See the course in IAM Catalogue or METU Catalogue

**Credit:**3(3-0);**ECTS:**8.0See the course in IAM Catalogue or METU Catalogue

7 Elective Courses (Total 42 credits)

See IAM Catalogue for possible elective courses.

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