Academic Catalog

IAM522 STOCHASTIC CALCULUS FOR FINANCE

Course Code: 9700522
METU Credit (Theoretical-Laboratory hours/week): 3(3-0)
ECTS Credit: 8.0
Department: Institute Of Applied Mathematics
Language of Instruction: English
Level of Study: Graduate
Course Coordinator: Assoc.Prof.Dr. AL DEVN SEZER
Offered Semester: Fall or Spring Semesters.

Course Content

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 It 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 option. Interest rate models: modeling principles, some classical models. Asset models with jumps: Poison process, dynamics of risky assets, pricing and hedging of options. Simulation and algorithms for financial models.