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: |
Prof.Dr. ALÝ DEVÝN SEZER |
| Offered Semester: |
Fall or Spring Semesters. |
| Prerequisite: |
Set 1: 9700541
|
| The course set above should be completed before taking
IAM522 STOCHASTIC CALCULUS FOR FINANCE . |
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 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 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.
