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.
