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| - | ==== Portfolio Optimization via Probability Estimation ==== | + | ==== On Pricing Dsicrete Barrier Options ==== |
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| - | <note warning> | + | **Description:**\\ |
| - | Already taken by Alexis Touon for Fall Semester 2007-2008 | + | Discrete barrier options will be studied, as well as hitting times of the geometric Brownian motion. The study will focus on European single barrier options, in particular the pricing and the hedging of discrete barrier options. Approximation methods exist for such options [3,4], but perform typically bad when the stock price gets close to the barrier at maturity. The goal of the project is to improve on these approximation methods in order to circumvent this problem. A new theoretical formula should therefore be proposed for the option price. The performance of the new formula will be evaluated on both simulated and real data.\\ |
| - | </note> | + | \\ |
| - | **Description:**\\ | + | **Prerequisites:**\\ |
| - | In this project, the student will be asked to understand the well-developed techniques of probability estimation (e.g. Laplace and Good-Turing estimators described in [1]) and apply them to a portofolio optimization problem, of the type described in [2]. | + | The student should be at ease with probability, stochastic calculus and Matlab programming.\\ |
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| - | **Prerequisites:**\\ | + | |
| - | The student should be at ease with both probability and Matlab programming. | + | |
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| **References:**\\ | **References:**\\ | ||
| - | [1] A. Orlitsky, N.P. Santhanam, and J. Zhang, "Always Good Turing: asymptotically optimal probability estimation" Proceedings of the 44th Anual Symposium on Foundations of Computer Science, October 2003, available on : http://kodiak.ucsd.edu/alon/publications.php\\ | + | [1] J. C. Hull, Options, Futures, and other Derivative Securities, 4th edition. Prentice Hall, New Jersey.\\ |
| - | [2] T. M. Cover, "Universal portfolios", Mathematical Finance, Vol. 1, No. 1, 1991, pp. 1-29. | + | |
| - | \\ | + | [2] P. Carr, A. Chou, Breaking Barriers, Risk magazine 10, 139-144, 1997.\\ |
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| + | [3] S. Kou, On Pricing of Discrete Barrier Options, Statistica Sinica 13, Columbia University, NY, 2003.\\ | ||
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| + | [4] P. Hörfelt, Extension of the Corrected Barrier Approximation by Broadie, Glasserman and Kou, Finance and Stochastics 7, 231-243, 2003.\\ | ||
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| **Supervisor:**\\ | **Supervisor:**\\ | ||
| - | Olivier Lévêque (LTHI) * Email: olivier.leveque#epfl.ch * Office: INR-132 * tel: 38112\\ | + | Dr. Olivier Lévêque (LTHI) * Email: olivier.leveque#epfl.ch * Office: INR 132 * Tel: 38112\\ |
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| - | [[en:projects:2007-2008:mtp|back to master thesis projects menu]] | + | [[en:projects:masterthesis:mtp|back to master thesis projects]] |