Mathematical models of financial derivatives markets II 1000-135IP2
1. Basic definitions of interest-rate derivatives. Martingale pricing. A change of numeraire toolkit.
2. Short rate models: Vasicek model, Hull-White model, CIR model. Affine models. Pricing derivatives in short-rate models. Calibration to market data.
3. Forward-rate models. Model HJM and its properties. Market model and the derivation of the Black pricing formula.
Type of course
Prerequisites (description)
Course coordinators
Learning outcomes
Student:
1. knows basic interest rate derivatives, understands the principle of martingale valuation of derivatives, knows the method of changing the numeraire as a derivative valuation technique;
2. knows basic stochastic models of short-term interest rate: Vasicek, Hulla-White, CIR and affine models; knows the basic properties of these models;
3. knows the methodology for the valuation of derivatives in short-term rate models;
4. knows how to calibrate short-term rate models to market data;
5. knows the basic stochastic model of the forward rate - the HJM model and its properties and limitations;
6. knows what the market model of the forward rate is; he knows the proof of Black's formula for caps.
Social competence:
1. understands the problem of stochastic interest rate modeling and the associated modeling of difficulties;
Assessment criteria
The result of the exam consists of the results from class (for solving homeworks, active participation) - 1/3 and the results of the written exam
consisting of problems and theoretical questions (2/3). Opportunity to improve the grade of the exam during the oral exam.
Bibliography
D. Brigo, F. Mercurio – Interest Rate Models – Theory and Practice, Springer, 2006.
J. Jakubowski, A. Palczewski, M. Rutkowski, Ł. Stettner – Matematyka finansowa, instrumenty pochodne. WNT, Warszawa 2006.
M. Baxter – General interest-rate models and the universality of HJM, w Mathematics of Derivative Securities, M. Dempster, S. Pliska Eds., Cambridge University Press 1997, str. 315--335.
D. Filipovic Term-Structure Models. A Graduate Course, Springer, 2009.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
- Bachelor's degree, first cycle programme, Mathematics
- Master's degree, second cycle programme, Mathematics
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: