20251 - FIXED INCOME (ADVANCED METHODS)
CLMG - M - IM - MM - AFC - CLAPI - CLEFIN-FINANCE - CLELI - ACME - DES-ESS - EMIT
Course taught in English
Go to class group/s: 31
The purpose of the course is to present the latest achievements in the term structure modeling for pricing and hedging interest rate derivatives. Emphasis is devoted to the theoretical and practical implementation of the models, and the suitability of different models in complex valuation and hedging problems of interest rate options, equity-linked fixed income securities and structured products. On completing the course the participants have a clear and thorough understanding of the different methodologies in the pricing and hedging of interest rate options. The course is quantitatively oriented, but financial and practical issues are greatly discussed.
Basic elements of financial mathematics. LIBOR rates and Eurodeposits, FRA, Eurofutures, Swap. Pricing Floating Rate Notes. Yield curve stripping. Caps and Swaptions. Interest rate modelling: the classical approach (Merton, Vasicek, Cox and Ingersoll). Stochastic differential equations, change of numeraire and the market practice: the Black model. Advanced term structure modelling: the Heath-Jarrow-Morton model and the LIBOR market model. Model calibration. Pricing of structured bonds. Modelling the Volatility Smile in the interest rate market. Credit risk issues. Laboratory session (with Excel and/or Matlab) for implementation issues.
The exam can have two different modalities:
Two partial examinations (closed books) are planned. The first follows the initial six lectures and is based on the first part of the course. The second examination occurs at the end of the course and is based on the second part of the course. Grades are assigned as follows: 40% for each partial examination plus a take home examination (20%), for which the use of a computer and Excel/Matlab is required. Groupwork (no more than 5 persons) is allowed for the take home examination. The deadline for the take home examination is set before the end of the course. If the grade of the midterm is not sufficient (less than 18), you cannot do the second partial examination and the take home examination.
A Final Examination at the end of the course is planned, and is based on the entire course. No take home examination is planned.
Lecture Slides available on the E-Learning platform.
D. BRIGO, F. MERCURIO, Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit, Springer Finance,2nd ed, 2007.
J. HULL, Options, Futures and Other Derivatives, Pearson Prentice, Hall, sixth edition.
L. MARTELLINI, P. PRIAULET, S. PRIAULET, Fixed-Income Securities: Valuation, Risk Management and Portfolio Strategies, John Wiley & Sons (July 7, 2003).
P. VERONESI, Fixed Income Securities: Valuation, Risk, and Risk Management, Wiley, 2009.
Basic knowledge of derivative instruments like futures and options, their pricing trough the no-arbitrage principle and the Black-Scholes formula as well as a basic knowledgeof stochastic calculus (at the level of the Hull textbook) and solution of stochastic differential equations (like arithmetic and geometric Brownian motion) are required as prerequisites.