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Finanzmathematik III / Fixed Income Markets and Credit Derivatives

Prof. Dr. Thilo Meyer-Brandis, Annika Steibel


Schedule and Venue

Lectures
Prof. Dr. Thilo Meyer-Brandis

Tuesday, 12.15 - 13.45

Thursday, 10.15 - 11.45

online

online

Exercise Classes
Annika Steibel

Thursday, 08.30 - 10.00

online

Supplementary Exercise Classes
Annika Steibel

Monday, 12 July 2021, 10.00 - 13.00 s.t.

Tuesday, 13 July 2021, 10.00 - 12.15 s.t.

online

Final Exam

Thursday, 15 July, 10.00 - 12.00 s.t.

Rooms: B051, B052

Retake Exam

Tuesday, 21 September, 12.00 - 14.00 s.t.

Room: B051

The course will be organised via Moodle (https://moodle.lmu.de) where you can log in using your LMU e-mail address (@campus.lmu.de). If you wish to participate in the course, please sign up by sending an e-mail from your LMU e-mail address to Annika Steibel (steibel@math.lmu.de).

The first lecture will be held on Tuesday, 13 April 2021. 

A registration for the exam as well as for the retake exam is mandatory.


Course Description

This lecture introduces into the arbitrage theory of fixed income markets and interest rate/credit derivatives. Topics that are covered include

  • Introduction to interest rates and interest rate derivatives: bonds, various interest rates, swaps, caps, floors, swaptions, market conventions
  • Arbitrage pricing: portfolios, arbitrage, hedging valuation.
  • Short-rate models
  • Affine term structure models
  • HJM models
  • Forward measures
  • LIBOR market models
  • Credit risk and Related Contracts
  • Structural Models
  • Reduced-Form Models

References

Main reference:

  • Filipovic: Term-Structure Models: A Graduate Course, Springer.

Additional literature:

  • Andersen and Piterbarg: Interest rate modelling, Volume 1,2,3, Atlantic Financial Press.
  • Björk: Arbitrage Theory in Continuous Time, Oxford University Press.
  • Brigo and Mercurio: Interest rate models-Theory and practice: With Smile, Inflation and Credit, Springer.
  • Lando: Credit Risk Modelling: Theory and Applications, Princeton Series in Finance.

For whom is this course?

Target Participants: Master students in Mathematics or Financial and Insurance Mathematics.

Pre-requisites: Proficiency in measure-theoretic probability, stochastic calculus, and fundamentals in Financial Mathematics is required, as f.ex. covered in the lecture Finanzmathematik II/Stochastic Calcuclus in Arbitrage Theory in Continnuous Time. Chapters 3.2, 3.3 A+B, 5.2 A+B and 5.3 A+B of Brownian Motion and Stochastic Calculus by I. Karatzas and S.E. Shreve (1991) can serve as an introduction/brush-up for stochastic calculus.

Applicable credits: Students may apply the credits from this course to the Master Finanz- und Versicherungsmathematik (WP37 (PO2011) resp. WP9 (PO2019)) or to the Master Mathematik (WP7).


Exercises

Problem Sheets: During the course, weekly problem sheets will be uploaded on Moodle.


Final Exams

The exam will take place on Thursday, 15 July 2021 (10.00 - 12.00 h) at the Mathematical Institute of the LMU (Rooms: B051, B052).

The retake exam will take place on Tuesday, 21 September 2021 (12.00 - 14.00 h) at the Mathematical Institute of the LMU (Room: B051).