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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, 12.00 - 14.00 c.t.

Thursday, 10.00 - 12.00 c.t.

Room B004

Room B004

Exercise Classes
Annika Steibel

Thursday, 08.30 - 10.00 s.t.

Room B004

Supplementary Exercise Classes
Annika Steibel

Friday, 24 July 2020, 13.00 - 16.00 s.t.

Monday, 27 July 2020, 14.00 - 16.15 s.t.

online

online

Final Exam

Tuesday, 28 July, 10.00 - 12.00 s.t.

Rooms: B004, B052

Retake Exam

Thursday, 08 October, 10.00 - 12.00 s.t.

Room B051

Note that due to the current circumstances the course will start online.

The start of lectures for this course has been postponed by one week. Thus, the first lecture will be held on Tuesday, 28 April 2020 during the usual time slot (12.00 - 14.00 c.t.) and will be broadcast via Zoom. All necessary information will be shared on Moodle so please make sure that you have signed up (see below) and check the Moodle page regularly.  

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).  To sign up for the course on Moodle, please send an e-mail from your LMU e-mail address to Annika Steibel (steibel@math.lmu.de).

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

Correcting your answers and thinking through the exercises is the best preparation for the exam. Please try to solve every problem sheet. Exercises marked with a star (*) will be valid for a bonus system for the final exam and can be handed in for correction. Each "star exercise" will be worth a certain number of points (not necessarily the same). Collecting at least 75% of the total points available during the whole semester will result, upon passing the exam, in a 0.3/0.4 bonus on the final grade.

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


Final Exams

The exam will take place on Tuesday, 28 July 2020 (10.00 -12.00 h) at the LMU Institute of Mathematics (Rooms: B004 and B052).

The retake exam will take place on Thursday, 08 October 2020 (10.00 - 12.00 h) at the LMU Institute of Mathematics (Room B051).

The so-called "Gefährdungsbeurteilung" (see below) is a document which explains the Corona specific safety measures concerning the final exams. In particular, it is important for you to bring a face mask which you have to wear as soon as you enter the building.