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Einführung in das LIBOR Market Model zur Bewertung von Zinsderivaten

Lecturer: Prof. Dr. Christian Fries, Assistants: Alessandro Gnoatto and Juan Miguel Montes


Schedule and Venue

Lectures
Prof. Dr. Christian Fries
Dates and Times:
  • Part 1: March 7th, 2013 14:00-17:30 & March 8th, 2013 08:30-17:30
  • Part 2: March 14th, 2013 14:00-17:30 & March 15th, 2013. 08:30-17:30
quantLab
Room B 121
IT Supervision and Support Dates and Times:
  • Part 1: March 7th, 2013 14:00-17:30 & March 8th, 2013. 08:30-17:30
  • Part 2: March 14th, 2013 14:00-17:30 & March 15th, 2013. 08:30-17:30
Exercises Dates and Times:
  • March, 13th, 2013 08:15-09:45, 10:15-12:45 and 14:15-15:45
  • March, 20th, 2013 08:15-09:45, 10:15-12:45 and 14:15-15:45

Location

LMU München, Mathematisches Institut, Raum B 120, Theresienstraße 39 (B).

The lecture will take place in a computer room with limited seats. In order to attend you have to register via email to email@christian-fries.de before 9:00 a.m. March 6, 2013.

Please also note that the lecture will be held in English, and that additional material will be distributed before the first lecture via e-mail.


Agenda (Tentative)

Part 1: Foundations, Single-Curve and Multi-Curve Interest Rate Theory

  1. Risk Neutral Valuation: A Review
    • Foundations from Probability Theory
    • Stochastic Processes
    • Brownian Motion
    • Geometric Brownian Motion
    • Ito Calculus
    • Replication
    • Change of Measure, Risk Neutral Measure
    • Black-Scholes Model and Monte-Carlo Simulation
  2. Interest Rates (Single Curve Interest Rates Theory)
    • Zero Coupon Bonds
    • Forward Rates
  3. Simple Interest Rates Products: Linear Products (Single Curve Interest Rates Theory)
    • Swaps
    • Swap Rates
  4. Simple Interest Rates Products: European Options (Single Curve Interest Rates Theory)
    • Caplets, Cap
    • Swaptions
  5. Collateralization, Funding and Basis-Spreads (Multi-Curve Interest Rates Theory)
    • Collateralization and Funding
    • Cross-Currency Analogy to Collateralization
  6. Curve Calibration (with object oriented implementation)
    • Discount Factors and Forwards
    • Swaptions
    The resources for this session (spreadsheet, source code) are available at www.finmath.net/topics/curvecalibration.

Part 2: LIBOR Market Model: Theory and Implementation

  1. LIBOR Market Model: Definition, Drift, Model Parameters (Single Curve Interest Rate Theory)
    • Motivation of the model.
    • LMM dynamic under spot and terminal measure.
    • Model parameters (intuition).
  2. LIBOR Market Model: Calibration (Single Curve Interest Rate Theory)
    • Calibration to forward rate curve.
    • Calibration to caplets.
    • Calibration to swaptions.
  3. Cross-Currency and Hybrid LIBOR Market Model
    • Motivation.
    • CCY LMM dynamic under spot and terminal measure.
    • Equity Hybrid LMM dynamic under spot and terminal measure.
    • Multi-Curve LMM.
    • Calibration.
  4. Discretization and Monte-Carlo Simulation
    • Monte-Carlo Simulation
    • Euler-Scheme
  5. Object Oriented Implementation
    • Object oriented implementation of a Monte-Carlo Simulation of the LMM
    • Calibration example (calibration to swaptions)
    The resources for this session (spreadsheet, source code) are available at www.finmath.net/topics/libormarketmodel.
  6. Valuation of Bermudan Option
    • Object oriented implementation of a Monte-Carlo Simulation of the LMM
    • Calibration example (calibration to swaptions)

Updates

For up to date information and detailed agenda see http://www.christian-fries.de/finmath/lecture13.1/

Updates to the lecture will also be posted via Twitter from @f2135 using the hashtag #frieslecture.

If you like to receive updates via mail, please write to email@christian-fries.de.


For Whom is this Course?

Pre-requisites: Die Vorlesung versucht "self-contained" einige Grundlagen der Finanzmathematik zu wiederholen, davon abgesehen werden Kennnisse der Stochastik / stochastischen Prozesse vorausgesetzt. Die Kenntnis einer objektorientierten Programmiersprache (Java, C++, C#) ist von Vorteil.

Interessentenkreis: Mathematiker, Natur- und Wirtschaftswissenschaftler mit mathematischer Ausrichtung, etc.