Introduction to the LIBOR Market Model and the Valuation of Interest Rate Products: Theory, Modeling and Implementation
(LMU Belegnummer 16536)
Lecture
Thursday March 7th, 2013 14:00-17:30 and Friday March 8th, 2013. 08:30-17:30 (Part 1)
Thursday March 14th, 2013 14:00-17:30 and Friday March 15th, 2013. 08:30-17:30 (Part 2)
LMU München, Mathematisches Institut, Raum B 121, Theresienstraße 39 (B).
Exercises
- 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
Note
Additional material will be distributed before the first lecture. To guarantee availability, please register for the mailing list by writing an email to email@christian-fries.de.
Agenda (Tentative)
Part 1: Foundations, Single-Curve and Multi-Curve Interest Rate Theory
- 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
- Interest Rates (Single Curve Interest Rates Theory)
- Zero Coupon Bonds
- Forward Rates
- Simple Interest Rates Products: Linear Products (Single Curve Interest Rates Theory)
- Simple Interest Rates Products: European Options (Single Curve Interest Rates Theory)
- Collateralization, Funding and Basis-Spreads (Multi-Curve Interest Rates Theory)
- Collateralization and Funding
- Cross-Currency Analogy to Collateralization
- 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
- 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).
- LIBOR Market Model: Calibration (Single Curve Interest Rate Theory)
- Calibration to forward rate curve.
- Calibration to caplets.
- Calibration to swaptions.
- 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.
- Discretization and Monte-Carlo Simulation
- Monte-Carlo Simulation
- Euler-Scheme
- 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.
- Valuation of Bermudan Option
- Object oriented implementation of a Monte-Carlo Simulation of the LMM
- Calibration example (calibration to swaptions)
Updates
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.
Dates and Location
- Location
- LMU München, Mathematisches Institut, Raum B 120, Theresienstraße 39 (B).
- Dates
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Thursday 07.03.2013
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14:00-15:30 Session 1
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16:00-17:30 Session 2
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Friday 08.03.2013
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08:30-10:00 Session 3
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10:30-12:00 Session 4
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14:00-15:30 Session 5
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16:00-17:30 Session 6
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Thursday 14.03.2013
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14:00-15:30 Session 7
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16:00-17:30 Session 8
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Friday 15.03.2013
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08:30-10:00 Session 9
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10:30-12:00 Session 10
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14:00-15:30 Session 11
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16:00-17:30 Session 12
Voraussetzungen
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.
Contact
email@christian-fries.de
Literature
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Fries, Christian: Mathematical Finance. Theory, Modeling, Implementation. Wiley 2007. ISBN 0-470-04722-4.
Office Hours
by appointment and via
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iMessage
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email@christian-fries.de
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Skype
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cpfries
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iChat / AIM
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cpfries