Workgroup Financial Mathematics

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Modern Interest Rate Modeling and Beyond

Multiple Curves, LIBOR Market Model and Portfolio Valuation Adjustments (xVA)

01.10.2015 – 02.10.2015


Interest rate modelling has become significantly more complex after the financial crisis. The so-called multiple curve framework has been developed in order to capture the changes observed on the market and has now become the new modeling standard. This workshop details the theoretical foundations and practical implications of the new modeling approaches. In particular, we focus on multi-curve extensions of the LIBOR Market Model. Additionally, the workshop will include a detailed discussion of the current hot topic of negative interest rates including stochastic volatility models in the context of negative rates.

A second focal point of the course will be the new pricing approach based on collateralization and CSA discounting which has been developed to account for the increasing effect of credit risk on derivatve valuation and risk management. We discuss the most recent theoretical developments and challenges on the practitioner's side. In this context, we make an excursion to value adjustments (xVA) and Portfolio simulation.  

The course will complement theoretical parts with a comprehensive discussion of the implementation and include hands-on exercises sessions.


  • Thursday, October 1st, 2015. 8:30-17:30
  • Friday, October 2nd, 2015. 08:30-17:30


The workshop takes place at

quantLab - Room B 121
LMU Institute of Mathematics
Theresienstr. 39
80333 Munich

 A detailed location plan can be found here.



Tentative Schedule:

Morning Session 1 08:30 - 10:00
Morning Session 2 10:30 - 12:00
Afternoon Session 1 14:00 - 15:30
Afternoon Session 2  16:00 - 17:30

Detailed Agenda

  • From classical interest rate modelling to funding and collateralization
  • Curve bootstrapping / calibration: Multi-curve modelling (OIS Discounting, cross-currency curves) - with sample code
  • Market data: Implications of the financial crisis on interbank interest rate markets
  • LIBOR Market Model: single curve and with deterministic basis) - with calibration and sample code
  • Modelling with negative interest rates: Lognormal, normal, displaced-lognormal
  • Excursion: CVA, KVA, FVA - a simple portfolio simulation using the LIBOR Market Model
  • Revisiting risk neutral valuation in the presence of collateralization
  • Multiple curve interest rate theory in a general HJM framework
  • Tractable model specifications driven by affine processes
  • Interest rate volatility modelling (under negative interest rates)
    • Normal, lognormal and in between
    • Volatility smile modelling
    • SABR model with negative rates


Prof. Dr. Christian Fries

Christian Fries is head of model development at DZ Bank’s risk control and Professor for Applied Mathematical Finance at Department of Mathematics, LMU Munich.

His current research interests are hybrid interest rate models, Monte Carlo methods, and valuation under funding and counterparty risk. His papers and lecture notes may be downloaded from

He is the author of “Mathematical Finance: Theory, Modeling, Implementation”, Wiley, 2007 and runs

Dr. Alessandro Gnoatto

Alessandro Gnoatto is a Specialist Counterparty Credit Risk and CVA Trading at Bayerische Landesbank. Before joining BLB, Alessandro worked as a post-doctoral researcher with the Workgroup Financial Mathematics of LMU Munich. His current research interests include advanced asset pricing models based on matrix-valued affine processes and their various applications, e.g. to multiple-curve interest rate models.

He is an experienced lecturer on a broad range of topics from mathematical finance such as interest rate models, Lévy processes and Monte Carlo methods and is a contributor to finmath. Alessandro holds a Ph.D. in Computational Mathematics.

Markus Meister

Markus Meister has more than 10 years experience as a front office quant for interest rates. Prior to joining Zinnegger Financial Risk Management Consulting GmbH in 2015, he worked eight years at Deutsche Bank as a VP in London and Frankfurt and as a Fixed Income Analyst at Millennium Capital Partners on curve building, smile modeling, money market indices and relative value trading.

He holds a Master of Business Administration and Industrial Engineering from Karlsruhe Institute of Technology and a Certificate of Quantitative Finance. He is the author of Smile Modeling in the LIBOR Market Model.

The payment of a workshop fee is required, according to the following table:

No. of Days Practitioner Rate Academic Rate *
1 Day  800€   150€ 
2 Days  1500€   300€ 

(*) Academics (post-graduate students, professors, etc.) must present proof of their academic affiliation (e.g. valid University Badge)

Note: The workshop is offered at a competitive price and will not include any catering (coffee, tea, lunch or dinner). However, located in Munich's "Maxvorstadt", corresponding locations are in short walking distance from the venue.

For registration please contact the Secretary of the Workgroup in Financial Mathematics via