Ever heard of Robust Finance?

In our MathFinance Colloquium in Frankfurt this week Thorsten Schmidt presented “Robust Finance” in a nutshell. The expectations around the term “robust” are very wide, but this is what we learned:

The goal is to achieve robustness against model risk. Sometimes this is proposed as the solution to the problems, which were responsible for the last financial crises.
Suppose you have N models – even different parameters under the same model is considered a model. Each model is represented by a probability measure P1,…, PN(e.g. of the distribution of the final spot price). Riskand ambiguity must be distinguished: risk is something to which we can assign probabilities. This henceforth will end up in a probability measure P . Ambiguity is something where we cannot assign a probability. Hence, all models are a priori equally possible.

Technical difficulties arise: for example, do the models have the same nullsets? (Example: Brownian motion vs. Poisson process). An arbitrage is a trading strategy which has non-negative payoff under all Pi  and does not vanish for at least one Pj.  This leads to new no-arbitrage conditions and robust formulations. The simplest is the dominated case: there exists one P*  that dominates all Pi.  A theoretically interesting approach would be to replace P(A)  by supi Pi(A),  which leads to a non-linear (i.e. sub-additive) probability measure. Similarities with risk measures are apparent. This is a highly problematic approach, because hedging strategies become very expensive as insurance against all possible models is required.

A possible solution could be Bayesian Finance: we assign probabilities to the Pi  and update with arriving information (filtering). This approach naturally can include jumps; the dominated case can always be reached in discrete time. However, hedging rules are yet completely unclear and many open questions arise. Nevertheless, the application in practice seems highly promising.

Bayesian Finance gives answers to:

  • Model risk
  • Simultaneous use of different models
  • Model governance

In our subsequent discussion, we noticed that robustness has a completely different meaning for an industry quant, for instance:

  • A recalibration of model parameters should generate small parameter changes if the input market data    change is small
  • Greeks should be smooth
  • The local volatility surface should be smooth
  • Calibration speed and precision should be reliable independent of market input data
  • Minimization of the hedging error when replicating contingent claims by trading in the underlying markets

From a practitioner’s view the upcoming research in robust finance is still in a very vague stage; for the moment, it might satisfy an aspect of model governance, where one can address the question of model risk in a fundamental way and then document that “we have thought about it”. As a more concrete contribution I would like to direct your attention to the recent paper on model risk¹ by Nils Detering and Nathalie Packham, where they develop a framework for measuring Value-at-Risk of model risk. As this is a framework, they have implemented probability weights via a simple AIC (Akaike Information Criterion) approach. Now it is the practitioners’ turn to develop the ideas further and make them work in the financial industry.


Professor Dr. Uwe Wystup, Managing Director of MathFinance AG



¹ http://www.tandfonline.com/eprint/WG3rAbrgvTsHKCdnWImK/full


Save the Date:

MathFinance Conference 2017
20th & 21st April 2017, Frankfurt

This conference is successfully running since 2000 and has become one of the top quant events of the year.

The conference is intended for practitioners in the areas of trading, quantitative or derivative research, risk and asset management, insurance, as well as for academics studying or researching in the field of financial mathematics or finance in general.

With around 100 attendees from industry and academia we provide an unparalleled networking opportunity. With our unique mixture of world renowned speakers we discuss a variety of cutting edge issues and research results from all different angles.

The conference will take place at Frankfurt School of Finance and Management, Sonnemannstraße 9-11, 60314 Frankfurt am Main.

Details will be published soon.

Please click here for registration (single / group).




Training on FX Exotic Options in Frankfurt on February 20 – 22, 2017
Lecturer: Prof. Dr. Uwe Wystup

Foreign Exchange options and exotics are becoming increasingly commonplace in today’s capital markets. The objective of this workshop is to develop a solid understanding of the current exotic currency derivatives used in international treasury management. This will give participants the mathematical and practical background necessary to deal with all the products on the market.

Learn how the FX Options market works from an extremely experienced practitioner, get the market view you can’t get from a text book, benefit from in-class case studies and exercises, immediate practice of the theory, learn about the FX smile surface, the way it is built, used and handled. Get the feeling of the hedging approach, understand what most off-the-shelf software provides: insights into pros and cons of financial models, understand structuring well so that you can do it yourself and not be cheated any longer, understand how to hedge which product and the market price of hedging strategies.

Uwe Wystup has been teaching this course for over 10 years and refines it constantly to the specific needs of the banking industry. Almost all known banks and software companies have sent regular participants to this course. Uwe and his team at MathFinance work on the current challenges of the financial industry in their projects on a daily basis. They belong to the few global hybrids working on bridging the gap between the derivatives market and academic research.

Please check our website for more information and registration.


The 16th Winter School on Mathematical Finance will take place on January 23-25, 2017 in Congrescentrum De Werelt, Lunteren, The Netherlands.

Special topics are Polynomial models and Market imperfections.

There will be two mini courses of 5 hours each by Damir Filipovic (EPFL Lausanne) and Jan Kallsen (Christian-Albrechts-Universität zu Kiel). Special invited lectures will be given by Erhan Bayraktar (University of Michigan), Thorsten Schmidt (University of Freiburg) and Wim Schoutens (KU Leuven). Four short lectures complete the programme.


Registration and further information on




MathFinance OpeningsSenior Quant/ Consultant

We are looking for senior quant/ consultant in the areas of


  • Actuary with 5 to 7 years of experience in insurance or re-insurance
  • Experience in quantitative Risk Management in relation to regulatory issues (Solvency II)
  • Experience in Capital Management


  • Quant with 5 to 7 years of experience in Banking, ideally in Trading
  • Experience in quantitative Risk Management in relation to regulatory issues (Basel III)
  • Experience in Capital Management


  • Quant with 5 to 7 years of experience in Asset Management (Funds, Insurance and Family Offices), ideally with emphasis on Risk Management
    Experience in quantitative Risk Management in relation to regulatory issues (German KAGB and KARBV)

Please send us your CV to recruitments@mathfinance.com


Junior Quant

Do the following apply to you?

  • Master degree or diploma in (business) mathematics or physics
  • PhD or CFA is a bonus
  • First experiences in mathematical finance is desirable
  • Very good programming skills, e.g. C++, Python or Matlab
  • Good language skills in German and English
  • Outstanding analytical skills and a problem-solving attitude
  • High motivation to develop your knowledge and skills
  • Good communication skills and team spirit

Then we would like to hear from you. Please send us your CV to recruitments@mathfinance.com