Skip to main content

Novel Methods in Computational Finance

Final Report Summary - STRIKE (Novel Methods in Computational Finance)

In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed a tremendous growth. Advanced numerical techniques are imperative for the most present-day applications in financial industry.
The motivation for this training network was the need for a network of highly educated European scientists in the field of financial mathematics and computational science, to exchange and discuss current insights and ideas, and to lay groundwork for future collaborations.
Besides a series of internationally recognized researchers from academics, leading quantitative analysts from the financial industry also participated in this network. The challenge lied in the necessity of combining transferable techniques and skills such as mathematical analysis, sophisticated numerical methods and stochastic simulation methods with deep qualitative and quantitative understanding of mathematical models arising from financial markets.
The main training objective was to prepare, at the highest possible level, young researchers with a broad scope of scientific knowledge and to teach transferable skills, like social awareness, which is very important in view of the recent financial crises.
The current topic in this network was that the financial crisis in the European countries is a contagion and herding effect and is clearly outside of the domain of validity of Black-Scholes and Merton’s theory, since the market is not Gaussian and it is not friction less and complete.
In this research training network our aim was to deeper understand complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This aim was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models.
In this ITN Research Project STRIKE – Novel Methods in Computational Finance, eleven universities cooperated: Bergische Universität Wuppertal (Germany; also coordinator), Comenius University Bratislava (Slovakia), Universitat Politècnica de València (Spain), Ruse University Angel Kanchev (Bulgaria), Instituto Superior de Economia e Gestão (ISEG) (Lisbon, Portugal), Hochschule Zittau/Görlitz (Germany), Technische Universiteit Delft (the Netherlands), University of Greenwich (United Kingdom), Universität Würzburg (Germany) and Universiteit Antwerpen (Belgium). In total there were 12 ESRs (Early Stage Researchers; PhD-students); additionally there were 5 ERs (Experienced Researchers, PostDocs).
Associated Partners provided market data and additional training and in several cases were host of the ESRs and ERs during secondments of these. At the start of the project we had the following Associated Partners: Université Paris VI (France), University of Sussex (United Kingdom), University of A Coruña (Spain), MathFinance (Waldems, Germany), d-fine GmbH (Frankfurt am Main, Germany) and Postbank AG (Bonn, Germany). Three additional companies became Associate Partner: The Numerical Algorithms Group (NAG, Oxford, UK), Yandex (Moscow, Russia) and MathConsult GmbH (Linz, Austria). Also the Dutch research institute Centrum voor Wiskunde en Informatica (CWI, Amsterdam, the Netherlands) became an Associate Partner. External Partners were: Ortec Finance (Rotterdam, the Netherlands), ING Bank (Amsterdam, the Netherlands), Rabobank (Utrecht, the Netherlands), SAM Sachsen Asset Management GmbH (Leipzig, Germany) and Deloitte & Touche GmbH (Düsseldorf, Germany). Postbank, d-fine, NAG, Yandex, CWI, SAM and Deloitte actively participated in training events.

Project outcomes and Highlights.
At the Public Closing Meeting in Antwerp (Dec. 6, 2016) an overview was given of the various research topics, ranging from modeling, to numerical methods, to highly efficient implementations and to applications in well-chosen case studies. The methods did apply to the Stochastic Differential Equations (SDEs), as well as to Partial Differential Equations (PDEs) Alternating Direct Explicit and Alternating Direction Implicit methods (also for American options); Model Order Reduction; Modelling of Nonlinear Black-Scholes Equations; Modeling contagion claims and other derivative claims involving Credit Value Adjustments; American option pricing problems that resulted in free boundary PDE problems to which special transformations were applied; Methods for nonlinear systems of parabolic equations modelling markets with liquidity shocks; Lévy market models with transaction costs and Partial-Integro Differential equations; Lie Group Analysis of nonlinear Black-Scholes Equations; Herding and Contagion Effects in Financial Markets; GPU acceleration of the Stochastic Grid Bundling Method, on efficient Monte Carlo simulation of the SABR model and on the data-driven COS method; Parallel solution techniques / GPU Computing, with applications to the Commodity Market; Fokker-Planck strategies for the optimal control of stochastic models that involved a jump-diffusion stochastic process.
The various training aspects were highlighted, including the several soft skills and involvement in organizing events. Concerning gender balance, initially we had 5 females out of 12 ESRs (later 4 out of 12). For the ERs we had 2 females out of 5. Five ESRs already defended their PhD-Thesis. The others are in the process of completing the PhD-Thesis. Most ESRs and ERs already found a job.
The Computational Finance Toolbox (CFT) is a joint highlight of the project.
At several events, STRIKE did present its CFT, which collects algorithms for several dimensions, documentations and test examples in a graphical user interface, yet available in Matlab. The spatial dimensions can be stock prices or the volatility of a stock price. There are linear and non-linear models in the CFT. The non-linearity can show itself for example in the coefficients of a partial differential equation or in non-linear coupled systems of differential equations, which means that several prices for different states are calculated. The options include European call and put options as well as American options. The CFT appeared to be an excellent demonstrator platform and strongly helps in communicating with industry. Recently, an extension in Python was finalized.
At our events and conferences interaction was with Postbank AG (Bonn), Deloitte & Touche (Düsseldorf), d-fine GmbH (Frankfurt am Main), European Patent Office (Munich), NAG (Oxford), and Techila Technologies (Tampere), MathFinance (Waldems/Frankfurt), Yandex (Berlin & Moscow), Quantstellation (London), ING Bank (Amsterdam), Rabobank (Utrecht), KBC Bank (Brussels), Banco Santander, Bloomberg, Ernst & Young, Datasim Financial Amsterdam, EDP - Energias de Portugal, BNP Paribas (Lisbon), Thalesians Ltd., NVIDIA, Llyods Banking (all London) and Murex (Luxembourg).
Many publications have been made and presentations have been given. In total the STRIKE teams generated 187 publications in journals and in conference proceedings; in 71 of these STRIKE Fellows were (co-)author. For presentations the corresponding numbers are 299 and 141.
There is still another highlight to come: a book STRIKE – Novel Methods in Computational Finance (Matthias Ehrhardt, Michael Günther, Jan ter Maten, Eds), for which Springer has been contacted and the preparation is nearly finalized. The publication is expected in the first half of 2017.