Model Order Reduction in Computational Finance: Let’s Break the Curse of Dimensionality

My name is Onkar Jadhav. I am a Ph.D. student at the Technical University of Berlin, Germany and working in collaboration with MathConsult GmbH, Linz, Austria. I am an early stage researcher (ESR 06) within a ‘Reduced Order Modelling, Simulation, and Optimization of Coupled Systems (ROMSOC)’ group. My Ph.D. project is a part of ROMSOC and has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 765374.

When I was considering my options after graduation, the idea of getting an advanced degree and learning a topic at a deeper level intrigues me. I feel that with my Ph.D. degree, I will get not only the technical tools but also enough confidence to analyze and solve the problems and deal with the unknown in my daily life. I know that the pursuit of a Ph.D. is an enduring daring adventure and I have already decided to outright it. 😉

My doctoral research is focused on reducing the computational complexity in the analysis of financial Risk. The technique so-called model order reduction also helps to reduce the computational time. Charles Babbage quoted once about the importance of efficiency concerning time:

One essential object is to choose that arrangement which shall tend to reduce to a minimum the time necessary for completing the calculation.

And my thesis work aims to establish such an arrangement. So, let’s embark on a brief journey through my research work.

Packaged retail investment and insurance products (PRIIPs) are at the essence of the retail investment market. PRIIPs offer considerable benefits for retail investors which make up a market in Europe worth up to € 10 trillion. However, the product information provided by financial institutions to investors can be overly complicated and contains confusing legalese. To overcome these shortcomings, the EU has introduced new regulations on PRIIPs (European Parliament Regulation (EU) No 1286/2014). According to this regulation, a PRIIP manufacturer must provide a key information document (KID) for an underlying product that is easy to read and understand.  Based on market risks, PRIIPs are divided into four categories. For my thesis, I concentrate on category III PRIIPs which are dependent on underlying interest rates. It includes, e.g., the interest rate derivatives.

The preparation of KIDs requires numerical simulations of financial instruments. In my case, I evaluate the interest rate derivatives based on the dynamics of the short-rate models. The model parameters are usually calibrated based on market structures like yield curves, cap volatilities, or swaption volatilities. The regulation demands to perform yield curve simulations at least 10,000 times.  The calibration based on several thousand simulated yield curves generates a high dimensional model parameter space. The simulations of such high dimensional parametric models are computationally costly and additionally, have the disadvantage of being affected by the so-called curse of dimensionality. To avoid this problem, I am working on a parametric model order reduction (MOR) approach based on proper orthogonal decomposition method.

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