PSD - Dr Linus Wunderlich

Low-rank function approximations for high-dimensional financial risk management

Supervisor: Dr Linus Wunderlich

Project Details :

As risk management becomes increasingly central to financial institutions, so do the computational methods that support it. This project investigates low-rank approximations to high-dimensional functions with applications to counterparty credit risk. 

Financial risk management, trading, and hedging require banks and other financial institutions to perform intricate simulations under realistic market conditions. The high complexity of financial instruments and interdependencies amongst market participants make this a high-dimensional and computationally intensive problem. Institutions are often forced to choose between an overwhelming computational burden or an oversimplification of risk.  

To address this challenge, we explore accelerated derivative pricing techniques. For one- and two-dimensional problems, we have successfully accelerated pricing by replacing frequently called derivative pricing functions with Chebyshev interpolants (https://arxiv.org/pdf/2507.09004). However, in higher dimensions, this approach suffers from the curse of dimensionality, diminishing its efficiency gain. To overcome this, we investigate low-rank tensor approximations and machine learning methods to reliably approximate pricing functions in high-dimensional settings. 

The PhD student under the guidance of Dr Wunderlich, and in collaboration with other members of the Centre, will 

• Conduct numerical experiment on low-rank approximations of derivative pricing functions used for counterparty credit exposure, considering advanced stochastic models and industry-standard exposure measures. 

• Theoretically investigate the methods used, considering convergence rates, stability in relevant function spaces and for wide classes of exposure measures. 

• Demonstrate practical relevance of the methodology. 

Applicants should possess a strong mathematical background and solid programming experience in python. Familiarity with tensor-train decompositions and machine learning is desirable. Prior knowledge of computational finance is beneficial but not essential.

References:

D. Demeterfi, K. Glau, L. Wunderlich. Function approximations for counterparty credit exposure calculations. https://arxiv.org/pdf/2507.09004

Funding Notes:

Further information: 
How to apply 
Entry requirements 
Fees and funding

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