@article{Guterding2023, author = {Guterding, Daniel}, title = {Sparse Modeling Approach to the Arbitrage-Free Interpolation of Plain-Vanilla Option Prices and Implied Volatilities}, series = {Risks}, journal = {Risks}, number = {11 (5)}, publisher = {MDPI AG}, doi = {https://doi.org/10.3390/risks11050083}, pages = {24}, year = {2023}, abstract = {We present a method for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, which is based on a system of integral equations that relates terminal density and option prices. Using a discretization of the terminal density, we write these integral equations as a system of linear equations. We show that the kernel matrix of this system is, in general, ill-conditioned, so that it cannot be solved for the discretized density using a naive approach. Instead, we construct a sparse model for the kernel matrix using singular value decomposition (SVD), which allows us not only to systematically improve the condition number of the kernel matrix, but also determines the computational effort and accuracy of our method. In order to allow for the treatment of realistic inputs that may contain arbitrage, we reformulate the system of linear equations as an optimization problem, in which the SVD-transformed density minimizes the error between the input prices and the arbitrage-free prices generated by our method. To further stabilize the method in the presence of noisy input prices or arbitrage, we apply an 𝐿1-regularization to the SVD-transformed density. Our approach, which is inspired by recent progress in theoretical physics, offers a flexible and efficient framework for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, without the need to explicitly specify a stochastic process, expansion basis functions or any other kind of model. We demonstrate the capabilities of our method in a number of artificial and realistic test cases.}, language = {en} } @article{XuShimizuGuterdingetal.2023, author = {Xu, Han-Xiang and Shimizu, Makoto and Guterding, Daniel and Otsuki, Junya and Jeschke, Harald O.}, title = {Pressure evolution of electronic structure and magnetism in the layered van der Waals ferromagnet CrGeTe3}, series = {Physical Review B}, journal = {Physical Review B}, number = {Vol. 108}, publisher = {American Physical Society}, doi = {https://doi.org/10.1103/PhysRevB.108.125142}, pages = {15}, year = {2023}, abstract = {Layered van der Waals ferromagnets, which preserve their magnetic properties down to exfoliated monolayers, are fueling an abundance of fundamental research and nanoscale device demonstration. CrGeTe3 is a prime example of this class of materials. Its temperature-pressure phase diagram features an insulator-to-metal transition and a significant increase in ferromagnetic Curie-Weiss temperatures upon entering the metallic state. We use density functional theory to understand the magnetic exchange interactions in CrGeTe3 at ambient and elevated pressures. We calculate Heisenberg exchange couplings, which provide the correct ferromagnetic ground state and explain the experimentally observed pressure dependence of magnetism in CrGeTe3. Furthermore, we combine density functional theory with dynamical mean-field theory to investigate the effects of electronic correlations and the nature of the high-pressure metallic state in CrGeTe3.}, language = {en} } @article{CatalanoNaselloGuterding2024, author = {Catalano, Francesco and Nasello, Laura and Guterding, Daniel}, title = {Quantum Computing Approach to Realistic ESG-Friendly Stock Portfolios}, series = {Risks}, volume = {12}, journal = {Risks}, number = {4}, publisher = {MDPI}, issn = {2227-9091}, doi = {10.3390/risks12040066}, pages = {1 -- 12}, year = {2024}, abstract = {Finding an optimal balance between risk and returns in investment portfolios is a central challenge in quantitative finance, often addressed through Markowitz portfolio theory (MPT). While traditional portfolio optimization is carried out in a continuous fashion, as if stocks could be bought in fractional increments, practical implementations often resort to approximations, as fractional stocks are typically not tradeable. While these approximations are effective for large investment budgets, they deteriorate as budgets decrease. To alleviate this issue, a discrete Markowitz portfolio theory (DMPT) with finite budgets and integer stock weights can be formulated, but results in a non-polynomial (NP)-hard problem. Recent progress in quantum processing units (QPUs), including quantum annealers, makes solving DMPT problems feasible. Our study explores portfolio optimization on quantum annealers, establishing a mapping between continuous and discrete Markowitz portfolio theories. We find that correctly normalized discrete portfolios converge to continuous solutions as budgets increase. Our DMPT implementation provides efficient frontier solutions, outperforming traditional rounding methods, even for moderate budgets. Responding to the demand for environmentally and socially responsible investments, we enhance our discrete portfolio optimization with ESG (environmental, social, governance) ratings for EURO STOXX 50 index stocks. We introduce a utility function incorporating ESG ratings to balance risk, return and ESG friendliness, and discuss implications for ESG-aware investors.}, language = {en} }