Finance
The famous Black-Scholes equation is an effective model for option pricing. It was named after the pioneers Black, Scholes and Merton who suggested it 1973.
In this research field our aim is the development of effective numerical schemes for solving linear and nonlinear problems arising in the mathematical theory of derivative pricing models.
An option is the right (not the duty) to buy (`call option') or to sell (`put option') an asset (typically a stock or a parcel of shares of a company) for a price E by the expiry date T. European options can only be exercised at the expiration date T. For American options exercise is permitted at any time until the expiry date. The standard approach for the scalar Black-Scholes equation for European (American) options results after a standard transformation in a diffusion equation posed on an bounded (unbounded) domain.
Another problem arises when considering American options (most of the options on stocks are American style). Then one has to compute numerically the solution on a semi-unbounded domain with a free boundary. Usually finite differences or finite elements are used to discretize the equation and artificial boundary conditions are introduced in order to confine the computational domain.
In this research field we want to design and analyze new efficient and robust numerical methods for the solution of highly nonlinear option pricing problems. Doing so, we have to solve adequately the problem of unbounded spatial domains by introducing artificial boundary conditions and show how to incorporate them in a high-order time splitting method.
Nonlinear Black-Scholes equations have been increasingly attracting interest over the last two decades, since they provide more accurate values than the classical linear model by taking into account more realistic assumptions, such as transaction costs, risks from an unprotected portfolio, large investor's preferences or illiquid markets, which may have an impact on the stock price, the volatility, the drift and the option price itself.
Special Interests
Publications
- 2023
4730.
Stroka, S.; Haussmann, N.; Clemens, M.
Bewertung niederfrequenter Magnetfeldexpositionen unter Einsatz ordnungsreduzierender Modelle
URSI e.V. Deutschland 2023 Kleinheubacher Tagung (KHB 2023)
Miltenberg, Germany
06 20234729.
[german] Venzlaff, Julian; Bohrmann-Linde, Claudia
Photoreformierung – grüner Wasserstoff aus Alkohol, Zucker und Stärke
CHEMKON, 30 (6) :254-259
Juni 20234728.
Mittendorf, Fabia
Total synthesis of both enantiomers of the biosurfactant aureosurfactin via bidirectional synthesis with a chiral Horner–Wittig building block
Organic & Biomolecular Chemistry, 2023 (21) :4574-4577
05 2023
Herausgeber: RSC4727.
Haussmann, N.; Stroka, S.; Tiemann, M.; David, A.; Schmuelling, B.; Clemens, M.
Vorstellung des MILAS Projektes: Autonome induktiv geladene Elektro-Shuttles im öffentlichen Nahverkehr
5. Wissenschaftsforum Mobilität 2023, „Next Chapter in Mobility“
Duisburg, Germany
5 20234726.
Kähne, B.; Clemens, M.
A ROW-Type Method for GPU-Accelerated Large-Scale Finite Element Simulations of Nonlinear Eddy Current Problems
The 13th International Symposium on Electric and Magnetic Fields (EMF 2023)
Marseilles, France
5 20234725.
Haussmann, N.; Stroka, S.; Clemens, M.
Reduction of the Numerical Error in High-Resolution Low-Frequency Magnetic-Field Exposure Scenarios of Human Models Utilizing Smoothing Methods
The 13th International Symposium on Electric and Magnetic Fields (EMF 2023)
Marseilles, France, 29.-31.08.2023
04 20234724.
Zhou, Yu; Centeno, Silvia P.; Zhang, Kuan; Zheng, Lifei; Göstl, Robert; Herrmann, Andreas
Fracture Detection in Bio-Glues with Fluorescent-Protein-Based Optical Force Probes
Advanced Materials, 35 (16) :2210052
April 2023
ISSN: 1521-40954723.
Thermolysis of Geminal Diazido Malonamides: Simple Access to Tetrazoles and Functionalization of In Situ Formed Isocyanates
European Journal of Organic Chemistry, 26 (18) :e2023002
04 2023
Herausgeber: Wiley
ISSN: 1434-193X4722.
Küng, Robin; Germann, Anne; Krüsmann, Marcel; Niggemann, Louisa P.; Meisner, Jan; Karg, Matthias; Göstl, Robert; Schmidt, Bernd M.
Mechanoresponsive Metal-Organic Cage-Crosslinked Polymer Hydrogels
Chemistry – A European Journal, 29 (18) :e202300079
März 2023
ISSN: 1521-37654721.
[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Dem Apfel ans Leder
Nachrichten aus der Chemie, 71 :12-14
März 20234720.
Ponce, Cristobal; Wu, Yongxin; Le Gorrec, Yann; Ramirez, Hector
Port-Hamiltonian modeling of multidimensional flexible mechanical structures defined by linear elastic relations
November 20234719.
Schäfers, Kevin; Bartel, Andreas; Günther, Michael; Hachtel, Christoph
Spline-oriented inter/extrapolation-based multirate schemes of higher order
Applied Mathematics Letters, 136 :108464
2023
Herausgeber: Pergamon4718.
Acu, Ana-Maria; Heilmann, Margareta; Raşa, Ioan
Some results for the inverse of a Bernstein–Schnabl type operator
Analysis and Mathematical Physics, 13 (1)
20234717.
Relton, Samuel D.; Schweitzer, Marcel
Structured level-2 condition numbers of matrix functions
20234716.
Schäfers, Kevin; Bartel, Andreas; Günther, Michael; Hachtel, Christoph
Spline-oriented inter/extrapolation-based multirate schemes of higher order
Applied Mathematics Letters, 136 :108464
2023
Herausgeber: Pergamon4715.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics, 193 :196–203
2023
Herausgeber: North-Holland4714.
Asatryan, Hayk; Gaul, Daniela; Gottschalk, Hanno; Klamroth, Kathrin; Stiglmayr, Michael
Ridepooling and public bus services: A comparative case-study
Submitted to Transportation
2023
Herausgeber: arXiv4713.
Muniz, Michelle; Ehrhardt, Matthias; Günther, Michael; Winkler, Renate
Strong stochastic Runge-Kutta–Munthe-Kaas methods for nonlinear Itô SDEs on manifolds
Applied Numerical Mathematics
2023
ISSN: 0168-92744712.
Günther, Michael; Jacob, Birgit; Totzeck, Claudia
Structure-preserving identification of port-Hamiltonian systems - a sensitivity-based approach
20234711.
Mui, Jonathan
Spectral properties of locally eventually positive operator semigroups
Semigroup Forum, 106 :460-480
20234710.
Abreu, P.; others
Search for photons above 10^{19} eV with the surface detector of the Pierre Auger Observatory
JCAP, 05 :021
20234709.
Giaccari, Ugo Gregorio; others
Simulations of the antenna response for the Auger Radio Detector
PoS, ARENA2022 :042
20234708.
Schweitzer, Marcel
Sketched and truncated polynomial Krylov methods: Matrix Equations
20234707.
Schweitzer, Marcel
Sketched and truncated polynomial Krylov methods: Evaluation of matrix functions
20234706.
Aad, Georges; others
Search for pair-produced vector-like top and bottom partners in events with large missing transverse momentum in pp collisions with the ATLAS detector
Eur. Phys. J. C, 83 (8) :719
2023