Fakultät für Mathematik und Naturwissenschaften

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



2022

5629.

Bohrmann-Linde, Claudia; Siehr, Ilona
CHEMIE Einführungsphase Nordrhein-Westfalen
Herausgeber: C.C.Buchner Verlag, Bamberg
August 2022

ISBN: 9783661060019

5628.

[german] Monique, Meier; Zeller, Diana; Stinken-Rösner, Lisa
Interaktive Videoformate für den naturwissenschaftlichen Unterricht. Vom Rezipieren zum Interagieren
Unterricht Biologie, 475 :44-47
07 2022

5627.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Strom aus Bäckerhefe
Nachrichten aus der Chemie, 70 (7-8) :18-21
Juli 2022

5626.

[german] Zeller, Diana
Medialab – ein dreistufiges Modul zur Entwicklung digitalisierungsbezogener Kompetenzen im Studium des Chemie‐ und Sachunterrichtslehramts
CHEMKON, 29 (S1) :287-292
Juni 2022

5625.

[german] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Entwicklung eines lowcost Experiments für den Chemieunterricht am Beispiel der enzymatischen Brennstoffzelle mit Lactase
CHEMKON, 29 (S1) :233-238
Juni 2022

5624.

[english] Bohrmann-Linde, Claudia; Zeller, Diana; Meuter, Nico; Tausch, Michael W.
Teaching Photochemistry: Experimental Approaches and Digital Media
ChemPhotoChem, 6 (6) :1-11
Juni 2022

5623.

[german] Zeller, Diana; Meier, Monique
Videos interaktiv erweitern - Forschendes Lernen vielseitig unterstützen
Digital Unterricht Biologie, 4 :10-11
Mai 2022

5622.

[german] Gökkus, Yasemin; Tausch, Michael W.
Explorative Studie zur partizipativen und nutzenorientierten Forschung in der Chemiedidaktik
CHEMKON, 29 (3) :117-124
April 2022

5621.

Frommer, Andreas; Kahl, Karsten; Schweitzer, Marcel; Tsolakis, Manuel
Krylov subspace restarting for matrix Laplace transforms
2022

5620.

Gerlach, Moritz; Glück, Jochen
On characteristics of the range of integral operators
2022

5619.

Bolten, M.; De Sturler, E.; Hahn, C.
Krylov Subspace Recycling for Evolving Structures
Comput. Methods Appl. Mech. Engrg., 391 :114222
2022

5618.

Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Ordinal Optimization Through Multi-objective Reformulation
math.OC, arXiv:2204.02003
2022
Herausgeber: arXiv

5617.

Jacob, Birgit; Morris, Kirsten
On solvability of dissipative partial differential-algebraic equations
IEEE Control. Syst. Lett., 6 :3188-3193
2022

5616.

Farkas, Bálint; Jacob, Birgit; Schmitz, Merlin
On exponential splitting methods for semilinear abstract Cauchy problems
2022

5615.

Botchev, M. A.; Knizhnerman, L. A.; Schweitzer, M.
Krylov subspace residual and restarting for certain second order differential equations
2022

5614.

Klamroth, Kathrin; Stiglmayr, Michael; Sudhoff, Julia
Multi-objective Matroid Optimization with Ordinal Weights
Discrete Applied Mathematics
2022

5613.

Frommer, Andreas; Kahl, Karsten; Schweitzer, Marcel; Tsolakis, Manuel
Krylov subspace restarting for matrix Laplace transforms
2022

5612.

Botchev, M. A.; Knizhnerman, L. A.; Schweitzer, M.
Krylov subspace residual and restarting for certain second order differential equations
2022

5611.

Daners, Daniel; Glück, Jochen; Mui, Jonathan
Local uniform convergence and eventual positivity of solutions to biharmonic heat equations
2022

5610.

[german] Tausch, Michael W.
LED statt Gasbrenner - Mehr Licht für nachhaltigen Chemieunterricht
Chemie in unserer Zeit, 56 (3/2022) :188–196
2022

5609.

Frommer, Andreas; Kahl, Karsten; Schweitzer, Marcel; Tsolakis, Manuel
Krylov subspace restarting for matrix Laplace transforms
2022

5608.

[german] Banerji, Amitabh; Dörschelln, Jennifer; Schwarz, D.
Organische Leuchtdioden im Chemieunterricht
Chemie in unserer Zeit, 52 (1) :34-41
2022

5607.

[german] Zeller, Diana; Bohrmann-Linde, Claudia
#debunk YouTube-Videos - Ein didaktisches Konzept zum Einsatz von Videos im Chemieunterricht zur Stärkung der Digital Scientific Literacy
MNU journal, 75 (03) :197-201
2022

5606.

Ballaschk, Frederic; Kirsch, Stefan F.
Oxidations with Iodine(V) Compounds – From Stoichiometric Compounds to Catalysts
In Ishihara, Kazuaki and Muñiz, Kilian, Editor, Iodine Catalysis in Organic Synthesis
Seite 299–334
Herausgeber: Wiley
1 Edition
2022
299–334

5605.

Teng, L.; Ehrhardt, M.; Günther, M.
Stochastic Correlation: Modelling, Analysis and Numerical Simulation with Applications in Finance
Herausgeber: World Scientific

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