Applied and Computational Mathematics (ACM)

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



2024

6956.

Celik, I. E.; Mittendorf, Fabia; Gómez-Suárez, Adrián; Kirsch, S. F.
Formal synthesis of bastimolide A using a chiral Horner-Wittig reagent and a bifunctional aldehyde as key building blocks
Tetrahedron Chem, 2024
02 2024
Herausgeber: Elsevier
ISSN: 2666-951X

6955.

Bensberg, Kathrin; Savvidis, Athanasios; Ballaschk, Frederic; Gómez-Suárez, Adrián; Kirsch, S. F.
Oxidation of Alcohols in Continuous Flow with a SolidPhase Hypervalent Iodine Catalyst
Chemistry A Eropean Journal, e202304011
02 2024
Herausgeber: Wiley
ISSN: 0947-6539

6954.

[german] Tausch, Michael W.; Schneidewind, Jacob
Mit Licht zu grünem Wasserstoff
Chemie in unserer Zeit, 58 (1)
Februar 2024

6953.

Ehrhardt, Matthias; Günther, Michael; Brunner, H; Dalhoff, A
Mathematical Modelling of Dengue Fever Epidemics

6952.

Ehrhardt, Matthias; Brunner, H
Mathematical Modelling of Monkeypox Epidemics

6951.

Ehrhardt, Matthias; Brunner, H
Mathematical Modelling of Monkeypox Epidemics

6950.

Ehrhardt, Matthias; Günther, Michael; Brunner, H
Mathematical Study of Grossman's model of investment in health capital

6949.

Ehrhardt, Matthias; Günther, Michael; Brunner, H
Mathematical Study of Grossman's model of investment in health capital

6948.

Ehrhardt, M; Günther, M; Bartel, PD Dr A
Mathematische Modellierung in Anwendungen

6947.

Silva, JP; Maten, J; Günther, M; Ehrhardt, M
Model Order Reduction Techniques for Basket Option Pricing

6946.

Silva, JP; Maten, J; Günther, M; Ehrhardt, M
Model Order Reduction Techniques for Basket Option Pricing

6945.

Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance

6944.

Petrov, Pavel S; Ehrhardt, Matthias; Kozitskiy, Sergey B
A generalization of the split-step Padé method to the case of coupled acoustic modes equation in a 3D waveguide
Journal of Sound and Vibration :118304
2024
Herausgeber: Elsevier

6943.

Ambartsumyan, I; Khattatov, E; Yotov, I; Zunino, P; Arnold, Anton; Ehrhardt, Matthias; Ashyralyev, Allaberen; Csomós, Petra; Faragó, István; Fekete, Imre; others
Invited Papers

6942.

Ehrhardt, Matthias; Günther, Michael
Modelling Stochastic Correlations in Finance

6941.

Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas; Maten, Jan
Modelling, Analysis and Simulation with Port-Hamiltonian Systems

6940.

Ehrhardt, Matthias; Günther, Michael; Jacob, Birgit; Bartel, PD Dr Andreas; Maten, Jan
Modelling, Analysis and Simulation with Port-Hamiltonian Systems

6939.

Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Seite 377

6938.

Maten, E Jan W; Ehrhardt, Matthias
MS40: Computational methods for finance and energy markets
19th European Conference on Mathematics for Industry, Seite 377

6937.

Putek, Piotr; PAPLICKI, Piotr; Pulch, Roland; Maten, Jan; Günther, Michael; PA{\L}KA, Ryszard
NONLINEAR MULTIOBJECTIVE TOPOLOGY OPTIMIZATION AND MULTIPHYSICS ANALYSIS OF A PERMANENT-MAGNET EXCITED SYNCHRONOUS MACHINE

6936.

Günther, Michael; Wandelt, Dipl Math Mich{\`e}le
Numerical Analysis and Simulation I: ODEs

6935.

Ehrhardt, Matthias; Günther, Michael
Numerical Evaluation of Complex Logarithms in the Cox-Ingersoll-Ross Model

6934.

Ehrhardt, Matthias; Günther, Michael; Brunner, H; Dalhoff, A
Mathematical Modelling of Dengue Fever Epidemics

6933.

Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael
Hybrid finite difference/pseudospectral methods for stochastic volatility models
19th European Conference on Mathematics for Industry, Seite 388

6932.

Ambartsumyan, I; Khattatov, E; Yotov, I; Zunino, P; Arnold, Anton; Ehrhardt, Matthias; Ashyralyev, Allaberen; Csom{\'o}s, Petra; Farag{\'o}, Istv{\'a}n; Fekete, Imre; others
Invited Papers

Weitere Infos über #UniWuppertal: