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



2025

5400.

Asya, Berçin V.; Wang, Sitao; Euchler, Eric; Khiêm, Vu Ngoc; Göstl, Robert
Optical Force Probes for Spatially Resolved Imaging of Polymer Damage and Failure
Aggregate, 6 :e70014
Februar 2025
ISSN: 2692-4560

5399.

Hahmann, Johannes; Schüpp, Boris N.; Ishaqat, Aman; Selvakumar, Arjuna; Göstl, Robert; Gräter, Frauke; Herrmann, Andreas
Sequence-specific, mechanophore-free mechanochemistry of DNA
Chem, 11 :102376
Januar 2025
ISSN: 2451-9294, 2451-9308

5398.

Clevenhaus, A.; Totzeck, C.; Ehrhardt, M.
A Space Mapping approach for the calibration of financial models with the application to the Heston model
2025

5397.

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

5396.

Ehrhardt, Matthias; Günther, Michael; Striebel, Michael
Geometric Numerical Integration Structure-Preserving Algorithms for Lattice QCD Simulations

5395.


High order tensor product interpolation in the Combination Technique
preprint, 14 :25

5394.

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

5393.

Ehrhardt, Matthias; Csomós, Petra; Faragó, István; others
Invited Papers

5392.

Ehrhardt, Matthias; Günther, Michael
Mathematical Modelling of Dengue Fever Epidemics

5391.

Ehrhardt, Matthias
Mathematical Modelling of Monkeypox Epidemics

5390.

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

5389.

Bartel, PD Dr A
Mathematische Modellierung in Anwendungen

5388.


Model Order Reduction Techniques for Basket Option Pricing

5387.

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

5386.

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

5385.

Gjonaj, Erion; Bahls, Christian Rüdiger; Bandlow, Bastian; Bartel, Andreas; Baumanns, Sascha; Belzen, F; Benderskaya, Galina; Benner, Peter; Beurden, MC; Blaszczyk, Andreas; others
Feldmann, Uwe, 143 Feng, Lihong, 515 De Gersem, Herbert, 341 Gim, Sebasti{\'a}n, 45, 333
MATHEMATICS IN INDUSTRY 14 :587

5384.

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

5383.

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

5382.

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

5381.

Ehrhardt, Matthias; Günther, Michael
Numerical Pricing of Game (Israeli) Options

5380.

Ehrhardt, Matthias; Farkas, Bálint; Günther, Michael; Jacob, Birgit
Operator Splitting and Multirate Schemes

5379.

Vázquez, C
PDE modeling and numerical methods for swing option pricing in electricity markets
19th European Conference on Mathematics for Industry, Seite 390

5378.

Ehrhardt, Matthias
Positive Schemes for Air Pollution Problems, Optimal Location of Industrial Enterprises and Optimization of their Emissions

5377.

Ehrhardt, Matthias; Vázquez, Carlos
Pricing swing options in electricity markets with two stochastic factors: PIDE modeling and numerical solution
3rd International Conference on Computational Finance (ICCF2019), Seite 89

5376.

Putek, PA; Ter Maten, EJW
Reliability-based Low Torque Ripple Design of Permanent Magnet Machine