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
5325.
Fan, Jilin; Xuan, Mingjun; Zhang, Kuan; Vinokur, Rostislav; Zheng, Lifei; Göstl, Robert; Herrmann, Andreas
Accelerated Mechanophore Activation and Drug Release in Network Core-Structured Star Polymers Using High-Intensity Focused Ultrasound
Small Science, 4 (8) :2400082
August 20245324.
Song, Yongcun; Wang, Ziqi; Zuazua, Enrique
Approximate and Weighted Data Reconstruction Attack in Federated Learning
08 20245323.
Fan, Jilin; Zhang, Kuan; Xuan, Mingjun; Gao, Xiang; Vinokur, Rostislav; Göstl, Robert; Zheng, Lifei; Herrmann, Andreas
High-Intensity Focused Ultrasound-Induced Disulfide Mechanophore Activation in Polymeric Nanostructures for Molecule Release
CCS Chemistry, 6 (8) :1895-1907
August 20245322.
A Formal Synthesis of (+)-Hannokinol Using a Chiral Horner–Wittig Reagent
Molecules, 29 :3710
07 2024
Herausgeber: MDPI
ISSN: 1420-30495321.
Alcalde, Albert; Fantuzzi, Giovanni; Zuazua, Enrique
Clustering in pure-attention hardmax transformers and its role in sentiment analysis
06 20245320.
Synthesis of the monomeric counterpart of Marinomycin A and B
Organic & Biomolecular Chemistry, 2024
06 2024
Herausgeber: RSC5319.
Aydonat, Simay; Hergesell, Adrian H.; Seitzinger, Claire L.; Lennarz, Regina; Chang, George; Sievers, Carsten; Meisner, Jan; Vollmer, Ina; Göstl, Robert
Leveraging mechanochemistry for sustainable polymer degradation
Polymer Journal, 56 (4) :249-268
April 2024
ISSN: 1349-05405318.
Glück, Jochen; Mui, Jonathan
Non-positivity of the heat equation with non-local Robin boundary conditions
04 20245317.
Rath, Wolfgang H.; Göstl, Robert; Herrmann, Andreas
Mechanochemical Activation of DNAzyme by Ultrasound
Advanced Science, 11 (8) :2306236
Februar 2024
ISSN: 2198-38445316.
[german] Tausch, Michael W.
Curriculare Innovation - Ein Imperativ für den Chemieunterricht
Band Chemie professionell unterrichten
Herausgeber: T. Palenta
Februar 2024ISBN: 9783758478413
5315.
Formal synthesis of bastimolide A using a chiral Horner-Wittig reagent and a bifunctional aldehyde as key building blocks
Tetrahedron Chem, 9
02 2024
Herausgeber: Elsevier
ISSN: 2666-951X5314.
Oxidation of Alcohols in Continuous Flow with a SolidPhase Hypervalent Iodine Catalyst
Chemistry - A European Journal, 2024 :e202304011
02 2024
Herausgeber: Wiley
ISSN: 0947-65395313.
[german] Tausch, Michael W.; Schneidewind, Jacob
Mit Licht zu grünem Wasserstoff
Chemie in unserer Zeit, 58 (1)
Februar 20245312.
Izak-Nau, Emilia; Niggemann, Louisa P.; Göstl, Robert
Brownian Relaxation Shakes and Breaks Magnetic Iron Oxide-Polymer Nanocomposites to Release Cargo
Small, 20 (4) :2304527
Januar 2024
ISSN: 1613-68295311.
[english] Wiebel, Michelle; Bensberg, Kathrin; Wende, Luca; Grandrath, Rebecca; Plitzko, Kathrin; Bohrmann-Linde, Claudia; Schebb, Nils Helge
Efficient and simple extraction protocol for triterpenic acids from apples
Journal of Chemical Education
April 2024
Herausgeber: American Chemical Society and Division of Chemical Education, Inc.5310.
Oleanolic Acid-Derived High-Glass-Transition-Temperature Methacrylic Polymers
Sustainable Chemistry & Engineering
Dezember 2024
Herausgeber: ACS
ISSN: 2168-04855309.
Krhac, Kaja; Maschke, Bernhard; van der Schaft, Arjan
Port-Hamiltonian systems with energy and power ports
IFAC-PapersOnLine, 58(6) :280-285
Mai 20245308.
Palitta, Davide; Schweitzer, Marcel; Simoncini, Valeria
Sketched and truncated polynomial Krylov subspace methods: Matrix Sylvester equations
Math. Comp.
20245307.
Liu, Qian
Small-signal synchronization stability of sequence-decomposed grid-forming IBRs
Dezember 20245306.
Santos, Daniela Scherer; Klamroth, Kathrin; Martins, Pedro; Paquete, Luís
Solving the multiobjective quasi-clique problem
20245305.
Ehrhardt, Matthias; Kruse, Thomas; Tordeux, Antoine
The collective dynamics of a stochastic port-Hamiltonian self-driven agent model in one dimension
ESAIM: Mathematical Modelling and Numerical Analysis, 58 (2) :515–544
2024
Herausgeber: EDP Sciences5304.
Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Self-exciting price impact via negative resilience in stochastic order books
Annals of Operations Research, 336 (1) :637–659
2024
Herausgeber: Springer Netherlands5303.
[english] Grandrath, Rebecca; Bohrmann-Linde, Claudia
Simple biofuel cells: the superpower of baker’s yeast
Science in School - The European journal for science teachers, 66
Februar 20245302.
Andersen, Kim Allan; Boomsma, Trine Krogh; Efkes, Britta; Forget, Nicolas
Sensitivity Analysis of the Cost Coefficients in Multiobjective Integer Linear Optimization
Management Science
20245301.
Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail
Self-exciting price impact via negative resilience in stochastic order books
Annals of Operations Research, 336 (1) :637–659
2024
Herausgeber: Springer Netherlands