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
4624.
Broschinski, Christian; Majer, Felix; He, Siyang; Kuehne, Alexander J. C.; Göstl, Robert
Mechanochemical Activation of Red-Light-Excited Triplet–Triplet Annihilation Photon Upconversion
ACS Applied Optical Materials, 2 (9) :1764–1769
September 20244623.
[german] Gökkus, Yasemin; Gutenberg, Janna; Kiesling, Elisabeth; Kremer, Richard; Wernicke, Anne; Bohrmann-Linde, Claudia
Sprachsensibler Chemieunterricht digital umgesetzt – Ein Seminarexkurs im Rahmen des Praxissemesters
DiMawe – Zeitschrift für Konzepte und Arbeitsmaterialien für Lehrer*innenbildung und Unterricht, 6 (1)
September 20244622.
Tapera, Michael; Chotia, Mohit; Mayer-Figge, Jan Lukas; Gómez-Suárez, Adrián; Kirsch, S. F.
anti-Dihydroxylation of olefins enabled by in situ generated peroxyacetic acid
Green Chemistry, 2024
09 2024
Herausgeber: RCS
ISSN: 1463-92704621.
[german] Hüsken, Daniel; Meuter, Nico
Galvanische Zellen erkunden – Eine ergänzende Lernumgebung zur Einführung in die elektrochemische Spannungsreihe
Unterricht Chemie, 202/203 :68-73
September 20244620.
[german] Kiesling, Elisabeth; Bohrmann-Linde, Claudia
What to do with CO2? – Eine bilinguale Schülerlaboreinheit als Beitrag zu BNE
Unterricht Chemie, 202/203 :86-91
September 20244619.
[german] Cornelius, Soraya; Bohrmann-Linde, Claudia
Der Fleck muss weg! – Mit Selbstlernbüchern digitale Lernumgebungen zum Kompetenzerwerb für die Produktion eines Erklärvideos schaffen
Unterricht Chemie, 202/203 :56-61
September 20244618.
[English] Schrader, Claudia; Diekmann, Charlotte; Schulz, Paulina; Mack, Nils; Bohrmann, Claudia; Zeller, Diana
Hands-on training: Effects on virtual presence, learning-centered emotions, cognitive load and learning outcome when learning with virtual reality
Computers in Human Behavior Reports (100487)
09 20244617.
[german] Zeller, Diana
Schritt für Schritt zum digitalen Versuchsprotokoll – Digitale Lernumgebungen mit Miro umsetzen
Unterricht Chemie, 202/203 :27-31
September 20244616.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Wlotzka, Petra
Selbstgesteuert und selbstorganisiert lernen – Digitale Lernumgebungen für den Chemieunterricht gestalten und einsetzen
Unterricht Chemie, 202/203 :2-7
September 20244615.
[german] Zeller, Diana; Bohrmann-Linde, Claudia; Diekmann, Charlotte; Mack, Nils; Schrader, Claudia
Die Teilchenebene in 3D erkunden – Potenziale und Herausforderungen von Virtual Reality im Unterricht
Unterricht Chemie, 202/203 :80-85
September 20244614.
[german] Zeller, Diana; Grandrath, Rebecca
Eigene interaktive Lernbücher gestalten – Ein Überblick für die Produktion mit Book Creator und Pages
Unterricht Chemie, 202/203 :8-13
September 20244613.
Ishaqat, Aman; Hahmann, Johannes; Lin, Cheng; Zhang, Xiaofeng; He, Chuanjiang; Rath, Wolfgang H.; Habib, Pardes; Sahnoun, Sabri E. M.; Rahimi, Khosrow; Vinokur, Rostislav; Mottaghy, Felix M.; Göstl, Robert; Bartneck, Matthias; Herrmann, Andreas
In Vivo Polymer Mechanochemistry with Polynucleotides
Advanced Materials, 36 (32) :2403752
August 2024
ISSN: 1521-40954612.
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 20244611.
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 20244610.
Tapera, Michael; Borghi, Federica; Mayer-Figge, Jan Lukas; Mittendorf, Fabia; Celik, I. E.; Gómez-Suárez, Adrián; Kirsch, S. F.
A Formal Synthesis of (+)-Hannokinol Using a Chiral Horner–Wittig Reagent
Molecules, 29 :3710
07 2024
Herausgeber: MDPI
ISSN: 1420-30494609.
Alcalde, Albert; Fantuzzi, Giovanni; Zuazua, Enrique
Clustering in pure-attention hardmax transformers and its role in sentiment analysis
06 20244608.
Ballaschk, Frederic; Bensberg, Kathrin; Crone, Benedikt; Kirsch, S. F.; Menz, Helge
Synthesis of the monomeric counterpart of Marinomycin A and B
Organic & Biomolecular Chemistry, 2024
06 2024
Herausgeber: RSC4607.
Xu, Zhuo; Tucsnak, Marius
LQR control for a system describing the interaction between a floating solid and the surrounding fluid
06 20244606.
Glück, Jochen; Mui, Jonathan
Non-positivity of the heat equation with non-local Robin boundary conditions
04 20244605.
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: 1349-05404604.
Rath, Wolfgang H.; Göstl, Robert; Herrmann, Andreas
Mechanochemical Activation of DNAzyme by Ultrasound
Advanced Science, 11 (8) :2306236
Februar 2024
ISSN: 2198-38444603.
[german] Tausch, Michael W.
Curriculare Innovation - Ein Imperativ für den Chemieunterricht
Band Chemie professionell unterrichten
Herausgeber: T. Palenta
Februar 2024ISBN: 9783758478413
4602.
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, 9
02 2024
Herausgeber: Elsevier
ISSN: 2666-951X4601.
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 European Journal, 2024 :e202304011
02 2024
Herausgeber: Wiley
ISSN: 0947-65394600.
[german] Tausch, Michael W.; Schneidewind, Jacob
Mit Licht zu grünem Wasserstoff
Chemie in unserer Zeit, 58 (1)
Februar 2024