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
- 1997
735.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
An ab Initio Study of the NH\(_{2}\)\(^{+}\) Absorption Spectrum
Journal of Molecular Spectroscopy, 186 (2) :319-334
1997734.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
An ab Initio Study of the NH\(_{2}\)\(^{+}\) Absorption Spectrum
Journal of Molecular Spectroscopy, 186 (2) :319-334
1997733.
Osmann, Gerald; Bunker, Philip R.; Jensen, Per; Kraemer, Wolfgang P.
An ab Initio Study of the NH2+ Absorption Spectrum
Journal of Molecular Spectroscopy, 186 (2) :319-334
1997732.
Günther, Michael; Feldmann, Uwe
CAD based electric modeling in Industry
1997731.
Spirko, Vladim{í}r; Mengel, Markus; Jensen, Per
Calculation of Rotation-Vibration Energy Levels in Ground State C\(_{3}\) by a Born-Oppenheimer-Type Separation of the Vibrational Motions
Journal of Molecular Spectroscopy, 183 (1) :129-138
1997
Herausgeber: Academic Press730.
Spirko, Vladim{í}r; Mengel, Markus; Jensen, Per
Calculation of Rotation-Vibration Energy Levels in Ground State C\(_{3}\) by a Born-Oppenheimer-Type Separation of the Vibrational Motions
Journal of Molecular Spectroscopy, 183 (1) :129-138
1997
Herausgeber: Academic Press729.
Spirko, Vladimír; Mengel, Markus; Jensen, Per
Calculation of Rotation-Vibration Energy Levels in Ground State C3 by a Born-Oppenheimer-Type Separation of the Vibrational Motions
Journal of Molecular Spectroscopy, 183 (1) :129-138
1997
Herausgeber: Academic Press728.
Ehrgott, Matthias; Klamroth, Kathrin
Connectedness of efficient solutions in multiple criteria combinatorial optimization
European Journal of Operational Research, 97 :159-166
1997727.
Discrete transparent boundary conditions for parabolic equations
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik, 77 (2) :543--544
1997
Herausgeber: Berlin, Akademie Verlag [etc.]726.
Ehrhardt, Matthias
Discrete transparent boundary conditions for parabolic equations
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik, 77 (S2) :S543–S592
1997
Herausgeber: WILEY-VCH Verlag725.
Kirchner, Ulf; Benter, Thorsten; Schindler, Ralph N.
Experimental verification of gas phase bromine enrichment in reactions of HOBr with sea salt doped ice surfaces
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (6) :975-977
1997724.
Kirchner, Ulf; Benter, Thorsten; Schindler, Ralph N.
Experimental verification of gas phase bromine enrichment in reactions of HOBr with sea salt doped ice surfaces
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (6) :975-977
1997723.
Kirchner, Ulf; Benter, Thorsten; Schindler, Ralph N.
Experimental verification of gas phase bromine enrichment in reactions of HOBr with sea salt doped ice surfaces
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (6) :975-977
1997722.
Fink, Ewald H.; Shestakov, Oleg; Setzer, Klaus-Dieter
Fine Structure Transitions of BiOH in the Near-Infrared Region
Journal of Molecular Spectroscopy, 183 (1) :163-167
1997
Herausgeber: Academic Press721.
Fink, Ewald H.; Shestakov, Oleg; Setzer, Klaus-Dieter
Fine Structure Transitions of BiOH in the Near-Infrared Region
Journal of Molecular Spectroscopy, 183 (1) :163-167
1997
Herausgeber: Academic Press720.
Fink, Ewald H.; Shestakov, Oleg; Setzer, Klaus-Dieter
Fine Structure Transitions of BiOH in the Near-Infrared Region
Journal of Molecular Spectroscopy, 183 (1) :163-167
1997
Herausgeber: Academic Press719.
G{{\'o}}mez, P. C.; Pacios, L. F.; Jensen, Per
Fourfold Clusters of Rovibrational Energies in H\(_{2}\)Po Studied with an ab Initio Potential Energy Function
Journal of Molecular Spectroscopy, 186 (1) :99-104
1997
Herausgeber: Academic Press718.
G{{\'o}}mez, P. C.; Pacios, L. F.; Jensen, Per
Fourfold Clusters of Rovibrational Energies in H\(_{2}\)Po Studied with an ab Initio Potential Energy Function
Journal of Molecular Spectroscopy, 186 (1) :99-104
1997
Herausgeber: Academic Press717.
Gómez, P. C.; Pacios, L. F.; Jensen, Per
Fourfold Clusters of Rovibrational Energies in H2Po Studied with an ab Initio Potential Energy Function
Journal of Molecular Spectroscopy, 186 (1) :99-104
1997
Herausgeber: Academic Press716.
Schindler, J. G.; Schindler, M. M.; Herna, K.; Kling, H.-W.
Glutardialdehyde and formaldehyde biosensors
Biomed. Tech. (Berl), 42 (9) :264
1997715.
Fink, Ewald H.; Ramsay, D. A.
High-resolution study of the A\verb=~= \(^{2}\)A' → X\verb=~= \(^{2}\)A'' transition of HO\(_{2}\): Analysis of the 000-000 band
Journal of Molecular Spectroscopy, 185 (2) :304-324
1997
Herausgeber: Academic Press714.
Fink, Ewald H.; Ramsay, D. A.
High-resolution study of the A\verb=~= \(^{2}\)A' → X\verb=~= \(^{2}\)A'' transition of HO\(_{2}\): Analysis of the 000-000 band
Journal of Molecular Spectroscopy, 185 (2) :304-324
1997
Herausgeber: Academic Press713.
Fink, Ewald H.; Ramsay, D. A.
High-resolution study of the A~ 2A' → X~ 2A" transition of HO2: Analysis of the 000-000 band
Journal of Molecular Spectroscopy, 185 (2) :304-324
1997
Herausgeber: Academic Press712.
Schindler, Ralph N.; Liesner, M.; Schmidt, Sven; Kirchner, Ulf; Benter, Thorsten
Identification of nascent products formed in the laser photolysis of CH\(_{3}\)OCl and HOCl at 308 nm and around 235 nm. Total Cl-atom quantum yields and the state and velocity distributions of Cl(\(^{2}\)P\(_{j}\))
Journal of Photochemistry and Photobiology A: Chemistry, 107 (1-3) :9-19
1997711.
Schindler, Ralph N.; Liesner, M.; Schmidt, Sven; Kirchner, Ulf; Benter, Thorsten
Identification of nascent products formed in the laser photolysis of CH\(_{3}\)OCl and HOCl at 308 nm and around 235 nm. Total Cl-atom quantum yields and the state and velocity distributions of Cl(\(^{2}\)P\(_{j}\))
Journal of Photochemistry and Photobiology A: Chemistry, 107 (1-3) :9-19
1997