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



1999

825.

Günther, Michael; Rentrop, Peter
PDAE-Netzwerkmodelle in der elektrischen Schaltungssimulation [PDAE networkmodels in electric switching simulation]
1999

824.

Langer, U; Rienen, U van
Resume of the collection of articles on scientific computing in electrical engineering
Surveys on Mathematics for Industry, 9 (2) :151--154
1999
Herausgeber: Wien; New York: Springer-Verlag, 1991-c2005.

823.

Kevenaar, T.A.M.; Maten, E.J.W.
RF IC simulation: state-of-the-art and future trends
International Conference on Simulation of Semiconductor Processes and Devices. {SISPAD}{\textquotesingle}99 ({IEEE} Cat. No.99TH8387), Seite 7-10
Herausgeber: Japan Soc. Appl. Phys
1999

822.

Günther, M.; Hoschek, M.
ROW-type integration methods for circuit simulation packages
In Arkeryd, Leif and Berg, Jöran and Brenner, Philip and Pettersson, Rolf, Editor
Seite 448–455
Herausgeber: B.G. Teubner, Stuttgart
1999
448–455

821.

Fateev, A. A.; Fink, Ewald H.; Pravilov, A. M.
Simple method of spectrometer/detector sensitivity calibrations in the 210-1150 nm range
Measurement Science and Technology, 10 (3) :182-189
1999

820.

Fateev, A. A.; Fink, Ewald H.; Pravilov, A. M.
Simple method of spectrometer/detector sensitivity calibrations in the 210-1150 nm range
Measurement Science and Technology, 10 (3) :182-189
1999

819.

Fateev, A. A.; Fink, Ewald H.; Pravilov, A. M.
Simple method of spectrometer/detector sensitivity calibrations in the 210-1150 nm range
Measurement Science and Technology, 10 (3) :182-189
1999

818.

Feldmann, U.; Günther, M.
Some remarks on regularization of circuit equations
In Mathis, W. and Schindler, T., Editor, Proceedings of the X International Symposium on Theoretical Electrical Engineering (ISTET '99), Seite 343–348
In Mathis, W. and Schindler, T., Editor
Herausgeber: Otto-von-Guericke-University Magdeburg
1999

817.

Feldmann, Uwe; Günther, Michael
Some remarks on regularization of circuit equations
In W. Mathis, Editor aus Conference Proceedings
Herausgeber: Universität Karlsruhe, Institut für Wissenschaftliches Rechnen und~…
1999

816.

Bunker, Philip R.; Jensen, Per
Spherical top molecules and the molecular symmetry group
Molecular Physics, 97 (1-2) :255-264
1999

815.

Bunker, Philip R.; Jensen, Per
Spherical top molecules and the molecular symmetry group
Molecular Physics, 97 (1-2) :255-264
1999

814.

Bunker, Philip R.; Jensen, Per
Spherical top molecules and the molecular symmetry group
Molecular Physics, 97 (1-2) :255-264
1999

813.

Foster, Krishna L.; Caldwell, Tracy E.; Benter, Thorsten; Langer, Sarka; Hemminger, John C.; Finlayson-Pitts, Barbara J.
Techniques for quantifying gaseous HOCl using atmospheric pressure ionization mass spectrometry
Physical Chemistry Chemical Physics, 1 (24) :5615-5621
1999

812.

Foster, Krishna L.; Caldwell, Tracy E.; Benter, Thorsten; Langer, Sarka; Hemminger, John C.; Finlayson-Pitts, Barbara J.
Techniques for quantifying gaseous HOCl using atmospheric pressure ionization mass spectrometry
Physical Chemistry Chemical Physics, 1 (24) :5615-5621
1999

811.

Foster, Krishna L.; Caldwell, Tracy E.; Benter, Thorsten; Langer, Sarka; Hemminger, John C.; Finlayson-Pitts, Barbara J.
Techniques for quantifying gaseous HOCl using atmospheric pressure ionization mass spectrometry
Physical Chemistry Chemical Physics, 1 (24) :5615-5621
1999

810.

Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\), X\(_{2}\)1) and a\(^{1}\)\(\Delta\)(a2) → X\(_{2}\)1 Transitions of AsI
Journal of Molecular Spectroscopy, 194 (2) :250-255
1999
Herausgeber: Academic Press

809.

Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\), X\(_{2}\)1) and a\(^{1}\)\(\Delta\)(a2) → X\(_{2}\)1 Transitions of AsI
Journal of Molecular Spectroscopy, 194 (2) :250-255
1999
Herausgeber: Academic Press

808.

Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\), X\(_{2}\)1) and a\(^{1}\)\(\Delta\)(a2) → X\(_{2}\)1 transitions of SbF, SbCl, SbBr, and SbI
Journal of Molecular Spectroscopy, 195 (1) :147-153
1999
Herausgeber: Academic Press

807.

Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b\(^{1}\)\(\Sigma\)\(^{+}\)(b0\(^{+}\)) → X\(^{3}\)\(\Sigma\)\(^{-}\)(X\(_{1}\)0\(^{+}\), X\(_{2}\)1) and a\(^{1}\)\(\Delta\)(a2) → X\(_{2}\)1 transitions of SbF, SbCl, SbBr, and SbI
Journal of Molecular Spectroscopy, 195 (1) :147-153
1999
Herausgeber: Academic Press

806.

Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b1Σ+(b0+) → X3Σ-(X10+, X21) and a1Δ(a2) → X21 Transitions of AsI
Journal of Molecular Spectroscopy, 194 (2) :250-255
1999
Herausgeber: Academic Press

805.

Beutel, M.; Setzer, Klaus-Dieter; Fink, Ewald H.
The b1Σ+(b0+) → X3Σ-(X10+, X21) and a1Δ(a2) → X21 transitions of SbF, SbCl, SbBr, and SbI
Journal of Molecular Spectroscopy, 195 (1) :147-153
1999
Herausgeber: Academic Press

804.

Bunker, Philip R.; Bludsk{{\'y}}, Ota; Jensen, Per; Wesolowski, Steven S.; Van Huis, T. J.; Yamaguchi, Yukio; Schaefer, Henry F.
The H\(_{2}\)O\(^{++}\) Ground State Potential Energy Surface
Journal of Molecular Spectroscopy, 198 (2) :371-375
1999

803.

Bunker, Philip R.; Bludsk{{\'y}}, Ota; Jensen, Per; Wesolowski, Steven S.; Van Huis, T. J.; Yamaguchi, Yukio; Schaefer, Henry F.
The H\(_{2}\)O\(^{++}\) Ground State Potential Energy Surface
Journal of Molecular Spectroscopy, 198 (2) :371-375
1999

802.

Bunker, Philip R.; Bludský, Ota; Jensen, Per; Wesolowski, Steven S.; Van Huis, T. J.; Yamaguchi, Yukio; Schaefer, Henry F.
The H2O++ Ground State Potential Energy Surface
Journal of Molecular Spectroscopy, 198 (2) :371-375
1999

801.

Becker, Karl Heinz; Freitas Dinis, Carlos M.; Geiger, Harald; Wiesen, Peter
The reactions of OH radicals with di-i-propoxymethane and di-sec-butoxymethane: Kinetic measurements and structure activity relationships
Physical Chemistry Chemical Physics, 1 (20) :4721-4726
1999