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



1997

705.

Arnold, A.; Ehrhardt, M.
A New Discrete Transparent Boundary Condition for Standard and Wide Angle 'Parabolic' Equations in Underwater Acoustics
Proceedings of the Third International Conference on Theoretical and Computational Acoustics, July 14-18, 1997, Newark, New Jersey, USA, Seite 623-635
1997

704.

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
1997

703.

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 Press

702.

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 Press

701.

Chance, K. V.; Park, K.; Evenson, K. M.; Zink, L. R.; Stroh, Fred; Fink, Ewald H.; Ramsay, D. A.
Improved Molecular Constants for the Ground State of HO\(_{2}\)
Journal of Molecular Spectroscopy, 183 (2) :418
1997
Herausgeber: Academic Press

700.

Günther, Michael; Ostermann, Alexander
Numerical treatment of ordinary and algebra-differential equations
Preprint (1934)
1997
Herausgeber: Technische Hochschule Darmstadt

699.

Ehrgott, Matthias; Klamroth, Kathrin
Nonconnected efficiency graphs in multiple criteria combinatorial optimization
In Caballero, R. and Ruiz, F. and Steuer, R.E., Editor, Advances in Multiple Objective and Goal ProgrammingBand455ausLecture Notes in Economics and Mathematical Systems, Seite 140-150
In Caballero, R. and Ruiz, F. and Steuer, R.E., Editor
1997

698.

Günther, Michael
Modelling transmission lines effects in integrated circuits by a mixed system of DAEs and PDEs
In Troch, I. and Breitenecker, F., Editor, 2nd MATHMOD Vienna. Proceedings IMACS Symposium on Mathematical ModellingBand11ausArgesim Report 15, Seite 535–540
In Troch, I. and Breitenecker, F., Editor
Herausgeber: TU Wien
1997

697.

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 Press

696.

Tausch, Michael W.; Brandl, H.
Lichtbeteiligung bei chemischen Reaktionen
MNU, 50 :206
1997

695.

Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Kinetics of the Reactions of NCO Radicals with NO and NH3
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (1) :128-133
1997

694.

Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Kinetics of the Reactions of NCO Radicals with NO and NH\(_{3}\)
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (1) :128-133
1997

693.

Becker, Karl Heinz; Kurtenbach, Ralf; Schmidt, Frank; Wiesen, Peter
Kinetics of the Reactions of NCO Radicals with NO and NH\(_{3}\)
Berichte der Bunsengesellschaft für physikalische Chemie, 101 (1) :128-133
1997

692.

Chance, K. V.; Park, K.; Evenson, K. M.; Zink, L. R.; Stroh, Fred; Fink, Ewald H.; Ramsay, D. A.
Improved Molecular Constants for the Ground State of HO2
Journal of Molecular Spectroscopy, 183 (2) :418
1997
Herausgeber: Academic Press

691.

Chance, K. V.; Park, K.; Evenson, K. M.; Zink, L. R.; Stroh, Fred; Fink, Ewald H.; Ramsay, D. A.
Improved Molecular Constants for the Ground State of HO\(_{2}\)
Journal of Molecular Spectroscopy, 183 (2) :418
1997
Herausgeber: Academic Press

690.

G\"unther, Michael
Modelling transmission lines effects in integrated circuits by a mixed system of {DAEs} and {PDEs}
In I.~Troch and F.~Breitenecker, Editor, 2nd MATHMOD Vienna. Proceedings IMACS Symposium on Mathematical ModellingBand11ausArgesim Report, Seite 535--540
In I.~Troch and F.~Breitenecker, Editor
Herausgeber: TU Wien
Februar 1997

689.

Schindler, Ralph N.; Liesner, M.; Schmidt, Sven; Kirchner, Ulf; Benter, Thorsten
Identification of nascent products formed in the laser photolysis of CH3OCl and HOCl at 308 nm and around 235 nm. Total Cl-atom quantum yields and the state and velocity distributions of Cl(2Pj)
Journal of Photochemistry and Photobiology A: Chemistry, 107 (1-3) :9-19
1997

688.

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 Press

687.

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 Press

686.

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

685.

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 Press

684.

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 Press

683.

Schindler, J. G.; Schindler, M. M.; Herna, K.; Kling, H.-W.
Glutardialdehyde and formaldehyde biosensors
Biomed. Tech. (Berl), 42 (9) :264
1997

682.

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 Press

681.

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 Press

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