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



1993

430.

Jensen, Per; Kozin, Igor N.
The Potential Energy Surface for the Electronic Ground State of H\(_{2}\)Se Derived from Experiment
Journal of Molecular Spectroscopy, 160 (1) :39-57
1993
Herausgeber: Academic Press

429.

Jensen, Per; Kozin, Igor N.
The Potential Energy Surface for the Electronic Ground State of H\(_{2}\)Se Derived from Experiment
Journal of Molecular Spectroscopy, 160 (1) :39-57
1993
Herausgeber: Academic Press

428.

Biggs, P.; Canosa-Mas, Carlos E.; Monks, P. S.; Wayne, Richard P.; Benter, Thorsten; Schindler, Ralph N.
The kinetics of the nitrate radical self-reaction
International Journal of Chemical Kinetics, 25 (10) :805-817
1993

427.

Biggs, P.; Canosa-Mas, Carlos E.; Monks, P. S.; Wayne, Richard P.; Benter, Thorsten; Schindler, Ralph N.
The kinetics of the nitrate radical self-reaction
International Journal of Chemical Kinetics, 25 (10) :805-817
1993

426.

Becker, Karl Heinz; Engelhardt, B.; Geiger, Harald; Kurtenbach, Ralf; Wiesen, Peter
Temperature dependence of the reactions of CH radicals with NO, NH\(_{3}\) and N\(_{2}\)O in the range 200-1300 K
Chemical Physics Letters, 210 (1-3) :135-140
1993

425.

Kozin, Igor N.; Klee, Stefan; Jensen, Per; Polyansky, Oleg L.; Pavlichenkov, I. M.
The Far-Infrared Fourier Transform Spectrum of H2Se
Journal of Molecular Spectroscopy, 158 (2) :409-422
1993
Herausgeber: Academic Press

424.

Kozin, Igor N.; Klee, Stefan; Jensen, Per; Polyansky, Oleg L.; Pavlichenkov, I. M.
The Far-Infrared Fourier Transform Spectrum of H\(_{2}\)Se
Journal of Molecular Spectroscopy, 158 (2) :409-422
1993
Herausgeber: Academic Press

423.

Kozin, Igor N.; Klee, Stefan; Jensen, Per; Polyansky, Oleg L.; Pavlichenkov, I. M.
The Far-Infrared Fourier Transform Spectrum of H\(_{2}\)Se
Journal of Molecular Spectroscopy, 158 (2) :409-422
1993
Herausgeber: Academic Press

422.

Jørgensen, Uffe G.; Jensen, Per
The Dipole Moment Surface and the Vibrational Transition Moments of H2O
Journal of Molecular Spectroscopy, 161 (1) :219-242
1993
Herausgeber: Academic Press

421.

J{\o}rgensen, Uffe G.; Jensen, Per
The Dipole Moment Surface and the Vibrational Transition Moments of H\(_{2}\)O
Journal of Molecular Spectroscopy, 161 (1) :219-242
1993
Herausgeber: Academic Press

420.

J{\o}rgensen, Uffe G.; Jensen, Per
The Dipole Moment Surface and the Vibrational Transition Moments of H\(_{2}\)O
Journal of Molecular Spectroscopy, 161 (1) :219-242
1993
Herausgeber: Academic Press

419.

Shestakov, Oleg; Fink, Ewald H.
The a3Σ+(a11) - X1Σ+(X0+) transition of BiN
Chemical Physics Letters, 211 (4-5) :473-477
1993

418.

Shestakov, Oleg; Fink, Ewald H.
The a\(^{3}\)\(\Sigma\)\(^{+}\)(a\(_{1}\)1) - X\(^{1}\)\(\Sigma\)\(^{+}\)(X0\(^{+}\)) transition of BiN
Chemical Physics Letters, 211 (4-5) :473-477
1993

417.

Shestakov, Oleg; Fink, Ewald H.
The a\(^{3}\)\(\Sigma\)\(^{+}\)(a\(_{1}\)1) - X\(^{1}\)\(\Sigma\)\(^{+}\)(X0\(^{+}\)) transition of BiN
Chemical Physics Letters, 211 (4-5) :473-477
1993

416.

Becker, Karl Heinz; Engelhardt, B.; Geiger, Harald; Kurtenbach, Ralf; Wiesen, Peter
Temperature dependence of the reactions of CH radicals with NO, NH3 and N2O in the range 200-1300 K
Chemical Physics Letters, 210 (1-3) :135-140
1993

415.

Becker, Karl Heinz; Engelhardt, B.; Geiger, Harald; Kurtenbach, Ralf; Wiesen, Peter
Temperature dependence of the reactions of CH radicals with NO, NH\(_{3}\) and N\(_{2}\)O in the range 200-1300 K
Chemical Physics Letters, 210 (1-3) :135-140
1993

414.

Denk, G.; G\"unther, Michael; Schmidt, W.
Olympische Chips: Schaltkreise -- Spannung in der Numerik
Technische Universit\"at M\"unchen, TUM-Sonderreihe Forschung f\"ur Bayern, Heft 6: Fakult\"at f\"ur Mathematik, Fakult\"at f\"ur Informatik, Seite 14--15
1993
1992

413.

Heilmann, Margareta
Rate of approximation of weighted derivatives by linear combinations of SMD-operators
Numerical Methods in Approximation Theory - Proceedings of the conference held in Oberwolfach Germany, November 24-30, 1991, Seite 97-115
In D. Braess et al., Editor
Herausgeber: Birkhäuser, Basel, Int. Ser. Numer. Math. 105
1992

412.

Bunker, Philip R.; Hamilton, I. P.; Jensen, Per
Rotation-vibration energies for the HO\(_{2}\) molecule
Journal of Molecular Spectroscopy, 155 (1) :44-54
1992

411.

Becker, Karl Heinz; Engelhardt, B.; Geiger, Harald; Kurtenbach, Ralf; Schrey, G.; Wiesen, Peter
Temperature dependence of the CH+N2 reaction at low total pressure
Chemical Physics Letters, 195 (4) :322-328
1992

410.

Shestakov, Oleg; Pravilov, A. M.; Demes, H.; Fink, Ewald H.
Radiative lifetime and quenching of the A \(^{2}\)\(\Sigma\)\(^{+}\) and X\(_{2}\) \(^{2}\)\(\Pi\)\(_{3/2}\) states of PbF
Chemical Physics, 165 (2-3) :415-427
1992

409.

Shestakov, Oleg; Pravilov, A. M.; Demes, H.; Fink, Ewald H.
Radiative lifetime and quenching of the A 2Σ+ and X2 2Π3/2 states of PbF
Chemical Physics, 165 (2-3) :415-427
1992

408.

Bunker, Philip R.; Hamilton, I. P.; Jensen, Per
Rotation-vibration energies for the HO\(_{2}\) molecule
Journal of Molecular Spectroscopy, 155 (1) :44-54
1992

407.

Bunker, Philip R.; Hamilton, I. P.; Jensen, Per
Rotation-vibration energies for the HO2 molecule
Journal of Molecular Spectroscopy, 155 (1) :44-54
1992

406.

Maten, E. J. W.; Melissen, J. B. M.
Simulation of inductive heating
{IEEE} Transactions on Magnetics, 28 (2) :1287--1290
März 1992
Herausgeber: Institute of Electrical and Electronics Engineers ({IEEE})

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