### Abstract

Solving Black-Scholes PDE of the arithmetic Asian option is outstanding problem in Mathematics, because the PDE is a degenerate partial differential equation in three dimension. Since there is no analytical solution for the arithmetic Asian option is known yet, we are thinking about modification the Black-Scholes Asian option equation. Using general stochastic differential equation we derive a modified partial differential equation for arithmetic Asian option. We provide four different modification, which some of them can be transformed to the classical Black-Scholes PDE and then to a parabolic equation with constant coefficient, which can solved analytically using means of partial differential equations.

Original language | English |
---|---|

Pages (from-to) | 1217-1227 |

Number of pages | 11 |

Journal | Applied Mathematical Sciences |

Volume | 5 |

Issue number | 25-28 |

Publication status | Published - 2011 |

### Fingerprint

### Keywords

- Arithmetic Asian option
- Partial differential equations
- Stochastic differential equation

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Applied Mathematical Sciences*,

*5*(25-28), 1217-1227.

**On the modified arithmetic Asian option equation and its analytical solution.** / Elshegmani, Zieneb Ali; Ahmed, Rokiah Rozita; Jaaman @ Sharman, Saiful Hafizah.

Research output: Contribution to journal › Article

*Applied Mathematical Sciences*, vol. 5, no. 25-28, pp. 1217-1227.

}

TY - JOUR

T1 - On the modified arithmetic Asian option equation and its analytical solution

AU - Elshegmani, Zieneb Ali

AU - Ahmed, Rokiah Rozita

AU - Jaaman @ Sharman, Saiful Hafizah

PY - 2011

Y1 - 2011

N2 - Solving Black-Scholes PDE of the arithmetic Asian option is outstanding problem in Mathematics, because the PDE is a degenerate partial differential equation in three dimension. Since there is no analytical solution for the arithmetic Asian option is known yet, we are thinking about modification the Black-Scholes Asian option equation. Using general stochastic differential equation we derive a modified partial differential equation for arithmetic Asian option. We provide four different modification, which some of them can be transformed to the classical Black-Scholes PDE and then to a parabolic equation with constant coefficient, which can solved analytically using means of partial differential equations.

AB - Solving Black-Scholes PDE of the arithmetic Asian option is outstanding problem in Mathematics, because the PDE is a degenerate partial differential equation in three dimension. Since there is no analytical solution for the arithmetic Asian option is known yet, we are thinking about modification the Black-Scholes Asian option equation. Using general stochastic differential equation we derive a modified partial differential equation for arithmetic Asian option. We provide four different modification, which some of them can be transformed to the classical Black-Scholes PDE and then to a parabolic equation with constant coefficient, which can solved analytically using means of partial differential equations.

KW - Arithmetic Asian option

KW - Partial differential equations

KW - Stochastic differential equation

UR - http://www.scopus.com/inward/record.url?scp=79959882948&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959882948&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79959882948

VL - 5

SP - 1217

EP - 1227

JO - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

SN - 1312-885X

IS - 25-28

ER -