### Abstract

Arithmetic Asian options are difficult to price and hedge, since at present, there is no closed-form analytical solution to price them. Transforming the PDE of the arithmetic the Asian option to a heat equation with constant coefficients is found to be difficult or impossible. Also, the numerical solution of the arithmetic Asian option PDE is not very accurate since the Asian option has low volatility level. In this paper, we analyze the value of the arithmetic Asian option with a new approach using means of partial differential equations (PDEs), and we transform the PDE to a parabolic equation with constant coefficients. It has been shown previously that the PDE of the arithmetic Asian option cannot be transformed to a heat equation with constant coefficients. We, however, approach the problem and obtain the analytical solution of the arithmetic Asian option PDE.

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

Article number | 401547 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 2011 |

DOIs | |

Publication status | Published - 2011 |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

*International Journal of Mathematics and Mathematical Sciences*,

*2011*, [401547]. https://doi.org/10.1155/2011/401547

**Transforming arithmetic Asian option PDE to the parabolic equation with constant coefficients.** / Elshegmani, Zieneb Ali; Ahmad, Rokiah @ Rozita; Jaaman @ Sharman, Saiful Hafizah; Zakaria, Roza Hazli.

Research output: Contribution to journal › Article

*International Journal of Mathematics and Mathematical Sciences*, vol. 2011, 401547. https://doi.org/10.1155/2011/401547

}

TY - JOUR

T1 - Transforming arithmetic Asian option PDE to the parabolic equation with constant coefficients

AU - Elshegmani, Zieneb Ali

AU - Ahmad, Rokiah @ Rozita

AU - Jaaman @ Sharman, Saiful Hafizah

AU - Zakaria, Roza Hazli

PY - 2011

Y1 - 2011

N2 - Arithmetic Asian options are difficult to price and hedge, since at present, there is no closed-form analytical solution to price them. Transforming the PDE of the arithmetic the Asian option to a heat equation with constant coefficients is found to be difficult or impossible. Also, the numerical solution of the arithmetic Asian option PDE is not very accurate since the Asian option has low volatility level. In this paper, we analyze the value of the arithmetic Asian option with a new approach using means of partial differential equations (PDEs), and we transform the PDE to a parabolic equation with constant coefficients. It has been shown previously that the PDE of the arithmetic Asian option cannot be transformed to a heat equation with constant coefficients. We, however, approach the problem and obtain the analytical solution of the arithmetic Asian option PDE.

AB - Arithmetic Asian options are difficult to price and hedge, since at present, there is no closed-form analytical solution to price them. Transforming the PDE of the arithmetic the Asian option to a heat equation with constant coefficients is found to be difficult or impossible. Also, the numerical solution of the arithmetic Asian option PDE is not very accurate since the Asian option has low volatility level. In this paper, we analyze the value of the arithmetic Asian option with a new approach using means of partial differential equations (PDEs), and we transform the PDE to a parabolic equation with constant coefficients. It has been shown previously that the PDE of the arithmetic Asian option cannot be transformed to a heat equation with constant coefficients. We, however, approach the problem and obtain the analytical solution of the arithmetic Asian option PDE.

UR - http://www.scopus.com/inward/record.url?scp=79959268541&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959268541&partnerID=8YFLogxK

U2 - 10.1155/2011/401547

DO - 10.1155/2011/401547

M3 - Article

AN - SCOPUS:79959268541

VL - 2011

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

M1 - 401547

ER -