# Solving an Asian option PDE via the Laplace transform

Zieneb Ali Elshegmani, Rokiah @ Rozita Ahmad

Research output: Contribution to journalArticle

4 Citations (Scopus)

### Abstract

Solving the Black-Scholes PDE of the arithmetic Asian options is one of the most difficult problems in financial mathematics. A variety of ways ways have been proposed to address the problem. In this study, we use the PDE approach by presenting an efficient method for pricing a continuous arithmetic Asian option. Using the Laplace transform we reduce the three-dimension partial differential equation of the arithmetic Asian option into a two-dimension ordinary differential equation. Its final analytical solution is presented. We conclude that this method is applicable to all types of arithmetic Asian options.

Original language English 67-69 3 ScienceAsia 39 SUPPL.1 https://doi.org/10.2306/scienceasia1513-1874.2013.39S.067 Published - Jul 2013

### Fingerprint

Asian Options
Laplace transform
Financial Mathematics
Black-Scholes
Pricing
Three-dimension
Two Dimensions
Analytical Solution
Ordinary differential equation
Partial differential equation

### Keywords

• Arithmetic Asian option
• Partial differential equations

• General

### Cite this

Solving an Asian option PDE via the Laplace transform. / Elshegmani, Zieneb Ali; Ahmad, Rokiah @ Rozita.

In: ScienceAsia, Vol. 39, No. SUPPL.1, 07.2013, p. 67-69.

Research output: Contribution to journalArticle

Elshegmani, Zieneb Ali ; Ahmad, Rokiah @ Rozita. / Solving an Asian option PDE via the Laplace transform. In: ScienceAsia. 2013 ; Vol. 39, No. SUPPL.1. pp. 67-69.
@article{c914a3169eef460481404ca428105c12,
title = "Solving an Asian option PDE via the Laplace transform",
abstract = "Solving the Black-Scholes PDE of the arithmetic Asian options is one of the most difficult problems in financial mathematics. A variety of ways ways have been proposed to address the problem. In this study, we use the PDE approach by presenting an efficient method for pricing a continuous arithmetic Asian option. Using the Laplace transform we reduce the three-dimension partial differential equation of the arithmetic Asian option into a two-dimension ordinary differential equation. Its final analytical solution is presented. We conclude that this method is applicable to all types of arithmetic Asian options.",
keywords = "Arithmetic Asian option, Partial differential equations",
author = "Elshegmani, {Zieneb Ali} and Ahmad, {Rokiah @ Rozita}",
year = "2013",
month = "7",
doi = "10.2306/scienceasia1513-1874.2013.39S.067",
language = "English",
volume = "39",
pages = "67--69",
journal = "ScienceAsia",
issn = "1513-1874",
publisher = "Science Society of Thailand under Royal Patronage",
number = "SUPPL.1",

}

TY - JOUR

T1 - Solving an Asian option PDE via the Laplace transform

AU - Elshegmani, Zieneb Ali

AU - Ahmad, Rokiah @ Rozita

PY - 2013/7

Y1 - 2013/7

N2 - Solving the Black-Scholes PDE of the arithmetic Asian options is one of the most difficult problems in financial mathematics. A variety of ways ways have been proposed to address the problem. In this study, we use the PDE approach by presenting an efficient method for pricing a continuous arithmetic Asian option. Using the Laplace transform we reduce the three-dimension partial differential equation of the arithmetic Asian option into a two-dimension ordinary differential equation. Its final analytical solution is presented. We conclude that this method is applicable to all types of arithmetic Asian options.

AB - Solving the Black-Scholes PDE of the arithmetic Asian options is one of the most difficult problems in financial mathematics. A variety of ways ways have been proposed to address the problem. In this study, we use the PDE approach by presenting an efficient method for pricing a continuous arithmetic Asian option. Using the Laplace transform we reduce the three-dimension partial differential equation of the arithmetic Asian option into a two-dimension ordinary differential equation. Its final analytical solution is presented. We conclude that this method is applicable to all types of arithmetic Asian options.

KW - Arithmetic Asian option

KW - Partial differential equations

UR - http://www.scopus.com/inward/record.url?scp=84888623918&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888623918&partnerID=8YFLogxK

U2 - 10.2306/scienceasia1513-1874.2013.39S.067

DO - 10.2306/scienceasia1513-1874.2013.39S.067

M3 - Article

AN - SCOPUS:84888623918

VL - 39

SP - 67

EP - 69

JO - ScienceAsia

JF - ScienceAsia

SN - 1513-1874

IS - SUPPL.1

ER -