Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes

Zhenyu Cui; Chihoon Lee; Yanchu Liu

doi:10.1016/j.ejor.2017.10.049

Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes

Zhenyu Cui
, Chihoon Lee
, Yanchu Liu

School of Business

Stevens Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Recently, Cai, Song, and Kou (2015) proposed closed-form double transform approximation formulas for prices of both discretely and continuously monitored Asian options under the setting of a general continuous-time Markov chain. In this note, we analytically invert the Z-transform and the Laplace transform involved in their final results, respectively, for the discretely and the continuously monitored cases, and we obtain explicit single Laplace transforms of option prices. This reduction in the dimension of numerical integral has meaningful consequences both in computational efficiency and in practical implementation of the formulas. Extensive numerical experiments illustrate the improved performance of our results.

Original language	English
Pages (from-to)	1134-1139
Number of pages	6
Journal	European Journal of Operational Research
Volume	266
Issue number	3
DOIs	https://doi.org/10.1016/j.ejor.2017.10.049
State	Published - May 1 2018

ASJC Scopus subject areas

General Computer Science
Modeling and Simulation
Management Science and Operations Research
Information Systems and Management

Keywords

Asian option
Continuous-time Markov chain
Finance
Laplace transform
Markov process

Access to Document

10.1016/j.ejor.2017.10.049

Cite this

@article{a450ad1c43314bc7b5364f7eb66ff2a4,

title = "Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes",

abstract = "Recently, Cai, Song, and Kou (2015) proposed closed-form double transform approximation formulas for prices of both discretely and continuously monitored Asian options under the setting of a general continuous-time Markov chain. In this note, we analytically invert the Z-transform and the Laplace transform involved in their final results, respectively, for the discretely and the continuously monitored cases, and we obtain explicit single Laplace transforms of option prices. This reduction in the dimension of numerical integral has meaningful consequences both in computational efficiency and in practical implementation of the formulas. Extensive numerical experiments illustrate the improved performance of our results.",

keywords = "Asian option, Continuous-time Markov chain, Finance, Laplace transform, Markov process",

author = "Zhenyu Cui and Chihoon Lee and Yanchu Liu",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

month = may,

day = "1",

doi = "10.1016/j.ejor.2017.10.049",

language = "English",

volume = "266",

pages = "1134--1139",

journal = "European Journal of Operational Research",

issn = "0377-2217",

publisher = "Elsevier B.V.",

number = "3",

}

TY - JOUR

T1 - Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes

AU - Cui, Zhenyu

AU - Lee, Chihoon

AU - Liu, Yanchu

PY - 2018/5/1

Y1 - 2018/5/1

N2 - Recently, Cai, Song, and Kou (2015) proposed closed-form double transform approximation formulas for prices of both discretely and continuously monitored Asian options under the setting of a general continuous-time Markov chain. In this note, we analytically invert the Z-transform and the Laplace transform involved in their final results, respectively, for the discretely and the continuously monitored cases, and we obtain explicit single Laplace transforms of option prices. This reduction in the dimension of numerical integral has meaningful consequences both in computational efficiency and in practical implementation of the formulas. Extensive numerical experiments illustrate the improved performance of our results.

AB - Recently, Cai, Song, and Kou (2015) proposed closed-form double transform approximation formulas for prices of both discretely and continuously monitored Asian options under the setting of a general continuous-time Markov chain. In this note, we analytically invert the Z-transform and the Laplace transform involved in their final results, respectively, for the discretely and the continuously monitored cases, and we obtain explicit single Laplace transforms of option prices. This reduction in the dimension of numerical integral has meaningful consequences both in computational efficiency and in practical implementation of the formulas. Extensive numerical experiments illustrate the improved performance of our results.

KW - Asian option

KW - Continuous-time Markov chain

KW - Finance

KW - Laplace transform

KW - Markov process

UR - https://www.scopus.com/pages/publications/85033403137

UR - https://www.scopus.com/pages/publications/85033403137#tab=citedBy

U2 - 10.1016/j.ejor.2017.10.049

DO - 10.1016/j.ejor.2017.10.049

M3 - Article

SN - 0377-2217

VL - 266

SP - 1134

EP - 1139

JO - European Journal of Operational Research

JF - European Journal of Operational Research

IS - 3

ER -

Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes

Abstract

ASJC Scopus subject areas

Keywords

Access to Document

Other files and links

Fingerprint

Cite this