Dimension Reduction for Pricing Options Under Multidimensional Lévy Processes

Research output: Contribution to journalArticle

Abstract

The aim of this study was to develop efficient quasi-Monte Carlo algorithms for pricing European derivative securities under multidimensional Lévy models. In the paper, we first introduce the multidimensional generalized hyperbolic distribution as a normal variance–mean mixture. Using this distribution, we can model a multidimensional generalized Lévy process as a subordinated Brownian motion. Under this process, we develop practically efficient dimension reduction methods that can enhance the numerical efficiency of the quasi-Monte Carlo method. The algorithms extend the generalized linear transformation method that was originally proposed for a univariate Lévy process. We also propose hybrid types of dimension reduction methods in which the dimension reduction techniques are applied separately to the subordinator and the Brownian motion. Through numerical examples we demonstrate that the proposed method realizes a substantial gain in efficiency, relative to the naive Monte Carlo and quasi-Monte Carlo methods in the context of pricing average options.

Original languageEnglish
JournalAsia-Pacific Financial Markets
Volume22
Issue number1
DOIs
Publication statusPublished - 2014

Fingerprint

Dimension reduction
Option pricing
Quasi-Monte Carlo methods
Brownian motion
Pricing
Quasi-Monte Carlo
Relative efficiency
Generalized hyperbolic distribution
Derivative securities

Keywords

  • Dimension reduction method
  • Multidimensional Lévy process
  • Normal variance–mean mixture
  • Quasi-Monte Carlo

ASJC Scopus subject areas

  • Finance

Cite this

Dimension Reduction for Pricing Options Under Multidimensional Lévy Processes. / Imai, Junichi.

In: Asia-Pacific Financial Markets, Vol. 22, No. 1, 2014.

Research output: Contribution to journalArticle

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