Adaptive lattice methods for multi-asset models

Kyoung Sook Moon; Won Jung Kim; Hongjoong Kim

doi:10.1016/j.camwa.2007.12.008

Adaptive lattice methods for multi-asset models

Kyoung Sook Moon, Won Jung Kim, Hongjoong Kim

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

11 Citations (Scopus)

Abstract

Adaptive lattice methods are developed to compute the price of multivariate contingent claims. A simple coordinate representation is used to extend one dimensional lattice methods to multivariate asset models. Two algorithms are proposed, one performing several levels of refinement for a time interval [T - Δ t, T] and the other performing one level of refinement for λ % of a given time domain [0, T], where T is the time to maturity, Δ t is the time step size and λ > 0 is a constant. Numerical experiments are carried out for the European and American barrier-type options with one, two, or three underlying assets. In our numerical experiments, both adaptive algorithms improve efficiency over lattice methods with a uniform time step for the same level of accuracy.

Original language	English
Pages (from-to)	352-366
Number of pages	15
Journal	Computers and Mathematics with Applications
Volume	56
Issue number	2
DOIs	https://doi.org/10.1016/j.camwa.2007.12.008
Publication status	Published - 2008 Jul

Bibliographical note

Funding Information:
This work of H. Kim was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2007-331-C00053). This research of K.-S. Moon was supported by the research fund (R0600842) of Seoul R&BD Program and the Kyungwon University Research Fund in 2007. This research of W.-J. Kim was supported by the research fund (R0600842) of Seoul R&BD Program.

Keywords

Adaptive mesh refinement
Lattice method
Multi-asset option pricing

ASJC Scopus subject areas

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2007.12.008

Cite this

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title = "Adaptive lattice methods for multi-asset models",

abstract = "Adaptive lattice methods are developed to compute the price of multivariate contingent claims. A simple coordinate representation is used to extend one dimensional lattice methods to multivariate asset models. Two algorithms are proposed, one performing several levels of refinement for a time interval [T - Δ t, T] and the other performing one level of refinement for λ % of a given time domain [0, T], where T is the time to maturity, Δ t is the time step size and λ > 0 is a constant. Numerical experiments are carried out for the European and American barrier-type options with one, two, or three underlying assets. In our numerical experiments, both adaptive algorithms improve efficiency over lattice methods with a uniform time step for the same level of accuracy.",

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AU - Kim, Hongjoong

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AB - Adaptive lattice methods are developed to compute the price of multivariate contingent claims. A simple coordinate representation is used to extend one dimensional lattice methods to multivariate asset models. Two algorithms are proposed, one performing several levels of refinement for a time interval [T - Δ t, T] and the other performing one level of refinement for λ % of a given time domain [0, T], where T is the time to maturity, Δ t is the time step size and λ > 0 is a constant. Numerical experiments are carried out for the European and American barrier-type options with one, two, or three underlying assets. In our numerical experiments, both adaptive algorithms improve efficiency over lattice methods with a uniform time step for the same level of accuracy.

KW - Adaptive mesh refinement

KW - Lattice method

KW - Multi-asset option pricing

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Adaptive lattice methods for multi-asset models

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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