TY - JOUR

T1 - Adaptive lattice methods for multi-asset models

AU - Moon, Kyoung Sook

AU - Kim, Won Jung

AU - Kim, Hongjoong

N1 - 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.

PY - 2008/7

Y1 - 2008/7

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=44149113558&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2007.12.008

DO - 10.1016/j.camwa.2007.12.008

M3 - Article

AN - SCOPUS:44149113558

SN - 0898-1221

VL - 56

SP - 352

EP - 366

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 2

ER -