An efficient convergent lattice algorithm for european asian options
Resource
Applied Mathematics and Computation 169,1458-1471
Journal
Applied Mathematics and Computation
Journal Volume
169
Journal Issue
2
Pages
1458-1471
Date Issued
2005
Date
2005
Author(s)
DOI
20060927122848148993
URI
Abstract
Financial options whose payo ?depends critically on historical prices are called path-
dependent options.Their prices are usually harder to calculate than options whose prices
do not depend on past histories.Asian options are popular path-dependent derivatives,
and it has been a long-standing problem to price them e ?ciently and accurately.No
known exact pricing formulas are available to price them under the continuous-time
Black –Scholes model.Although approximate pricing formulas exist,they lack accuracy
guarantees.Asian options can be priced numerically on the lattice.A lattice divides the
time to maturity into n equal-length time steps.The option price computed by the lattice
converges to the option value under the Black –Scholes model as n
!1
.Unfortunately,
only subexponential-time algorithms are available if Asian options are to be priced on the lattice without approximations.E ?cient approximation algorithms are available for the
lattice.The fastest lattice algorithm published in the literature runs in O(n
3.5
)-time,
whereas for the related PDE method,the fastest one runs in O(n
3
)time.This paper pre-
sents a new lattice algorithm that runs in O(n
2.5
)time,the best in the literature for such
methods.Our algorithm exploits the method of Lagrange multipliers to minimize the
approximation error.Numerical results verify its accuracy and the excellent performance.
Subjects
Option pricing
Lattice
Path-dependent derivative
Asian option
Approximation alg-
orithm
orithm
Lagrange multiplier
Other Subjects
Approximation theory; Computational methods; Crystal lattices; Finance; Lagrange multipliers; Mathematical models; Approximation algorithms; Asian option; Lattice; Option pricing; Path-dependent derivatives; Algorithms
Type
journal article
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