Adaptive wavelet based scheme for option pricing

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dc.contributor.authorFiněk, Václav
dc.date.accessioned2019-11-13T07:38:45Z
dc.date.available2019-11-13T07:38:45Z
dc.date.issued2018
dc.description.abstractThis contribution deals with the numerical solution of the Black-Scholes equation. The Crank-Nicolson scheme is applied for time discretization and wavelets are applied for space discretization. Hermite cubic spline wavelets with four vanishing moments are adaptively used because they enable higher order approximations, are well-conditioned, have short supports, have a high potential in adaptive methods due to the four vanishing wavelet moments and mainly because arising stiffness matrices are sparse in wavelet coordinates. Due to irregularities of the initial data in the Black-Scholes model, the use of the second-order Crank-Nicolson scheme usually requires a certain amount of damping to compensate for the known weak stability of this scheme. We numerically show here that optimal convergence rate for a proposed adaptive wavelet discretization in space can be obtained without any damping and without any restriction on the time step. A numerical example is given for the Black-Scholes equation with real data from the Frankfurt Stock Exchange. We also compare numerical results for adaptive and non-adaptive wavelet discretization in space.cs
dc.format.extent5 strancs
dc.identifier.doi10.1109/MCSI.2018.00034
dc.identifier.urihttps://dspace.tul.cz/handle/15240/154236
dc.identifier.urihttps://ieeexplore.ieee.org/abstract/document/8769814
dc.language.isocscs
dc.publisherIEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA
dc.relation.ispartof2018 5TH INTERNATIONAL CONFERENCE ON MATHEMATICS AND COMPUTERS IN SCIENCES AND INDUSTRY (MCSI 2018)
dc.subjectoptionscs
dc.subjectthe Black-Scholes equationcs
dc.subjectthe Crank-Nicolson schemecs
dc.subjectHermite cubic spline waveletscs
dc.subjectadaptivitycs
dc.titleAdaptive wavelet based scheme for option pricingcs
dc.typeProceedings Paper
local.citation.epage113
local.citation.spage109
local.event.edate2018-08-27
local.event.locationCorfu, GREECE
local.event.sdate2018-08-24
local.event.title5th International Conference on Mathematics and Computers in Sciences and Industry (MCSI)
local.identifier.publikace7363
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