Title
Analytic models for parameter dependency in option price modelling
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Basel ,
Subject
Mathematics
Source (journal)
Numerical algorithms. - Basel
Volume/pages
73(2016) :1 , p. 15-31
ISSN
1017-1398
ISI
000382145200002
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Options are a type of financial instrument classed as derivatives, as they derive their value from an underlying asset. The equations used to model the option price are often expressed as partial differential equations (PDEs). Once expressed in this form, a discretization method on a finite grid can be applied and the numerical valuation obtained. Remains the problem of writing down an (approximate) closed-form analytic model for the option price in function of all the variables and parameters, which is the main objective of this paper. At the same time we also consider the Greeks, which are the quantities representing the sensitivities of the price to a change in the underlying variables or parameters. Discrete values for these Greeks can again be derived, either directly from the differentiation matrices occurring in the option price PDE or by solving new but similar PDEs. Next, analytic models for the Greeks are computed in the same way as for the option price. As a prototype case, The Black-Scholes PDE for European call options is considered.
E-info
https://repository.uantwerpen.be/docman/iruaauth/d4cf70/135521.pdf
Full text (open access)
https://repository.uantwerpen.be/docman/irua/4f2944/135521.pdf
E-info
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Handle