Numerical pricing of American options on extrema with continuous sampling

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F21%3A00009605" target="_blank" >RIV/46747885:24510/21:00009605 - isvavai.cz</a>
Result on the web
<a href="https://www.ekf.vsb.cz/cerei/cs/aktualni-cislo/archiv/rocnik-24/" target="_blank" >https://www.ekf.vsb.cz/cerei/cs/aktualni-cislo/archiv/rocnik-24/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7327/cerei.2021.03.03" target="_blank" >10.7327/cerei.2021.03.03</a>

Result language
angličtina
Original language name
Numerical pricing of American options on extrema with continuous sampling
Original language description
One of the typical option classes is formed by lookback options whose values depend also on the extrema of the underlying asset over a certain period of time. Moreover, incorporating the American constraint, which admits early exercise, has increased the popularity of these hedging and speculation instruments over recent years. In this paper, we consider the problem of pricing continuously observed American-style lookback options with fixed strike. Since no analytic formulae exist for this case, we follow an approach that formulates the corresponding option pricing problem as the parabolic partial differential inequality subject to a constraint, handled by a penalty technique. As a result, we obtain the pricing equation restricted to a triangular domain, where the path-dependent variable appears as a parameter only in the initial and boundary conditions. The contribution of the paper lies in the proposal of a numerical scheme that solves this option pricing problem. The numerical technique proposed arises from the discontinuous Galerkin that enables easy implementation of penalties and weak enforcement of boundary conditions. Finally, the capabilities of the numerical scheme are demonstrated within a simple empirical study on the reference experiments.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical
Ekonomická revue – Central European Review of Economic Issues
ISSN
1212-3951
e-ISSN
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Volume of the periodical
24
Issue of the periodical within the volume
1
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
8
Pages from-to
23–30
UT code for WoS article
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EID of the result in the Scopus database
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