Numerical Valuation of the Investment Project with Expansion Options Based on the PDE Approach

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F21%3A00010949" target="_blank" >RIV/46747885:24510/21:00010949 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27510/21:10252996

Výsledek na webu

<a href="https://mme2021.v2.czu.cz/dl/99363?lang=en" target="_blank" >https://mme2021.v2.czu.cz/dl/99363?lang=en</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Numerical Valuation of the Investment Project with Expansion Options Based on the PDE Approach

Popis výsledku v původním jazyce

Compared to the standard DCF methodology, the real options approach provides a solution to optimal investment decisions that captures the value of flexibilities embedded in a project. In this paper we focus on one specific kind of investment decisions - an option to expand. Assuming values of both the project and the embedded option are determined in terms of time and underlying output price, driven by a relevant stochastic process, one can unify the PDE approach to describe the development of values of the project and options. More precisely, the link is realized through a payoff function enforced at a fixed time. As a result, we obtain a system of relevant governing equations of the Black-Scholes type. Since explicit formulae are known for this type of PDE problem only in specific cases, one must turn to some approximation methods. With reference to the results obtained in valuing financial options, we apply the discontinuous Galerkin method to solve the relevant governing equations. The obtained numerical scheme is applied to a simple illustrative expansion decision problem.

Název v anglickém jazyce

Numerical Valuation of the Investment Project with Expansion Options Based on the PDE Approach

Popis výsledku anglicky

Compared to the standard DCF methodology, the real options approach provides a solution to optimal investment decisions that captures the value of flexibilities embedded in a project. In this paper we focus on one specific kind of investment decisions - an option to expand. Assuming values of both the project and the embedded option are determined in terms of time and underlying output price, driven by a relevant stochastic process, one can unify the PDE approach to describe the development of values of the project and options. More precisely, the link is realized through a payoff function enforced at a fixed time. As a result, we obtain a system of relevant governing equations of the Black-Scholes type. Since explicit formulae are known for this type of PDE problem only in specific cases, one must turn to some approximation methods. With reference to the results obtained in valuing financial options, we apply the discontinuous Galerkin method to solve the relevant governing equations. The obtained numerical scheme is applied to a simple illustrative expansion decision problem.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

39th International Conference on Mathematical Methods in Economics

ISBN

978-80-213-3126-6

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

185-190

Název nakladatele

Czech University of Life Sciences Prague

Místo vydání

Praha

Místo konání akce

Praha

Datum konání akce

1. 1. 2021

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000936369700030