Numerical Valuation of the Investment Project Flexibility Based on the PDE Approach: An Option to Contract

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F22%3A10253000" target="_blank" >RIV/61989100:27510/22:10253000 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/46747885:24510/22:00011007

Výsledek na webu

<a href="https://mme2022.vspj.cz/download/proceedings-4.pdf" target="_blank" >https://mme2022.vspj.cz/download/proceedings-4.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Numerical Valuation of the Investment Project Flexibility Based on the PDE Approach: An Option to Contract

Popis výsledku v původním jazyce

The solution to the optimal investment decision, which captures the value of a flexibility embedded in a project, plays an important role in the decision-making process. In this paper we focus on a real options approach interpreting the flexibility value as the option premium and we extend our previous research to an option to contract operating scale according to market conditions. Following a contingent claim analysis the values of both the project and the embedded flexibility, expressed as functions of time and underlying output price (following a stochastic process), can be identified as solutions of relevant PDE systems of the Black-Scholes type. More precisely, the link between project and flexibility values is realized through a payoff function, which can be enforced with respect to the flexibility type at any time prior to or at expiration date. Due to the presence of the American constraint the real option pricing problem is not solvable analytically in general, and therefore appropriate numerical methods have to be employed. Analogously to pricing of financial options and in line with our results achieved in this field of financial engineering, the discontinuous Galerkin method is applied to solve the relevant governing equations. The capabilities of the numerical scheme resulted are illustrated on a simple contraction decision problem.

Název v anglickém jazyce

Numerical Valuation of the Investment Project Flexibility Based on the PDE Approach: An Option to Contract

Popis výsledku anglicky

The solution to the optimal investment decision, which captures the value of a flexibility embedded in a project, plays an important role in the decision-making process. In this paper we focus on a real options approach interpreting the flexibility value as the option premium and we extend our previous research to an option to contract operating scale according to market conditions. Following a contingent claim analysis the values of both the project and the embedded flexibility, expressed as functions of time and underlying output price (following a stochastic process), can be identified as solutions of relevant PDE systems of the Black-Scholes type. More precisely, the link between project and flexibility values is realized through a payoff function, which can be enforced with respect to the flexibility type at any time prior to or at expiration date. Due to the presence of the American constraint the real option pricing problem is not solvable analytically in general, and therefore appropriate numerical methods have to be employed. Analogously to pricing of financial options and in line with our results achieved in this field of financial engineering, the discontinuous Galerkin method is applied to solve the relevant governing equations. The capabilities of the numerical scheme resulted are illustrated on a simple contraction decision problem.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

50200 - Economics and Business

Projekt

<a href="/cs/project/GA22-17028S" target="_blank" >GA22-17028S: Flexibilní nástroje pro strategické investice a rozhodování: analýza, oceňování a implementace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název statě ve sborníku

40th International Conference Mathematical Methods in Economics 2022 : Proceedings : College of Polytechnics Jihlava : 7 – 9 September 2022, Jihlava, Czech Republic

ISBN

978-80-88064-62-6

ISSN

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e-ISSN

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Počet stran výsledku

7

Strana od-do

122-128

Název nakladatele

College of Polytechnics Jihlava

Místo vydání

Jihlava

Místo konání akce

Coll Polytechn Jihlava

Datum konání akce

7. 9. 2022

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000936355000020