Valuation of Two-Stage Contraction Options with the American Exercise Right: A Discontinuous Galerkin Approach

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F25%3A00014629" target="_blank" >RIV/46747885:24510/25:00014629 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Valuation of Two-Stage Contraction Options with the American Exercise Right: A Discontinuous Galerkin Approach

Popis výsledku v původním jazyce

Determining the true profitability of investment opportunities is essential in decision-making. This is particularly typical for sequential investments that follow a specific order. This study focuses on a specific type of sequential investment, known as a compound option to contract. When applying the real options approach, the values of investments projects are governed by a relevant partial differential equation of two variables: time and output commodity price, which follows a relevant stochastic process. As the investment project’s flexibility is similar to an American-style put on put option, traditional valuation techniques of conventional financial options can be easily applied. In order to improve the numerical evaluation procedure, we employ a semi-implicit time stepping scheme together with a discontinuous Galerkin approach for spatial discretization, incorporating a penalty technique to handle the early exercise constraint. We follow a backward induction, beginning with the finished project, calculating the values of the option to contract in the second stage and in the first stage (subsequently) to find a present value of the compound option. Finally, the proposed numerical scheme is applied to a simple conceptual decision-making problem.

Název v anglickém jazyce

Valuation of Two-Stage Contraction Options with the American Exercise Right: A Discontinuous Galerkin Approach

Popis výsledku anglicky

Determining the true profitability of investment opportunities is essential in decision-making. This is particularly typical for sequential investments that follow a specific order. This study focuses on a specific type of sequential investment, known as a compound option to contract. When applying the real options approach, the values of investments projects are governed by a relevant partial differential equation of two variables: time and output commodity price, which follows a relevant stochastic process. As the investment project’s flexibility is similar to an American-style put on put option, traditional valuation techniques of conventional financial options can be easily applied. In order to improve the numerical evaluation procedure, we employ a semi-implicit time stepping scheme together with a discontinuous Galerkin approach for spatial discretization, incorporating a penalty technique to handle the early exercise constraint. We follow a backward induction, beginning with the finished project, calculating the values of the option to contract in the second stage and in the first stage (subsequently) to find a present value of the compound option. Finally, the proposed numerical scheme is applied to a simple conceptual decision-making problem.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10102 - Applied mathematics

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

2025

Kód důvěrnosti údajů

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