Orthogonal Wavelet Method for Multi-Stage Expansion and Contraction Options Under Stochastic Volatility

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F25%3A00013162" target="_blank" >RIV/46747885:24510/25:00013162 - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S016892742500025X" target="_blank" >https://www.sciencedirect.com/science/article/pii/S016892742500025X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.apnum.2025.02.001" target="_blank" >10.1016/j.apnum.2025.02.001</a>

Result language

angličtina

Original language name

Orthogonal Wavelet Method for Multi-Stage Expansion and Contraction Options Under Stochastic Volatility

Original language description

Multi-stage expansion and contraction options are real options enabling an investment project to be scaled up or down in response to market conditions at predetermined future dates. We examine an investment project focused on producing a specific commodity, with the project value dependent on the market price of this commodity. We then study the value of options to either increase or decrease production at specific future dates based on predetermined factors and costs. Under the assumption that the commodity price follows a geometric Brownian motion and the volatility is stochastic, multiple partial differential equations represent the valuation model for these options. This paper aims to establish two new pricing models for multi-stage expansion and contraction options: one where variance follows a geometric Brownian motion and another governed by the Cox–Ingersoll–Ross process. Another aim is to propose and analyze an efficient wavelet-based numerical method for these models. The method employs the Galerkin method with a recently constructed orthogonal cubic spline wavelet basis and the Crank-Nicolson scheme enhanced by Richardson extrapolation. We establish the existence and uniqueness of the solution, provide error estimates for the proposed method, and derive bounds for condition numbers of the resulting matrices arising from discretization. The method is applied to options related to iron-ore mining investment projects to verify the relevance of the method and show its benefits, which are a high-order convergence rate, well-conditioned discretization matrices, and an efficient solution of the resulting system of equations using a small number of iterations.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/GA22-17028S" target="_blank" >GA22-17028S: Flexible tools for strategic investments and decision-making: analysis, valuation and implementation</a><br>

Continuities

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

Publication year

2025

Confidentiality

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

Name of the periodical

Applied Numerical Mathematics>

ISSN

0168-9274

e-ISSN

—

Volume of the periodical

212

Issue of the periodical within the volume

JUNE 2025

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

21

Pages from-to

155-175

UT code for WoS article

001425699800001

EID of the result in the Scopus database

2-s2.0-85217077095