Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/253824 
Year of Publication: 
2021
Citation: 
[Journal:] Journal of Economics, Finance and Administrative Science [ISSN:] 2218-0648 [Volume:] 26 [Issue:] 52 [Publisher:] Emerald Publishing Limited [Place:] Bingley [Year:] 2021 [Pages:] 282-299
Publisher: 
Emerald Publishing Limited, Bingley
Abstract: 
Purpose - The purpose of this article is to propose a detailed methodology to estimate, model and incorporate the non-constant volatility onto a numerical tree scheme, to evaluate a real option, using a quadrinomial multiplicative recombination. Design/methodology/approach - This article uses the multiplicative quadrinomial tree numerical method with non-constant volatility, based on stochastic differential equations of the GARCH-diffusion type to value real options when the volatility is stochastic. Findings - Findings showed that in the proposed method with volatility tends to zero, the multiplicative binomial traditional method is a particular case, and results are comparable between these methodologies, as well as to the exact solution offered by the Black-Scholes model. Originality/value - The originality of this paper lies in try to model the implicit (conditional) market volatility to assess, based on that, a real option using a quadrinomial tree, including into this valuation the stochastic volatility of the underlying asset. The main contribution is the formal derivation of a risk-neutral valuation as well as the market risk premium associated with volatility, verifying this condition via numerical test on simulated and real data, showing that our proposal is consistent with Black and Scholes formula and multiplicative binomial trees method.
Subjects: 
Diffusion processes
GARCH-diffusion
Quadrinomial numerical method
Real options
Stochastic volatility
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article

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