Option pricing and the Greeks under Gaussian fuzzy environments

Chen, Hongming; Hu, Cheng-Feng; Yeh, Wei-Chang

doi:10.1007/s00500-019-03876-w

Cited by 11 publications

(6 citation statements)

References 28 publications

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“…In most cases, the assumed form of the fuzzy magnitude is linear, i.e., triangular or trapezoidal. However, within type-1 fuzzy numbers, the literature has also used other shapes, such as adaptive fuzzy numbers [36,56,57], Gaussian fuzzy numbers [35], or parabolic fuzzy numbers [94]. The parameters that are considered crisp and those that are considered fuzzy are established ad hoc depending on the problem being addressed.…”

Section: Classificationmentioning

confidence: 99%

“…However, other types of options, such as American [47,71,72,94], binary [47,49,55,89], exchange [26,27,29,61], or compound [60,91,98] options, have been analysed. Sensitivity analysis of option prices from the perspective of the BSM model has been the subject of attention by various authors [35,36,41,46,69]. Likewise, while fuzzy Malliavin calculus has been applied in [43,80], [25] shows that the use of Greeks can be useful in the linear approximation of the membership functions of fuzzy option prices.…”

Section: Classificationmentioning

confidence: 99%

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Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure

Andrés-Sánchez¹

2023

Preprint

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This paper has a twofold objective. The first aim is to present a comprehensive bibliographical analysis of journal articles and book chapters on fuzzy-random option pricing (FROP) over the WoS and SCOPUS databases. It follows PRISMA criteria and takes special care of developments in continuous time. Thus, we described the principal findings about the research streams, outlets and authors of this topic and lets us suggest further research. The second contribution is motivated by the fact that the bibliographical revision has identified a lack of developments on equilibrium models on the yield curve. This question motivates extending Vasicek’s yield curve equilibrium model to introduce fuzziness in the parameters that govern interest rate movements (speed of reversion, equilibrium short-term interest rate, and volatility). Likewise, this paper develops an empirical application on the term structure of fixed income public bonds with the highest credit rating in the Euro area.

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Section: Classificationmentioning

confidence: 99%

Section: Classificationmentioning

confidence: 99%

Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure

Andrés-Sánchez¹

2023

Preprint

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“…In most cases, the assumed form of the fuzzy magnitude is linear, i.e., triangular or trapezoidal. However, within type-1 fuzzy numbers, the literature has also used other shapes, such as adaptive fuzzy numbers [14,39,40], Gaussian fuzzy numbers [28], or parabolic fuzzy numbers [17]. The parameters that are considered crisp and those that are considered fuzzy are estab-lished ad hoc depending on the problem being addressed.…”

Section: Classificationmentioning

confidence: 99%

Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure

Andrés-Sánchez

2023

Mathematics

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Fuzzy random option pricing in continuous time (FROPCT) has emerged as an active research field over the past two decades; thus, there is a need for a comprehensive review that provides a broad perspective on the literature and identifies research gaps. In this regard, we conducted a structure review of the literature by using the WoS and SCOPUS databases while following the PRISMA criteria. With this review, we outline the primary research streams, publication outlets, and notable authors in this domain. Furthermore, the literature review revealed a lack of advancements for the equilibrium models of the yield curve. This finding serves as a primary motivation for the second contribution of this paper, which involves an extension of Vasicek’s yield curve equilibrium model. Specifically, we introduce the existence of fuzzy uncertainty in the parameters governing interest rate movements, including the speed of reversion, equilibrium short-term interest rate, and volatility. By incorporating fuzzy uncertainty, we enhance the model’s ability to capture the complexities of real-world interest rate dynamics. Moreover, this paper presents an empirical application of the proposed extension to the term structure of fixed-income public bonds in European Union. The empirical analysis suggests the suitability of the proposed extension of Vasicek’s model for practical applications.

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“…The authors' experimental results show that the proposed model overcomes other time series models and can handle large amounts of data. Chen et al (2019) dealt with the pricing of a European call option and studying Greek letters of options in a fuzzy environment. The authors deal with the development of a fuzzy pattern of European call option provided that the stock return is a Gaussian fuzzy number.…”

Section: Literature Reviewmentioning

confidence: 99%

Investment Decision Support Based on Interval Type-2 Fuzzy Expert System

Janková

Jana

Dostál

2021

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The decision-making process on investing in financial markets is a very complex and difficult task, mainly due to the chaotic behavior and high uncertainty in the development of the prices of investment instruments. For this reason, financial markets are increasingly using means of artificial intelligence, namely fuzzy logic, which is able to capture the nonlinear behavior.Fuzzy logic provides a way to draw definitive conclusions from vague, ambiguous, or inaccurate information.However, there are some drawbacks associated with type-1 fuzzy logic, so the type-2 fuzzy logic comes forward, which can work with greater uncertainty. Type-2 fuzzy logic works with a new third dimension fuzzy set that provides additional degrees of freedom and allows to model and process numerical and linguistic uncertainties directly. The paper applies type-2 fuzzy logic to the stock market with the aim to create a simple and understandable model for deciding on investing in investment instruments, which is important for investors in this area. The proposed type-2 fuzzy model uses return, risk, dividend and total expense ratio of ETF as input variables. The created system is able to generate aggregated models from a certain number of language rules, which allows the investor to understand the created financial model. Using type-2 fuzzy logic can lead to more realistic and accurate results than type-1 fuzzy logic.

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Option pricing and the Greeks under Gaussian fuzzy environments

Cited by 11 publications

References 28 publications

Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure

Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure

Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure

Investment Decision Support Based on Interval Type-2 Fuzzy Expert System

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