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The purpose of this study is to analyse and compile the literature on various option pricing models (OPM) or methodologies. The report highlights the gaps in the existing literature review and builds recommendations for potential scholars interested in the subject area.

In this study, the researchers used a systematic literature review procedure to collect data from Scopus. Bibliometric and structured network analyses were used to examine the bibliometric properties of 864 research documents.

As per the findings of the study, publication in the field has been increasing at a rate of 6% on average. This study also includes a list of the most influential and productive researchers, frequently used keywords and primary publications in this subject area. In particular, Thematic map and Sankey’s diagram for conceptual structure and for intellectual structure co-citation analysis and bibliographic coupling were used.

Based on the conclusion presented in this paper, there are several potential implications for research, practice and society.

This study provides useful insights for future research in the area of OPM in financial derivatives. Researchers can focus on impactful authors, significant work and productive countries and identify potential collaborators. The study also highlights the commonly used OPMs and emerging themes like machine learning and deep neural network models, which can inform practitioners about new developments in the field and guide the development of new models to address existing limitations.

The accurate pricing of financial derivatives has significant implications for society, as it can impact the stability of financial markets and the wider economy. The findings of this study, which identify the most commonly used OPMs and emerging themes, can help improve the accuracy of pricing and risk management in the financial derivatives sector, which can ultimately benefit society as a whole.

It is possibly the initial effort to consolidate the literature on calibration on option price by evaluating and analysing alternative OPM applied by researchers to guide future research in the right direction.

To propose a new investment-income valuation model by real options approach (ROA) for old community renewal (OCR) projects, which could help the government attract private capital's participation.

The new model is proposed by identifying the types of options private capital has in the OCR project, selecting the option model most suitable for private capital investment decisions, improving the valuation model through the triangular fuzzy numbers to take into account the uncertainty and flexibility, and demonstrating the feasibility of the calculation model through an actual OCR project case.

The new model can valuate OCR projects more accurately based on considering uncertainty and flexibility, compared with conventional methods that often underestimate the value of OCR projects.

The investment-income of OCR projects shall be re-valuated from the lens of real options, which could help reveal more real benefits beyond the capital growth of OCR projects, enable the government to attract private capital's investment in OCR, and alleviate government fiscal pressure.

The proposed OCR-oriented investment-income valuation model systematically analyzes the applicability of real option value (ROV) to OCR projects, innovatively integrates the ROV and the net present value (NPV) as expanded net present value (ENPV), and accurately evaluate real benefits in comparison with existing models. Furthermore, the newly proposed model holds the potential to be transferred to various social welfare projects as a tool to attract private capital's participation.

Financial mathematics is one of the most rapidly evolving fields in today’s banking and cooperative industries. In the current study, a new fractional differentiation operator with a nonsingular kernel based on the Robotnov fractional exponential function (RFEF) is considered for the Black–Scholes model, which is the most important model in finance. For simulations, homotopy perturbation and the Laplace transform are used and the obtained solutions are expressed in terms of the generalized Mittag-Leffler function (MLF).

The homotopy perturbation method (HPM) with the help of the Laplace transform is presented here to check the behaviours of the solutions of the Black–Scholes model. HPM is well known for its accuracy and simplicity.

In this attempt, the exact solutions to a famous financial market problem, namely, the BS option pricing model, are obtained using homotopy perturbation and the LT method, where the fractional derivative is taken in a new YAC sense. We obtained solutions for each financial market problem in terms of the generalized Mittag-Leffler function.

The Black–Scholes model is presented using a new kind of operator, the Yang-Abdel-Aty-Cattani (YAC) operator. That is a new concept. The revised model is solved using a well-known semi-analytic technique, the homotopy perturbation method (HPM), with the help of the Laplace transform. Also, the obtained solutions are compared with the exact solutions to prove the effectiveness of the proposed work. The different characteristics of the solutions are investigated for different values of fractional-order derivatives.

The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.

In this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.

We develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.

Owing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.

Studying the shear stress and pressure resulting on the walls of blood vessels, especially during high-pressure cases, which may lead to the explosion or rupture of these vessels, can also lead to the death of many patients. Therefore, it was necessary to try to control the shear and normal stresses on these veins through nanoparticles in the presence of some external forces, such as exposure to some electromagnetic shocks, to reduce the risk of high pressure and stress on those blood vessels. This study aims to examines the shear and normal stresses of electroosmotic-magnetized Sutterby Buongiorno’s nanofluid in a symmetric peristaltic channel with a moderate Reynolds number and curvature. The production of thermal radiation is also considered. Sutterby nanofluids equations of motion, energy equation, nanoparticles concentration, induced magnetic field and electric potential are calculated without approximation using small and long wavelengths with moderate Reynolds numbers.

The Adomian decomposition method solves the nonlinear partial differential equations with related boundary conditions. Graphs and tables show flow features and biophysical factors like shear and normal stresses.

This study found that when curvature and a moderate Reynolds number are present, the non-Newtonian Sutterby fluid raises shear stress across all domains due to velocity decay, resulting in high shear stress. Additionally, modest mobility increases shear stress across all channel domains. The Sutterby parameter causes fluid motion resistance, which results in low energy generation and a decrease in the temperature distribution.

Equations of motion, energy equation, nanoparticle concentration, induced magnetic field and electric potential for Sutterby nano-fluids are obtained without any approximation i.e. the authors take small and long wavelengths and also moderate Reynolds numbers.

The concept of online shopping has been in vogue for the past two decades and is on the rise. Even developing countries like Pakistan are using electronic platforms to buy and sell goods and services, and the trend has been increasing ever since the COVID-19 pandemic. Drawing on the expectancy-disconfirmation theory, this study aims to test the e-service quality (E-SQ) and e-customer satisfaction (ECS) linkage with the mediating roles of functional values (FVs) and hedonic values (HVs).

The data have been collected from 298 customers of AliExpress and Daraz e-commerce platforms and analyzed using covariance-based structural equation modeling (CB-SEM).

The results of the study showed a significant positive relationship between E-SQ and ECS and indirect linkage through FVs and HVs have also been established.

E-commerce platforms, particularly in Pakistan, should place a strong emphasis on FVs by providing accurate product details, user-friendly navigation, transparent pricing and streamlined transactions. Customers' trust and confidence will increase if they have a smooth and effective online purchasing experience. Customer satisfaction may be influenced by regular platform functionality and usability changes.

The use of functional and HVs is considered to be a novel factor in testing the relationship between E-SQ and ECS.