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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.

The empirical studies of the options market efficiency have reported contradictory results, which sometimes confuse practitioners and academicians. The aim of this study was to clarify several aspects of options market efficiency by exploring the answers to two main questions: Under what conditions is the options market more efficient? Are the discrepancies in the estimated efficiency due to the reality of efficiency or mismeasurement?

Using a meta-analysis approach, 54 studies have been analyzed, which included 1,315 tests. The sum of the observations for all of the tests is 3.7 m observation sets. The effect size (type r) has been used to compare the different statistics in different studies. The cumulative effect size and its diversification have been calculated by the random effects model and Q statistic, respectively.

The most interesting finding of the study was that the options market, in all circumstances, is significantly inefficient. Another important finding was that the heterogeneity of options market efficiency is due to the complexity of pricing relations, test time, violation index and price type. To overcome this heterogeneity and accuracy, future studies should test the no-arbitrage options pricing relations at different times and by different price types, using complex and simple pricing relations and either mean violation or violation ratio efficiency measures.

Public disagreement about the options market efficiency in past studies means that this variable is heterogeneous in different conditions. As a significant contribution, this study develops the literature by proposing the causes of options market efficiency heterogeneity.

We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis demonstrates that, under these conditions, the perpetual put option consistently commands a higher price during periods of high volatility compared to those of low volatility. Moreover, we establish that the optimal exercise boundary is lower in high-volatility regimes than in low-volatility regimes. Additionally, we develop an analytical framework to describe American puts with an Erlang-distributed random-time horizon, which allows us to propose a numerical technique for approximating the value of American puts with finite expiry. We also show that a combined approach involving randomization and Richardson extrapolation can be a robust numerical algorithm for estimating American put prices with finite expiry.

The Public–Private Partnership (PPP) modality plays an important role in the procurement of global infrastructure projects. Regarding PPP's complex transaction structure, pricing of a PPP project is critical to both parties where the government pursues a high value for money (VFM) and the investor strives to maximize its financial gains. Despite the straightforward win–win principle, a formidable compromise is often the case to end up with a fairly acceptable price, subject to many determinants such as the risk profile, expected return, technological innovation and capacities of both parties. Among them, this study chooses to examine the “managing flexibility” (MF) capacity of investors in pricing of a PPP project, in light of the widely recognized importance of a real-option perspective toward the long term, complex and uncertain PPP arrangement. This study addresses two major questions: (1) how is MF in PPP projects to be valued and (2) how are PPP projects to be priced when considering a project's MF value.

A binomial tree model is used to evaluate the MF value in PPP projects. Based on the developed MF pricing model, net present value (NPV) and adjusted VFM value are then calculated. Finally, a multi-objective decision-making method (MODM) was adopted to determine the optimal level of returns based on invested capital (ROIC), return on operation maintenance (ROOM) and concession period.

The applicability and functionality of the proposed model is investigated using a real project case. For a given return, extended NPV and adjusted VFM value were calculated and analyzed using sensitivity analysis. Factor influence is shown by the model to be dependent on factor impact on cash flow. Subsequently, a multi-objective decision-making (MODM) model was adopted to determine the optimal level of returns, where the solution approximates the real-world bidding price. Results confirm that the pricing model provides a reliable and practical PPP proposal pricing tool.

This study proposes an integrated framework for valuing MF in PPP projects and thus more accurately determine optimal pricing of PPP projects than revealed in extant research. The model offers a practical tool to aid in the valuation of PPP projects.

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.

International Accounting Standards Rule 37 (IAS 37) for Contingent Liabilities and Assets were designed to make analysis of exposures facing a corporate entity easier to understand, but the rules may be insufficiently prescriptive making provisions inadequate predictors of potential outlays. The purpose of this research is to redress this problem. We apply financial option theory to objectively mark-to-market the appropriateness of provisions replacing subjective inputs with market derived calculations.

This study applies financial option theory to determine whether provisions are appropriate according to market data. This research supports inferences regarding the probability of a provision being used while evidencing scope for earnings management.

In addition to showing how IAS 37 provisions may be calibrated against market data, from the large sample of UK-listed companies, the proposition that over-provisioning is common and related to share price volatility, is supported, supporting the view that IAS 37 rules may facilitate earnings management.

The financial and reporting community have struggled in interpreting the appropriateness of IAS 37 provisions. Are they too large or too small? What is the probability they will be used? Using option theory and market data, various subjective judgements may now be validated. This research should have tangible value to analysts, auditors, investors and other stakeholders concerned in the accurate valuation of potential liabilities.

Replacing subjective judgement and insufficiently prescriptive guidance, this study shows that financial option theory and share price data may be used to objectively calibrate the size of IAS 37 provisions.

This paper contributes to the literature as follows. First, it examines if option and stock compensations raise creditor's risk, and which one is more important than the other. Second, it explores if CEO's compensation interacts with CEO overconfidence to raise creditor's risk. Third, it investigates how banks use different loan terms to alleviate their credit risk.

This study used advanced regression analysis and use of generalized methods of moment methodology.

The results show that option compensation is more important than stock compensation in raising credit risk; option compensation interacts with CEO overconfidence, giving rise to a much higher credit risk; and covenant usage is more important than other loan contract terms in mitigating credit risk given that covenant use could not be substituted away by using other loan contract terms such as increasing interest rate, reducing principal or shortening loan duration. This paper has practical implications for credit markets.

The main implication is that hand-collect data are available up to 2010.

It informs creditors the potential sources of loan risk emanating from option rather than stock incentives; it informs creditors that option incentive interacts with CEO overconfidence rendering the credit risk bigger than expected, and it informs creditors the importance of using covenants vis-à-vis other loan contract terms for mitigating compensation and overconfidence risk.

Banks are alerted to the risk due to the interaction between overconfidence and compensations, implying that overconfident managers remunerated with options compensations are more risky than overconfident managers who are not remunerated as such.

This paper is original: (1) The authors show that option compensation is more risky than stock compensation from viewpoint of creditors. This has not been assessed. (2) Interaction between managerial compensation and managerial overconfidence has not been assessed before. (3) Use of different loan contract terms to alleviate risk from overconfident managers (who are prone to over investment but who are innovative according to the literature) has not been evaluated.

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.

Under the trend of global economic integration and the new context of stagflation, frequent fluctuations in international interest rates are exerting far-reaching impacts on the world economy. In this paper, the transmission mechanism of the impact of fluctuations in international interest rates (specifically, the American interest rate) on the bankruptcy risk in China's pillar industry, the construction industry (which is also sensitive to interest rates), is examined.

Using an improved contingent claims analysis, the bankruptcy risk of enterprises is calculated in this paper. Additionally, an individual fixed-effects model is developed to investigate the mediating effects of international interest rates on the bankruptcy risk in the Chinese construction industry. The heterogeneity of subindustries in the industrial chain and the impact of China's energy consumption structure are also analysed in this paper.

The findings show that fluctuations in international interest rates, which affect the bankruptcy risk of China's construction industry, are mainly transmitted through two major pathways, namely, commodity price effects and exchange rate effects. In addition, the authors examine the important impact of China's energy consumption structure on risk transmission and assess the transmission and sharing of risks within the industrial chain.

First, in the research field, the study of international interest rate risk is extended to domestic-oriented industries. Second, in terms of the research content, this paper is focused on China-specific issues, including the significant influence of China's energy consumption structure characteristics and the risk contagion (and risk sharing) as determined by the current development of the Chinese construction industry. Third, in terms of research methods a modified contingent claim analysis approach to bankruptcy risk indicators is adopted for this study, thus overcoming the problems of data frequency, market sentiment and financial data fraud, which are issues that are ignored by most relevant studies.

This study aims to investigate the connectivity among four principal implied volatility (“fear”) markets in the USA.

The empirical analysis relies on daily data (“fear gauge indices”) for the period 2017–2023 and the quantile vector autoregressive (QVAR) approach that allows connectivity (that is, the network topology of interrelated markets) to be quantile-dependent and time-varying.

Extreme increases in fear are transmitted with higher intensity relative to extreme decreases in it. The implied volatility markets for gold and for stocks are the main risk connectors in the network and also net transmitters of shocks to the implied volatility markets for crude oil and for the euro-dollar exchange rate. Major events such as the COVID-19 pandemic and the war in Ukraine increase connectivity; this increase, however, is likely to be more pronounced at the median than the extremes of the joint distribution of the four fear indices.

This is the first work that uses the QVAR approach to implied volatility markets. The empirical results provide useful insights into how fear spreads across stock and commodities markets, something that is important for risk management, option pricing and forecasting.