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Option pricing theory enables computation of the price of an option using different variables associated with the underlying security and options contract. The purpose of this study is to assess research trends that emerged in the field of option pricing. This study reviews existing literature of the option pricing domain, both qualitatively and quantitatively, and identifies potential themes for future research.

This study adopts bibliometric analysis method to explore literature published in the option pricing domain. As part of bibliometric analysis, this study considers both descriptive and network analysis to assess publication trends. For descriptive analysis, the “bibliometrix” package proposed by Aria and Cuccurullo (2017) is used and for network analysis, VOS viewer (Van Eck and Waltman, 2017) and Gephi (Bastian et al., 2009) are used.

This study identifies research trends, top researchers, articles, journals and contributions from institutions and countries in the option pricing domain. It identifies four clusters that show different directions and also focuses on past studies on the same subject. It explores research gaps by performing an in-depth analysis of existing literature on option pricing and suggests the way forward for research in this area.

To the best of the authors’ knowledge, no previous studies have attempted to analyze the literature published in the option pricing domain. This study fulfils this research gap by conducting a comprehensive analysis of studies in the option pricing area. This study identifies quality research work published in the domain, research trends, contribution by most relevant researchers, contributions across geographies and institutions and the connections among these aspects. This study also identifies important themes and provides directions for future research.

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.

This paper aims to discuss the suitability of topic modeling as a review method, identifies and compares the machine learning (ML) research trends in five primary business organization verticals.

This study presents a review framework of published research about adopting ML techniques in a business organization context. It identifies research trends and issues using topic modeling through the Latent Dirichlet allocation technique in conjunction with other text analysis techniques in five primary business verticals – human resources (HR), marketing, operations, strategy and finance.

The results identify that the ML adoption is maximum in the marketing domain and minimum in the HR domain. The operations domain witnesses the application of ML to the maximum number of distinct research areas. The results also help to identify the potential areas of ML applications in future.

This paper contributes to the existing literature by finding trends of ML applications in the business domain through the review of published research. Although there is a growth of research publications in ML in the business domain, literature review papers are scarce. Therefore, the endeavor of this study is to do a thorough review of the current status of ML applications in business by analyzing research articles published in the past ten years in various journals.

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 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.

Three scenario-based experiments were conducted to explore the influence of the base option’s price format (just-at vs just-below) on tourists’ upgrade intention. The findings of this research indicated that tourists are more inclined to upgrade the option when the base option’s price is presented in a just-at condition due to the mediating role of tourists’ price perceptions of the upgrade option. This study discovered that the just-at (vs just-below) pricing strategy can lower tourists’ price perceptions of the upgrade choice. This research further explored the moderating of tourists’ mindsets. It was found the threshold-crossing effect will disappear for tourists with fixed mindsets. This study also provides practical implications for travel service providers to set up appropriate pricing strategies to attract tourists to make upgrade decisions.

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 understand the profit implications of analytics-driven centralized discriminatory pricing at the headquarter level compared with sales force price delegation in the purchase of an aftermarket good through an indirect retail channel with symmetric information.

Using individual-level loan application and approval data from a North American financial institution and segment-level customer risk as the price discrimination criterion for the firm, the authors develop a three-stage model that accounts for the salesperson’s price decision within the limits of the latitude provided by the firm; the firm’s decision to approve or not approve a sales application; and the customer’s decision to accept or reject a sales offer conditional on the firm’s approval. Next, the authors compare the profitability of this sales force price delegation model to that of a segment-level centralized pricing model where agent incentives and consumer prices are simultaneously optimized using a quasi-Newton nonlinear optimization algorithm (i.e. Broyden–Fletcher–Goldfarb–Shanno algorithm).

The results suggest that implementation of analytics-driven centralized discriminatory pricing and optimal sales force incentives leads to double-digit lifts in firm profits. Moreover, the authors find that the high-risk customer segment is less price-sensitive and firms, upon leveraging this segment’s willingness to pay, not only improve their bottom-line but also allow these marginalized customers with traditionally low approval rates access to loans. This points out the important customer welfare implications of the findings.

Substantively, to the best of the authors’ knowledge, this paper is the first to empirically investigate the profitability of analytics-driven segment-level (i.e. discriminatory) centralized pricing compared with sales force price delegation in indirect retail channels (i.e. where agents are external to the firm and have access to competitor products), taking into account the decisions of the three key stakeholders of the process, namely, the consumer, the salesperson and the firm and simultaneously optimizing sales commission and centralized consumer price.

This study aims to examine the value of the call option contract in hedging the risks in the supply chain. The decentralized supply chain without call option contract is first studied as the criterion model for evaluations. This paper addresses several questions: What will be the optimal manufacturer’s production quantity, retailer’s ordering and pricing policies in the presence of random demand and random yield by applying the downconversion approach? How will the call option contract influence the optimal decisions for the members of the supply chain? Can the risk from randomness be divided among the members in the supply chain through the call option contract?

This paper considers a two-level decentralized supply chain under random yield and random demand in which the manufacturer takes advantage of the downconversion approach with two scenarios, with and without option contract. To the best of the authors’ knowledge, no article or study uses the downconversion approach in a supply chain regarding random yield and random demand. Furthermore, the paper considers pricing with option contract in the supply chain, which makes this article stands out significantly from other articles in the literature.

This study shows that the downconversion approach would reduce the risk caused by the random yield, which appears to be the appropriate method for the environmental goal of the supply chains. Moreover, adopting a call option contract can increase flexibility and mitigate risks, resulting in more expected members’ profits.

To simplify the model, the authors assume one manufacturer and one retailer, so extending the model to consider multiple retailers instead of one retailer and inventory sharing between them would be interesting. Considering the option and exercise prices as decision variables would be important future research topics. Put option and bidirectional option contracts could be investigated in the future. Another extension is modeling asymmetry of information in supply chain.

This paper provides managerial insights on dealing with both demand and yield risks in a manufacturer–retailer supply chain. The manufacturer has a random yield production and produces two types of vertical products: low-end and high-end. To reduce waste caused by the random yield, the manufacturer uses a downconversion approach in which low-end products are made by converting the defective high-end products. The manufacturer purchased a shortage of high-end products from the secondary market (i.e. emergency sourcing). High-end products are sold through the retailer, and low-end products are sold directly by the manufacturer. The customer demand for high-end products in the end market is random and depends on the selling price, and the customer demand for the low-end products in the secondary market is independent and random. The retailer contracts the manufacturer with the call option to obtain high-end products to meet a random demand; in fact, by using the call option contract, the authors try to balance the risks between two members. Two scenarios of with and without call option contract are proposed. After the high-end product demand is observed, the retailer would exercise the option order quantity in the call option contract scenario and then place an instant order with the manufacturer if necessary. In each scenario, the manufacturer and the retailer make their decisions simultaneously (static game) to determine the retailer’s optimal ordering and pricing policies and the optimal production quantity of the manufacturer (Nash equilibrium) by maximizing their expected profits. Finally, the impact of the model parameters on the supply chain is expressed through numerical examples. The numerical analysis shows that the call option contract provides greater profit than the wholesale price contract.