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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.

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.

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 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.

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.

This paper provides a structural model to value startup companies and determine the optimal level of research and development (R&D) spending by these companies.

This paper describes a new variant of float-the-money options, which can act as a financial instrument for financing R&D expenses for a specific time horizon or development stage, allowing the investor to share in the startup's value appreciation over that duration. Another innovation of this paper is that it develops a structural model for evaluating optimal level of R&D spending over a given time horizon. The paper deploys the Gompertz-Cox model for the R&D project outcomes, which facilitates investigation of how increased level of R&D input can enhance the company's value growth.

The author first introduces a time-varying drift term into standard Black-Scholes model to account for the varying growth rates of the startup at different stages, and the author interprets venture capital's investment in the startup as a “float-the-money” option. The author then incorporates the probabilities of startup failures at multiple stages into their financial valuation. The author gets a closed-form pricing formula for the contingent option of value appreciation. Finally, the author utilizes Cox proportional hazards model to analyze the optimal level of R&D input that maximizes the return on investment.

The integrated contingent claims model links the change in the financial valuation of startups with the incremental R&D spending. The Gompertz-Cox contingency model for R&D success rate is used to quantify the optimal level of R&D input. This model assumption may be simplistic, but nevertheless illustrative.

Once supplemented with actual transaction data, the model can serve as a reference benchmark valuation of new project deals and previously invested projects seeking exit.

The integrated structural model can potentially have much wider applications beyond valuation of startup companies. For instance, in valuing a company's risk management, the level of R&D spending in the model can be replaced by the company's budget for risk management. As another promising application, in evaluating a country's economic growth rate in the face of rising climate risks, the level of R&D spending in this paper can be replaced by a country's investment in addressing climate risks.

This paper is the first to develop an integrated valuation model for startups by combining the real-world R&D project contingencies with risk-neutral valuation of the potential payoffs.

This short case could be handed out at the end of class discussion on “J&L Railroad” [UVA-F-1053] in preparation for the following class, or if students are more experienced with hedging and option pricing, the instructor may choose to cover both cases in a single class period. It is the companion case to “J&L Railroad” [UVA-F-1053], and presents more technical issues regarding the hedging problem by requiring students to understand option-pricing principles. The board likes the CFO's hedging recommendations, but it wants a more careful analysis of the bank's prices for its risk-management products: the caps and floors. Besides demanding an understanding of option pricing, this case puts particular emphasis on the calculation and use of implied volatility.

Despite service downgrades' undisputed practical relevance, service downgrades (e.g. customers shifting the price tier downward) have received surprisingly little attention from scholars. Previous studies have focussed on either the public policy issue of tiered pricing or optimal pricing by the service provider. Only a few studies have examined why customers shift across different price tiers and how such activities indicate their future behaviour.

Based on customer data collected from a major telecommunications company, the authors use a logistic regression model to investigate how two service modification levers (i.e. transaction- and relationship-level factors) influence the likelihood of service downgrade. The authors apply a survival model to study how service downgrades affect customer churn.

Transaction-level factors such as service usage (e.g. the frequency and recency of underuse experiences) are positively associated with the likelihood of a downgrade. However, relationship-level factors (e.g. relationship duration and customer status) are negatively associated with the likelihood of downgrades. Customers engaging in downgrades are more likely to churn in the future.

The authors focus on downgrade behaviour, which can be perceived as customers' choice to move down the price tier, which likely ruins the service provider's performance. The authors conceptualise two fundamental driving forces behind a service downgrade: the misfits between the actual usage and the service plan chosen and the deteriorating relationships. The authors' empirical findings on the factors influencing downgrades provide insights for service providers seeking to prevent such behaviour.