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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.

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.

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.

After completion of the case study, the students will be able to understand the different risks associated with a business, focusing on price risk and the importance of price risk management in business; understand and evaluate the products available for hedging price risk through exchange-traded derivatives in the Indian scenario; and understand and evaluate the different strategies for price risk management through exchange-traded derivatives in the Indian scenario.

The case study pertains to a small business, M/s Sethi Jewellers. The enterprise is being run by Shri Charan Jeet Sethi and his son Tejinder Sethi. The business is located in Jain Bazar, Jammu, UT, in Northern India. The business was started in 1972 by Charan Jeet’s father. They deal in a wide range of jewelry products and are well-established jewelers known for selling quality ornaments. Tejinder (MBA in marketing) was instrumental in revamping his business recently. Under his leadership, the business has experienced rapid transformation. The business has grown from a one-room shop fully managed by Tejinder’s grandfather to a multistory showroom with several artisans, sales staff and security persons. Through his e-store, Tejinder has a bulk order from a client where the client requires him to accept the order with a small token at the current price and deliver the final product three months from now. Tejinder is in a dilemma about accepting or rejecting the large order. Second, if he accepts, should he buy the entire gold now or wait to buy it later at a lower price? He is also considering hedging the price risk through exchange-traded derivatives. However, he is not entirely sure, as he has a few apprehensions regarding the same, and he is also not fully aware of the process and the instruments he has to use for hedging the price risk on the exchange.

The case study is aimed to cater to undergraduate, postgraduate and MBA students in the field of finance. This case study can be used for students interested in commodity derivatives, risk management and market microstructure.

Teaching notes are available for educators only.

CSS 1: Accounting and finance.

In Chapter 1, we critically reviewed the foundations of the free enterprise capital system (FECS), which has been successful primarily because of its wealth and asset accumulation potentiality and actuality. In this chapter, we critically argue that this capacity has been grounded upon the profit maximization (PM) theories, models, and paradigms of FECS. The intent of this chapter is not anti-PM. The PM models of FECS have worked and performed well for more than 200 years of the economic history of the United States and other developed countries, and this phenomenon is celebrated and featured as “market performativity.” However, market performativity has not truly benefitted the poor and the marginalized; on the contrary, market performativity has wittingly or unwittingly created gaping inequalities of wealth, income, opportunity, and prosperity. Critical thinking does not combat PM but challenges it with alternative models of profit sharing that promote social wealth, social welfare, social progress, and opportunity for all, which we explore here. Economic development without social progress breeds economic inequality and social injustice. Economic development alone is not enough; we should create a new paradigm in which economic development is the servant of social progress, not vice versa. Such a paradigm shift involves integrating the creativity and innovativity of market performativity and the goals and drives of social performativity together with PM, that is, from market performativity to social performativity.

The increasing globalization and technological advancements have increased the information spillover on stock markets from various variables. However, there is a dearth of a comprehensive review of how stock market volatility is influenced by macro and firm-level factors. Therefore, this study aims to fill this gap by systematically reviewing the major factors impacting stock market volatility.

This study uses a combination of bibliometric and systematic literature review techniques. A data set of 54 articles published in quality journals from the Australian Business Deans Council (ABDC) list is gathered from the Scopus database. This data set is used to determine the leading contributors and contributions. The content analysis of these articles sheds light on the factors influencing market volatility and the potential research directions in this subject area.

The findings show that researchers in this sector are becoming more interested in studying the association of stock markets with “cryptocurrencies” and “bitcoin” during “COVID-19.” The outcomes of this study indicate that most studies found oil prices, policy uncertainty and investor sentiments have a significant impact on market volatility. However, there were mixed results on the impact of institutional flows and algorithmic trading on stock volatility, and a consensus cannot be established. This study also identifies the gaps and paves the way for future research in this subject area.

This paper fills the gap in the existing literature by comprehensively reviewing the articles on major factors impacting stock market volatility highlighting the theoretical relationship and empirical results.

Using the next-day and next-week returns of stocks in the Korean market, we examine the association of option volume ratios – i.e. the option-to-stock (O/S) ratio, which is the total volume of put options and call options scaled by total underlying equity volume, and the put-call (P/C) ratio, which is the put volume scaled by total put and call volume – with future returns. We find that O/S ratios are positively related to future returns, but P/C ratios have no significant association with returns. We calculate individual, institutional, and foreign investors’ option ratios to determine which ratios are significantly related to future returns and find that, for all investors, higher O/S ratios predict higher future returns. The predictability of P/C depends on the investors: institutional and individual investors’ P/C ratios are not related to returns, but foreign P/C predicts negative next-day returns. For net-buying O/S ratios, institutional net-buying put-to-stock ratios consistently predict negative future returns. Institutions’ buying and selling put ratios also predict returns. In short, institutional put-to-share ratios predict future returns when we use various option ratios, but individual option ratios do not.