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Our result of this paper aims to indicate that the beta pricing formula could be applied in a long-term model setting as well.

In this paper, we show that the capital asset pricing model can be derived from a three-period general equilibrium model.

We show that our extended model yields a Pareto efficient outcome.

The capital asset pricing model (CAPM) model can be used for pricing long-lived assets.

Long-term modelling and sustainability can be modelled in our setting.

Our results were only known for two periods. The extension to 3 periods opens up a large scope of applicational possibilities in asset pricing, behavioural analysis and long-term efficiency.

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.

Investors who can transfer their savings to investments in a well-regulated market benefit not only themselves but also economic development. Hence, it is crucial for fund owners to evaluate their stock market investment decisions. The goal of the study is to understand which model determines the asset returns most efficiently. In this regard, the validity of single and multi-index asset pricing models (capital asset pricing model-CAPM and Fama–French models) has been examined in the Turkish Stock Exchange for 2009–2020, with the quantile regression (QR) approach.

On 18 portfolios comprised of quoted stocks in the Istanbul Stock Exchange 100 (ISE-100/BIST-100), we test the CAPM, the Fama and French three factor model (FF3) and the Fama and French five factor model (FF5). Empirical analyses have been carried out via QR approach regressing the portfolios' average weekly excess returns on risk premium/market factor (Rm-Rf), firm size, book value/market value (B/M), profitability and investments factors. QR estimation has been employed since QR is more effective and provides a better definition of the distribution’s tails.

Our empirical findings have revealed that the average excess weekly returns can be explained more strongly via CAPM. Moreover, Fama and French models are expected to give more reliable result with more data, whereas the market premium would give robust results for the Turkish Capital Market.

Individuals investing in financial assets must find the price model that best fits the market. The return can be approximated in the most appropriate manner using the right variables.

The study differs from other research by comparing the asset pricing models via examining the assets' weekly returns with QR in the Istanbul Stock Exchange 100 (ISE-100).

Given the cryptocurrency market boom in recent years, this study aims to identify the factors influencing cryptocurrency pricing and the major gaps for future research.

A systematic literature review was undertaken. Three databases, Scopus, Web of Science and EBSCOhost, were used for this review. The final analysis comprised 88 articles that met the eligibility criteria.

The influential factors were identified and categorized as supply and demand, technology, economics, market volatility, investors’ attributes and social media. This review provides a comprehensive and consolidated view of cryptocurrency pricing and maps the significant influential factors.

This paper is the first to systematically and comprehensively review the relevant literature on cryptocurrency to identify the factors of pricing fluctuation. This research contributes to cryptocurrency research as well as to consumer behaviors and marketing discipline in broad.

We propose a risk factor for idiosyncratic entropy and explore the relationship between this factor and expected stock returns.

We estimate a cross-sectional model of expected entropy that uses several common risk factors to predict idiosyncratic entropy.

We find a negative relationship between expected idiosyncratic entropy and returns. Specifically, the Carhart alpha of a low expected entropy portfolio exceeds the alpha of a high expected entropy portfolio by −2.37% per month. We also find a negative and significant price of expected idiosyncratic entropy risk using the Fama-MacBeth cross-sectional regressions. Interestingly, expected entropy helps us explain the idiosyncratic volatility puzzle that stocks with high idiosyncratic volatility earn low expected returns.

We propose a risk factor of idiosyncratic entropy and explore the relationship between this factor and expected stock returns. Interestingly, expected entropy helps us explain the idiosyncratic volatility puzzle that stocks with high idiosyncratic volatility earn low expected returns.

A stylized fact in finance literature is the belief in positive relationship between ex ante return and risk. Hence, a rational investor, by utility preference axiom can only consider committing fund in asset which promises commensurate higher return for higher risk. Questions have been asked as to whether this holds true across securities, sectors and markets. Empirical evidence appears less convincing, especially in developing markets. Accordingly, the author investigates the nature of reward for taking risk in the Nigerian Capital Market within the context of individual assets and markets.

The author employed ex post design to collect weekly stock prices of firms listed on the Premium Board of Nigerian Stock Exchange for period 2014–2022 to attempt to answer research questions. Data were analyzed using a unique M Vec TGarch-in-Mean model considered to be robust in handling many assets, and hence portfolio management.

The study found that idea of risk-expected return trade-off is perhaps more general than as depicted by traditional finance literature. The regression revealed that conditional variance and covariance risks reveal minimal or no differences in sign and sizes of coefficients. However, standard errors were also found to be large suggesting somewhat inconclusive evidence of existence of defined incentive structure for taking additional risk in the market.

In terms of choice of methodology and outcomes, this research adds substantial value to body of knowledge. The adapted multivariate model used in this paper is a rare approach especially for management of portfolios in developing markets. Remarkably, the research found empirical evidence that positive risk-expected return trade-off, as known in mainstream literature, is not supported especially using a typical developing country data.

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.

The study aims to test prospect theory (PT) predictions in the cryptocurrency (CC) market. It proposes a new asset pricing model that explores the potential of prospect theory value (PTV) as a significant predictor of CC returns.

The study comprehensively analyses a large sample set of 1,629 CCs, representing more than 95% of the CC market. The study uses a portfolio analysis approach, employing univariate and bivariate sorting techniques with equal-weighted and value-weighted portfolios. The study also employs ordinary least squares (OLS) regression, panel data methods and quantile regression (QR) to estimate the models.

This study demonstrates an average inverse relationship between PTV and CC returns. However, this relationship exhibits asymmetry across different quantiles, indicating that investor reactions vary based on market conditions. Moreover, PTV provides more robust predictions for smaller CCs characterized by high volatility and illiquidity. Notably, the findings highlight the dominant role of the probability weighting (PW) component in PT for predicting CC behaviors, suggesting a preference for lottery-like characteristics among CC investors.

The study is one of the early studies on CC price dynamics from the PT perspective. The study is the first to apply a QR approach to analyze the cross-section of CCs using a PT-based asset pricing model. The results shed light on CC investors' decision-making processes and risk perception, offering valuable insights to regulators, policymakers and market participants. From a practical perspective, a trading strategy centered around the PTV effect can be implemented.

The purpose of this paper is to investigate the effect of equity market misvaluation on manager behavior. Using a sample of 535 French-listed over 2000–2018, the authors analyze whether corporate investment decision is sensitive to equity market overvaluation.

The study adopts market-to-book (M/B) decomposition developed by Rhodes-Kropf and Viswanathan (2004, RKV) that proxies for market misvaluation at the firm and industry levels. The authors conducted a long-term performance analysis via a portfolio sorting procedure and a Carhart (1997) four-factor pricing model. The authors tested the relationship between equity misvaluation, corporate investment decisions and equity issuance. The authors ran several robustness tests.

The empirical results show that equity market misvaluation affects corporate investment positively as the stock price deviates further away from its fundamental. Based on market timing theory, the authors find that corporate investment occurs in periods of high valuation motivated by equity issuance to benefit from the low cost of capital. This effect is more prominent for financially constrained firms. Consistent with the catering channel, the authors find that the misvaluation-investment nexus is more pronounced in firms with short-horizon investors. By examining the stocks’ long-term performance of misvalued firms, via a sorting portfolio procedure, the authors find that undervalued firms outperform and generate higher abnormal returns (Jensen’s alpha) than overvalued firms, suggesting that mispricing-driven investment appear to be short-lived and lead to lower return in the long term.

Corporate decision-makers and governance structures should pay attention to the rationality of the corporate investment decision in the context of equity market misvaluation. Managers who focus on maximizing the stock market value in the short-run at the expense of its long-term performance must give preference to value-creating investment, not driven by an external mechanism such as equity market mispricing. More generally, investors and portfolio managers must take into account the market mispricing process in decision-making. Nonetheless, from the portfolio sorting perspective, decision-makers must act in terms of high governance quality to mitigate suboptimal investment due to stock market mispricing (Jensen, 2005). Finally, equity market overvaluation, leading managers to invest via equity financing in particular, should be a signal to attract investors’ attention to seize the window of opportunity and embark on a short-term portfolio strategy. Such a strategy promises high returns in the short term.

This paper investigates jointly two theoretical channels: equity market timing and catering. The authors propose for the analysis three components of the M/B decomposition to dissociate market misvaluation at the firm and industry level from the fundamental component of market value (growth). This procedure provides a better understanding of the role of firm and industry misvaluation in explaining corporate investments. The authors provide evidence of the equity market misvaluation via a portfolio sorting procedure and a Carhart (1997) four-factor pricing model. The authors examine the effect of misvaluation on both the investment and the financing decisions.

We form portfolios based on return and liquidity and examine the effects of liquidity and other risk factors on asset pricing in the Chinese stock market. Our results show that the past loser-and-illiquid stock portfolios tend to outperform the past winner-and-liquid stock portfolios in the 1–12 months holding period. The excess return is significantly associated with the market-wide liquidity factor even when we control the three Fama-French and momentum factors. Cross-sectionally, the liquidity beta significantly affects the excess return even with control of other risk betas and other traditional liquidity proxies.