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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 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.

This study aims to determine the contributing factors to technical knowledge valuation at the related quadruple levels of commercialisation, including the idea, benchtop technical knowledge, prototype technical knowledge and commercialised technical knowledge, and then classify the factors by the valuation objectives.

The study method is descriptive-causal, and documentation tools of published scientific research articles in authentic local and international journals were used to extract the contributing factors to technical knowledge valuation. Moreover, the Likert spectrum-based questionnaire is used to determine the weight of each determined component. On the other hand, hierarchical analysis is used based on the extracted results from the distributed classification questionnaire among scholars to determine the allocable weight of each component.

The results indicate that at the idea step, the highest ranks among the contributing factors to technical knowledge valuation are for the indicators of innovation rate enhancement, novelty, creation of new products, profitability growth and dependence decline. In the benchtop technical knowledge step, the indicators of profitability growth, product quality enhancement, novelty, production risk drop, innovation rate enhancement, production costs drop, product price competitiveness and independence from rare machinery have the highest impact coefficients on valuation. Moreover, the prioritisation of factors in prototype technical knowledge shows that the indicators of productive risk decline, infrastructure, decrease in product delivery time, productivity growth and profitability growth are the most critical factors in technical knowledge valuation. Finally, profitability growth factors, production cost drop, productive risk drop, creating a new product, product price competitiveness and dependence decline determine the most valuable technical knowledge in the commercialisation phase.

The most salient innovation of the study involves the development levels of technical knowledge in the commercialisation cycle for determining the contributing factors to technical knowledge valuation and using multivariate decision-making methods to classify the so-called factors. The major limitation can be the context of the study because the paper was carried out by Iranian assessors and specialists using the experiences, opinions and approaches of opinion leaders based on the dominant social, cultural and accounting background of a developing country, not a developed one.

This paper is applicable because it elucidates the technical knowledge valuation factors for managers and owners of technological and knowledge-based companies to facilitate value determination and register the technical knowledge of innovative products in financial statements for the logical presentation of available intangible assets in the economic unit. Besides, in the high-tech area, collecting information from the contributing factors to technical knowledge valuation provides an opportunity to support intellectual property rights and facilitate transaction processes. Finally, in legal areas, in cases of breaching intellectual property rights relative to technical knowledge, the determination of technical knowledge value provides a solid basis for estimating the damage rate.