<abstract><title style='display:none'>Abstract</title>This paper reviews the binomial and trinomial option pricing models and their convergence to the Black-Scholes model result. These models are generalized for the European and American options. The trinomial models are said to be more accurate than the binomial when fewer steps are modelled. These models are widely used for the usual vanilla option types, European or American options, that respectively can be exercised only at the expiration date and at any time before the expiration date. The results are supportive of the conventional wisdom that trinomial option pricing models such as the Kamrad-Ritchken model and the Boyle model are converging faster than the binomial models. When binomial models are compared in terms of convergence, the most efficient model is the Jarrow-Rudd model. This paper concludes that improved binomial models such as the Haahtela model are converging faster to the BS model result. After some trials, binomial distribution follows log-normal distribution assumed by the Black-Scholes model.</abstract>

A Review of the Binomial and Trinomial Models for Option Pricing and their Convergence to the Black-Scholes Model Determined Option Prices

<abstract><title style='display:none'>Abstract</title>In videogames industry, time series analysis can be very useful in determining the general evolution and behaviour of the market dynamics. These methods are applicable to any time series forecasting problem, regardless of the application sector. This article discusses time series approaches to forecast the sales of console games for the Italian market. In particular two univariate techniques were evaluated, exponential smoothing and the SARIMA technique. The aim is to exploit the capabilities of these statistical methods in order to have a comparison of the results and to choose the most accurate model through an ex-post evaluation. Using monthly time-series data from November 2005 to September 2017, the selection of the most suitable model was indicated by the smallest value of the measures of accuracy (MAPE, sMAPE, RMSE) for the out-of-sample observations regarding the period October 2017-September 2018. The implementation of the models was done using Forecast PRO and Gretl. The time series involved is related to the sales regarding the first party manufacturers of consoles and handhelds (Microsoft, Sony and Nintendo).</abstract>

Forecasting the Sales of Console Games for the Italian Market

<abstract>
<title style='display:none'>Abstract</title>
The information society is a product of the intersection of socio-historical-technological contexts, where the development of science and industry has a global reach. The pervasiveness of new information and communication technologies makes it an essential component of a new civilization, affecting every country in varying degrees. Although this techniques approach is grounded in some truth, it neglects other vital aspects that challenge the idea of an information society that prioritizes human needs. The leading nations have achieved this through active research and development, driven by government involvement and the significant contributions of universities. Furthermore, the collaboration of diverse economic, institutional, social, and civic actors has played an essential role in its advancement. However, constructing and promoting an information society transcends infrastructure. It involves political actions that consider the socio-technological nature of this development and its impact on society and other sectors of activity. The objective of this article is twofold. On the one hand, the study analysed the situation of Algeria and its position in relation to other countries regarding the information society, and the other examined the factors that influence the development of the information society in Algeria, trying to identify the most important ones. Finally, the authors proposed a development strategy in this area. The research thesis was formulated as follows: What are the key variables that have an impact on the development of digitalization and the information society in Algeria? Thus, the regulatory frameworks of the most advanced countries are central to the initiatives aimed at its development. To foster the emergence of an information society in Algeria, solidarity must be strengthened, diversity promoted, and the potential of all citizens catalysed.
</abstract>

Digitalization and the Information Society in Algeria: Digital Transformation Actors and Key Variables

<abstract><title style='display:none'>Abstract</title> The purpose of the publication is to indicate the need for a well thought-out combination of quantitative marketing research with qualitative research. The result of this research approach should be a fuller understanding of the research problem and the ability to interpret results more closely, while maintaining the reliability of the whole research process. In the theoretical part of the article, the essence of quantitative and qualitative research, with particular emphasis on the limitations and strengths of both research approaches, is presented. The increasing popularity of qualitative research does not absolve researchers from the prudent attitude towards the whole marketing research process − including the need to verify hypotheses or research questions. Excessive simplification in the approach to qualitative research can distort the essence of marketing research. In the empirical part of the article, the authors presented an example of combining quantitative marketing research with qualitative research − for this purpose, the results of their research will be used (scientific grant from National Science Centre). The CAPI technique (n = 1103) was used in the quantitative study, and observation diaries (n = 110) were used for qualitative research.</abstract>

Synergy of Quantitative and Qualitative Marketing Research − Capi and Observation Diary

<abstract><title style='display:none'>Abstract</title>The traditional methods of risk quantification include a sensitivity analysis, a scenario analysis and a historical simulation. The true nature of risk factors changes is ignored in the traditional ‘ceteris paribus’ approach to a sensitivity analysis, hence it can be reflected in a scenario analysis and a historical simulation. The most significant disadvantage of a scenario analysis is the limited number of scenarios, whereas a historical simulation depends on historical data availability and adequacy. The Monte Carlo simulation is a clear answer to the limitations of traditional methods. The changes of risk factors reflected in the Monte Carlo simulation are simultaneous, non-linear and interdependent. The most important aspect of this method is the stage of taking up the assumptions. The purpose of the paper is to indicate that considering several reasonable sets of assumptions for the Monte Carlo simulation simultaneously can bring even more comprehensive information about enterprise risk.</abstract>

Several Sets of Assumptions for the Monte Carlo Simulation for a More Precise Analysis of Enterprise Risk

<abstract>
<title style='display:none'>Abstract</title>
The purpose of the paper was to investigate by the kernel method a nonparametric estimate of the conditional density function of a scalar response variable given a random variable taking values in a separable real Hilbert space when the observations are quasi-associated dependent. Under some general conditions, the authors established the pointwise almost complete consistencies with rates of this estimator. The principal aim is the investigate the convergence rate of the proposed estimator.
</abstract>

Asymptotic Properties of the Estimator of the Conditional Distribution for Associated Functional Data

<abstract>
<title style='display:none'>Abstract</title>
<sec><title style='display:none'>Aim</title>
In the conducted research, profiles of seasonality in the housing market were determined, which provided an opportunity to answer two fundamental questions: what is the nature of harmonic variation in the seasonality and periodicity of the studied components of the construction process? what parameters of the ARIMA model optimally describe the construction market?
</sec>
<sec><title style='display:none'>Methodology</title>
In the conducted research, using the X13-ARIMA-SEATS model, seasonal decomposition was carried out in the various stages of the housing construction process.
</sec>
<sec><title style='display:none'>Results</title>
The research process conducted to identify seasonal fluctuations in the housing construction market showed that harmonic fluctuation profiles can be identified on an annual basis. An analysis of seasonal fluctuations was carried out for each of the three stages of the housing construction process, while also checking how these profiles function for Poland in general, and for individual investors, and for those building apartments for sale or to rent. The study showed that the market for real estate development activity differs in its seasonal characteristics from that of individual investors.
</sec>
<sec><title style='display:none'>Implications and recommendations</title>
The conclusions obtained from the research can provide support in the decision-making process, both from a macro and microeconomic perspective. Parameterisation of the occurring fluctuations, and taking them into account in the process of developing a forecast can provide decision-making rationale in the implementation of macroprudential and financial stability policies
</sec>
<sec><title style='display:none'>Originality/Value</title>
A novelty is in the demonstration that the residential real estate market in Poland shows different seasonal parameters, divided into the market of individual investors and investors who build apartments for sale or rent.
</sec>
</abstract>

The Identification of Seasonality in the Housing Market Using the X13-ARIMA-SEATS Model

<abstract>
<title style='display:none'>Abstract</title>
<sec><title style='display:none'>Research background</title>
The phenomenon of low fertility in Poland is a vital subject of demographic analysis. In recent years, not only have there been changes in procreative and family models, but also in the age structure of society. This is particularly significant in the context of population ageing, which is becoming increasingly evident and brings numerous challenges such as increased burden on healthcare systems, a decrease in the active workforce, and the need to secure adequate retirement funds. Despite the desire to have children, many individuals refrain from making such a decision, and the reasons for this choice are diverse. Therefore, it was essential to conduct an analysis of the factors determining fertility in Poland, considering both the economic and social aspects. Understanding how the economic situation, labour market conditions, and changes in social structure impact on the decision-making process regarding childbearing is essential.
</sec>
<sec><title style='display:none'>Purpose of the paper</title>
The objective of this article was to analyse fertility rates in Poland for the period 2004-2020. The conducted research identified the factors influencing the observed state of low generational replacement and determining their intensity.
</sec>
<sec><title style='display:none'>Methodology/Methods/Data sources</title>
The data used in this article were sourced from the Central Statistical Office and covered the years 2004-2020. The study was based on literature concerning demography and econometrics. Three statistical methods were applied in the analysis of fertility in Poland: the Classical Method of Least Squares (CMLS) model, the Fixed Effects (FE) estimator, and the Random Effects (RE) estimator. Fertility analysis was conducted at regional level by dividing Poland into 16 administrative units (voivodeships). A panel model was employed for the analysis, and the results were subjected to Wald, Breusch-Pagan, and Hausman tests to compare the outcomes obtained from different models.
</sec>
<sec><title style='display:none'>Findings</title>
The results of the analysis indicate that the economic situation and the labour market significantly influence the decision to have children in Poland. The trend of low fertility, although showing some increase, is still characteristic of the country compared to other EU nations. The analysis of the factors determining fertility is vital for understanding the decisions of young generations of Poles regarding parenthood.
</sec>
</abstract>

Demographic Challenges in Poland: Understanding Low Fertility

<abstract>
<title style='display:none'>Abstract</title>
<sec><title style='display:none'>Aim</title>
The paper aims to propose a new estimation method for the Cholesky Multivariate Stochastic Volatility Model based on the iterated filtering algorithm (Ionides et al., 2006, 2015).
</sec>
<sec><title style='display:none'>Methodology</title>
The iterated filtering method is a frequentist-based technique that through multiple repetitions of the filtering process, provides a sequence of iteratively updated parameter estimates that converge towards the maximum likelihood estimate.
</sec>
<sec><title style='display:none'>Results</title>
The effectiveness of the proposed estimation method was shown in an empirical example in which the Cholesky Multivariate Stochastic Volatility Model was used in a study on safe-haven assets of one market index: Standard and Poor’s 500 and three safe-haven candidates: gold, Bitcoin and Ethereum.
Implications and recommendations: In further research, the iterating filtering method may be used for more advanced multivariate stochastic volatility models that take into account, for example, the leverage effect (as in Ishihara et al., 2016) and heavy-tailed errors (as in Ishihara and Omori, 2012).
</sec>
<sec><title style='display:none'>Originality/Value</title>
The main contribution of the paper is the proposition of a new estimation method for the Cholesky Multivariate Stochastic Volatility Model based on iterated filtering algorithm This is one of the few frequentist-based statistical inference methods for multivariate stochastic volatility models.
</sec>
</abstract>

Estimation of the Cholesky Multivariate Stochastic Volatility Model Using Iterated Filtering

<abstract>
<title style='display:none'>Abstract</title>
<sec><title style='display:none'>Aim</title>
Multidimensional unfolding allows representing both columns (e.g. products, services) and rows (e.g. customers) of the preference matrix on the same low-dimensional map (usually it’s a two or three-dimensional map). The main aim of the paper was to propose how to perform unfolding analysis for symbolic objects.
</sec>
<sec><title style='display:none'>Methodology</title>
The paper describes the possible ways of performing unfolding analysis for symbolic interval-valued data. The external unfolding is described in the details and used in the empirical part of the paper. The data (preferences and dissimilarities) were gathered by using the incomplete method of triads.
</sec>
<sec><title style='display:none'>Results</title>
The empirical part presents an application for unfolding symbolic data to evaluate customers’ preferences, where car advertisements are used as the example. The results presented on a two--dimensional perceptual map allowed to discover seven groups of respondents with different preferences; most of them prefer Skoda, Audi, Volkswagen, and Honda advertisements to Toyota and Volvo.
</sec>
<sec><title style='display:none'>Implications and recommendations</title>
The proposed external approach for symbolic data allows to represent objects as rectangles (on two-dimensional map) or cuboids (in the case of three dimensions). The respondents are represented as points. Further work should focus on creating an algorithm that allows for the presentation of both symbolic objects and preferences expressed by respondents in the form of rectangles or cuboids.
</sec>
<sec><title style='display:none'>Originality/Value</title>
The paper presents an innovative and previously unpresented external unfolding for symbolic data. Besides that it presents how other unfolding approaches could be adapted for symbolic data.
</sec>
</abstract>

The Unfolding Analysis for Symbolic Objects Based on the Example of the External Car Advertisement Evaluation

<abstract>
<title style='display:none'>Abstract</title>
The primary goal of this research was to estimate the quantile of a conditional distribution using a semi-parametric approach in the presence of randomly missing data, where the predictor variable belongs to a semi-metric space. The authors assumed a single index structure to link the explanatory and response variable. First, a kernel estimator was proposed for the conditional distribution function, assuming that the data were selected from a stationary process with missing data at random (MAR). By imposing certain general conditions, the study established the model’s uniform almost complete consistencies with convergence rates.
</abstract>

Single Functional Index Quantile Regression for Functional Data with Missing Data at Random

<abstract>
<title style='display:none'>Abstract</title>
The article considers the problems of young people aged 20-24 on the labour market affected by unemployment in European Union countries. Unemployment is one of the most important economic and social problems, which at the same time constitutes one of the biggest measures characterising the condition of the economy. The diversity of the economic situation in EU countries directly affects young people, an individual group of people entering the labour market and have little or no professional experience. At the same time, they are ready to start work, facing great difficulties in entering the market, influenced by socio-economic as well as demographic factors which directly and indirectly affect employment. Considering the above premise, the aim of the article was to identify the determinants of unemployment of young people aged 20-24 in the EU. The study used data from two years: 2010 and 2020, and applied multiple regression. Statistical data were taken from Eurostat databases. The study allowed to examine the dependence of the influence of individual socioeconomic as well as demographic factors on youth unemployment. The study found that the multivariate regression showed that factors related to young people's participation in education and training (including the NEET rate) relative to labour market status, as well as social inclusion, had a significant impact on the unemployment studied. Over the decade, a decrease was seen in unemployment in most EU member states, in as many as 19 countries, while the remaining eight countries showed an increase.
</abstract>

Evaluation of the Labour Market Situation of Young People in EU Countries – The Multiple Regression Approach

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Econometrics

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 The Econometrics journal has been published continuously since 1998. Starting from the first issue, Józef Dziechciarz has been an Editor-in-Chief of the...

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