Research

Jump to: Review

Open AccessArticle

Circular-Statistics-Based Estimators and Tests for the Index Parameter α of Distributions for High-Volatility Financial Markets

by

Ashis SenGupta

and

Moumita Roy

J. Risk Financial Manag. 2023, 16(9), 405; https://doi.org/10.3390/jrfm16090405 - 11 Sep 2023

Viewed by 292

Abstract

The distributions for highly volatile financial time-series data are playing an increasingly important role in current financial scenarios and signal analyses. An important characteristic of such a probability distribution is its tail behaviour, determined through its tail thickness. This can be achieved by [...] Read more.

The distributions for highly volatile financial time-series data are playing an increasingly important role in current financial scenarios and signal analyses. An important characteristic of such a probability distribution is its tail behaviour, determined through its tail thickness. This can be achieved by estimating the index parameter of the corresponding distribution. The normal and Cauchy distributions, and, sometimes, a mixture of the normal and Cauchy distributions, are suitable for modelling such financial data. The family of stable distributions can provide better modelling for such financial data sets. Financial data in high-volatility markets may be better modelled, in many cases, by the Linnik distribution in comparison to the stable distribution. This highly flexible family of distributions is better capable of modelling the inflection points and tail behaviour compared to the other existing models. The estimation of the tail thickness of heavy-tailed financial data is important in the context of modelling. However, the new probability distributions do not admit any closed analytical form of representation. Thus, novel methods need to be developed, as only a few can be found in the literature. Here, we recall a recent novel method, developed by the authors, based on a trigonometric moment estimator using circular distributions. The linear data may be transformed to yield circular data. This transformation is solely for yielding a suitable estimator. Our aim in this paper is to provide a review of the few existing methods, discuss some of their drawbacks, and also provide a universal (

\forall α \in (0, 2]

), efficient, and easily implementable estimator of

α

based on the transformation mentioned above. Novel, circular-statistics-based tests for the index parameter

α

of the stable and Linnik distributions are introduced and also exemplified with real-life financial data. Two real-life data sets are analysed to exemplify the methods recommended and enhanced by the authors. Full article

(This article belongs to the Special Issue Financial Data Analytics and Statistical Learning)

► Show Figures

Figure 1

Open AccessArticle

Elliptical and Skew-Elliptical Regression Models and Their Applications to Financial Data Analytics

by

,

,

and

J. Risk Financial Manag. 2023, 16(7), 310; https://doi.org/10.3390/jrfm16070310 - 27 Jun 2023

Viewed by 450

Abstract

Various statistical distributions have played significant roles in financial data analytics in recent decades. Among these, elliptical modeling has gained popularity, while the study and application of skew-elliptical modeling have garnered increased attention in various domains. This paper begins by acknowledging the notable [...] Read more.

Various statistical distributions have played significant roles in financial data analytics in recent decades. Among these, elliptical modeling has gained popularity, while the study and application of skew-elliptical modeling have garnered increased attention in various domains. This paper begins by acknowledging the notable accomplishments and contributions of Professor Chris Heyde in the field of financial data modeling. We provide a comprehensive review of elliptical and skew-elliptical modeling, summarizing the latest advancements. In particular, we focus on the characteristics, estimation methods, and diagnostics of elliptical and skew-elliptical distributions in regression and time series models, as well as copula modeling. Furthermore, we discuss several related applications in regression and time series models, including estimation and diagnostic methods. The main objective of this paper is to address the critical need for accurately identifying the underlying elliptical distribution, whether it is elliptical or skew-elliptical. This identification is essential for conducting local influence diagnostics and employing appropriate regression methods using suitable elliptical modeling techniques. To illustrate this process, we present examples that demonstrate the identification of the elliptical distribution, starting with the Box–Jenkins methodology and progressing to copula modeling. The inclusion of copula modeling is motivated by its effectiveness in conjunction with elliptical and skew-elliptical distributions, as it aids in distinguishing between the two. Ultimately, the findings of this paper offer valuable insights, as correctly determining the elliptical and skew-elliptical distribution enables the application of suitable local influence and regression methods, thereby contributing to financial portfolio management, business analytics, and insurance analytics, ensuring the accurate specification of models. Full article

(This article belongs to the Special Issue Financial Data Analytics and Statistical Learning)

► Show Figures

Figure 1

Open AccessArticle

Exponential Stability of Fractional Large-Scale Neutral Stochastic Delay Systems with Fractional Brownian Motion

by

T. Sathiyaraj

,

T. Ambika

and

Ong Seng Huat

J. Risk Financial Manag. 2023, 16(5), 278; https://doi.org/10.3390/jrfm16050278 - 19 May 2023

Viewed by 555

Abstract

Mathematics plays an important role in many fields of finance. In particular, it presents theories and tools widely used in all areas of finance. Moreover, fractional Brownian motion (fBm) and related stochastic systems have been used to model stock prices and other phenomena [...] Read more.

Mathematics plays an important role in many fields of finance. In particular, it presents theories and tools widely used in all areas of finance. Moreover, fractional Brownian motion (fBm) and related stochastic systems have been used to model stock prices and other phenomena in finance due to the long memory property of such systems. This manuscript provides the exponential stability of fractional-order Large-Scale neutral stochastic delay systems with fBm. Based on fractional calculus (FC),

R^{n}

stochastic space and Banach fixed point theory, sufficiently useful conditions are derived for the existence of solution and exponential stability results. In this study, we tackle the nonlinear terms of the considered systems by applying local assumptions. Finally, to verify the theoretical results, a numerical simulation is provided. Full article

(This article belongs to the Special Issue Financial Data Analytics and Statistical Learning)

► Show Figures

Figure 1

Open AccessArticle

Bayesian Statistics for Loan Default

by

Allan W. Tham

,

Kazuhiko Kakamu

and

Shuangzhe Liu

J. Risk Financial Manag. 2023, 16(3), 203; https://doi.org/10.3390/jrfm16030203 - 15 Mar 2023

Viewed by 1333

Abstract

Bayesian inference has gained popularity in the last half of the twentieth century thanks to the wider applications in numerous fields such as economics, finance, physics, engineering, life sciences, environmental studies, and so forth. In this paper, we studied some key benefits of [...] Read more.

Bayesian inference has gained popularity in the last half of the twentieth century thanks to the wider applications in numerous fields such as economics, finance, physics, engineering, life sciences, environmental studies, and so forth. In this paper, we studied some key benefits of Bayesian inference and how they can be used in predicting loan default in the banking sector. Various traditional classification techniques are also presented to draw comparisons primarily in terms of the ease of interpretability and model performance. This paper includes the use of non-informative priors to attempt to arrive to the convergence of posterior distribution. Finally, with the Bayesian techniques proven to be an alternative to the classical approaches, the paper attempted to demonstrate that Bayesian techniques are indeed powerful in financial data analytics and applications. Full article

(This article belongs to the Special Issue Financial Data Analytics and Statistical Learning)

► Show Figures

Figure 1

Open AccessArticle

The Naive Estimator of a Poisson Regression Model with a Measurement Error

by

Kentarou Wada

and

Takeshi Kurosawa

J. Risk Financial Manag. 2023, 16(3), 186; https://doi.org/10.3390/jrfm16030186 - 09 Mar 2023

Viewed by 671

Abstract

We generalize the naive estimator of a Poisson regression model with a measurement error as discussed in Kukush et al. in 2004. The explanatory variable is not always normally distributed as they assume. In this study, we assume that the explanatory variable and [...] Read more.

We generalize the naive estimator of a Poisson regression model with a measurement error as discussed in Kukush et al. in 2004. The explanatory variable is not always normally distributed as they assume. In this study, we assume that the explanatory variable and measurement error are not limited to a normal distribution. We clarify the requirements for the existence of the naive estimator and derive its asymptotic bias and asymptotic mean squared error (MSE). The requirements for the existence of the naive estimator can be expressed using an implicit function, which the requirements can be deduced by the characteristic of the Poisson regression models. In addition, using the implicit function obtained from the system of equations of the Poisson regression models, we propose a consistent estimator of the true parameter by correcting the bias of the naive estimator. As illustrative examples, we present simulation studies that compare the performance of the naive estimator and new estimator for a Gamma explanatory variable with a normal error or a Gamma error. Full article

(This article belongs to the Special Issue Financial Data Analytics and Statistical Learning)

► Show Figures

Figure 1

Open AccessArticle

Modelling of Loan Non-Payments with Count Distributions Arising from Non-Exponential Inter-Arrival Times

by

Yeh-Ching Low

and

Seng-Huat Ong

J. Risk Financial Manag. 2023, 16(3), 150; https://doi.org/10.3390/jrfm16030150 - 23 Feb 2023

Viewed by 711

Abstract

The number of non-payments is an indicator of delinquent behaviour in credit scoring, hence its estimation and prediction are of interest. The modelling of the number of non-payments, as count data, can be examined as a renewal process. In a renewal process, the [...] Read more.

The number of non-payments is an indicator of delinquent behaviour in credit scoring, hence its estimation and prediction are of interest. The modelling of the number of non-payments, as count data, can be examined as a renewal process. In a renewal process, the number of events (such as non-payments) which has occurred up to a fixed time t is intimately connected with the inter-arrival times between the events. In the context of non-payments, the inter-arrival times correspond to the time between two subsequent non-payments. The probability mass function and the renewal function of the count distribution are often complicated, with terms involving factorial and gamma functions, and thus their computation may encounter numerical difficulties. In this paper, with the motivation of modelling the number of non-payments through a renewal process, a general method for computing the probabilities and the renewal function based on numerical Laplace transform inversion is discussed. This method is applied to some count distributions which are derived given the distributions of the inter-arrival times. Parameter estimation with maximum likelihood estimation is considered, with an application to a data set on number of non-payments from the literature. Full article

(This article belongs to the Special Issue Financial Data Analytics and Statistical Learning)

► Show Figures

Figure 1

Open AccessArticle

On the Contaminated Weighted Exponential Distribution: Applications to Modeling Insurance Claim Data

by

Abbas Mahdavi

,

Omid Kharazmi

and

Javier E. Contreras-Reyes

J. Risk Financial Manag. 2022, 15(11), 500; https://doi.org/10.3390/jrfm15110500 - 27 Oct 2022

Viewed by 920

Abstract

Deriving loss distribution from insurance data is a challenging task, as loss distribution is strongly skewed with heavy tails with some levels of outliers. This paper extends the weighted exponential (WE) family to the contaminated WE (CWE) family, which offers many flexible features, [...] Read more.

Deriving loss distribution from insurance data is a challenging task, as loss distribution is strongly skewed with heavy tails with some levels of outliers. This paper extends the weighted exponential (WE) family to the contaminated WE (CWE) family, which offers many flexible features, including bimodality and a wide range of skewness and kurtosis. We adopt Expectation-Maximization (EM) and Bayesian approaches to estimate the model, providing the likelihood and the priors for all unknown parameters. Finally, two sets of claims data are analyzed to illustrate the efficiency of the proposed method in detecting outliers. Full article

(This article belongs to the Special Issue Financial Data Analytics and Statistical Learning)

► Show Figures

Figure 1

Open AccessArticle

On Financial Distributions Modelling Methods: Application on Regression Models for Time Series

by

Paul R. Dewick

J. Risk Financial Manag. 2022, 15(10), 461; https://doi.org/10.3390/jrfm15100461 - 13 Oct 2022

Cited by 2 | Viewed by 1149

Abstract

The financial market is a complex system with chaotic behavior that can lead to wild swings within the financial system. This can drive the system into a variety of interesting phenomenon such as phase transitions, bubbles, and crashes, and so on. Of interest [...] Read more.

The financial market is a complex system with chaotic behavior that can lead to wild swings within the financial system. This can drive the system into a variety of interesting phenomenon such as phase transitions, bubbles, and crashes, and so on. Of interest in financial modelling is identifying the distribution and the stylized facts of a particular time series, as the distribution and stylized facts can determine if volatility is present, resulting in financial risk and contagion. Regression modelling has been used within this study as a methodology to identify the goodness-of-fit between the original and generated time series model, which serves as a criterion for model selection. Different time series modelling methods that include the common Box–Jenkins ARIMA, ARMA-GARCH type methods, the Geometric Brownian Motion type models and Tsallis entropy based models when data size permits, can use this methodology in model selection. Determining the time series distribution and stylized facts has utility, as the distribution allows for further modelling opportunities such as bivariate regression and copula modelling, apart from the usual forecasting. Determining the distribution and stylized facts also allows for the identification of the parameters that are used within a Geometric Brownian Motion forecasting model. This study has used the Carbon Emissions Futures price between the dates of 1 May 2012 and 1 May 2022, to highlight this application of regression modelling. Full article

(This article belongs to the Special Issue Financial Data Analytics and Statistical Learning)

► Show Figures

Figure 1

Open AccessArticle

Modeling Bivariate Dependency in Insurance Data via Copula: A Brief Study

by

Indranil Ghosh

,

Dalton Watts

and

Subrata Chakraborty

J. Risk Financial Manag. 2022, 15(8), 329; https://doi.org/10.3390/jrfm15080329 - 25 Jul 2022

Cited by 1 | Viewed by 1622

Abstract

Copulas are a quite flexible and useful tool for modeling the dependence structure between two or more variables or components of bivariate and multivariate vectors, in particular, to predict losses in insurance and finance. In this article, we use the VineCopula package in [...] Read more.

Copulas are a quite flexible and useful tool for modeling the dependence structure between two or more variables or components of bivariate and multivariate vectors, in particular, to predict losses in insurance and finance. In this article, we use the VineCopula package in R to study the dependence structure of some well-known real-life insurance data and identify the best bivariate copula in each case. Associated structural properties of these bivariate copulas are also discussed with a major focus on their tail dependence structure. This study shows that certain types of Archimedean copula with the heavy tail dependence property are a reasonable framework to start in terms modeling insurance claim data both in the bivariate as well as in the case of multivariate domains as appropriate. Full article

(This article belongs to the Special Issue Financial Data Analytics and Statistical Learning)

► Show Figures

Figure 1

Review

Jump to: Research

Open AccessReview

On Asymmetric Correlations and Their Applications in Financial Markets

by

,

,

and

J. Risk Financial Manag. 2023, 16(3), 187; https://doi.org/10.3390/jrfm16030187 - 09 Mar 2023

Cited by 1 | Viewed by 919

Abstract

Progress on asymmetric correlations of asset returns has recently advanced considerably. Asymmetric correlations can cause problems in hedging effectiveness and overstate the value of diversification. Furthermore, considering the asymmetric correlations in portfolio construction significantly enhances performance. The purpose of this paper is to [...] Read more.

Progress on asymmetric correlations of asset returns has recently advanced considerably. Asymmetric correlations can cause problems in hedging effectiveness and overstate the value of diversification. Furthermore, considering the asymmetric correlations in portfolio construction significantly enhances performance. The purpose of this paper is to trace developments and identify areas that require further research. We examine three aspects of asymmetric correlations: first, the existence of asymmetric correlations between asset returns and their significance tests; second, the test on the existence of asymmetric correlations between different markets and financial assets; and third, the root cause analysis of asymmetric correlations. In the first part, the contents of extreme value theory, the H statistic and a model-free test are covered. In the second part, commonly used models such as copula and GARCH are included. In addition to the GARCH and copula formulations, many other methods are included, such as regime switching, the Markov switching model, and the multifractal asymmetric detrend cross-correlation analysis method. In addition, we compare the advantages and differences between the models. In the third part, the causes of asymmetry are discussed, for example, higher common fundamental risk, correlation of individual fundamental risk, and so on. Full article

(This article belongs to the Special Issue Financial Data Analytics and Statistical Learning)

► Show Figures