Volatility Models Applied to Geophysics, Financial Market Data and Other Disciplines

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: closed (30 April 2021) | Viewed by 30139

Special Issue Editor


E-Mail Website
Guest Editor
Department of Mathematical Sciences, University of Texas at El Paso, 500 University Ave., Bell Hall 124, El Paso, TX 79968-0514, USA
Interests: stochastic processes; nonlinear partial differential equations; mathematical finance; mathematical physics; numerical methods; geophysics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Over the past few decades, several volatility models have been developed to describe phenomenon arising in Geophysics, Financial Markets and other disciplines. Many known methods both deterministic and stochastic has been used to study the volatility structures of datasets arising in geophysical and financial time series. Many of these deterministic and stochastic models provide interesting, potentially useful tools for modeling and describing volatility structures in these time series.

In this Special Issue, we invite and welcome commentaries, review, expository, and original research articles dealing with the recent advances in the theory and applications of volatility models to data sets arising in geophysics, financial markets data and other disciplines.

Prof. Dr. Maria C Mariani
Guest Editor

Keywords

  • Stochastic volatility models
  • Deterministic volatility models
  • Geophysics
  • Financial market data
  • Time series analysis
  • High frequency data

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (9 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

15 pages, 4437 KiB  
Article
The Impact of Regulatory Reforms on Demand Weighted Average Prices
by Sherzod N. Tashpulatov
Mathematics 2021, 9(10), 1112; https://doi.org/10.3390/math9101112 - 14 May 2021
Cited by 2 | Viewed by 1433
Abstract
Average prices are popularly used in the literature on price modeling. Calculating daily or weekly prices as an average over hourly or half-hourly trading periods assumes the same weight ignoring demand or traded volumes during those periods. Analyzing demand weighted average prices is [...] Read more.
Average prices are popularly used in the literature on price modeling. Calculating daily or weekly prices as an average over hourly or half-hourly trading periods assumes the same weight ignoring demand or traded volumes during those periods. Analyzing demand weighted average prices is important if producers may affect prices by decreasing them during low-demand periods and increasing them during high-demand periods within a day. The prediction of this price manipulation might have motivated the regulatory authority to introduce price caps not only on annual average prices but also on annual demand weighted average prices in the England and Wales wholesale electricity market. The dynamics of demand weighted average prices of electricity has been analyzed little in the literature. We show that skew generalized error distribution (SGED) is the appropriate assumption for model residuals. The estimated volatility model is used for evaluating the impact of regulatory reforms on demand weighted average prices during the complete history of the England and Wales wholesale electricity market. Full article
Show Figures

Figure 1

30 pages, 1533 KiB  
Article
Analyzing Medical Data by Using Statistical Learning Models
by Maria C. Mariani, Francis Biney and Osei K. Tweneboah
Mathematics 2021, 9(9), 968; https://doi.org/10.3390/math9090968 - 26 Apr 2021
Cited by 1 | Viewed by 2612
Abstract
In this work, we investigated the prognosis of three medical data specifically, breast cancer, heart disease, and prostate cancer by using 10 machine learning models. We applied all 10 models to each dataset to identify patterns in them. Furthermore, we use the models [...] Read more.
In this work, we investigated the prognosis of three medical data specifically, breast cancer, heart disease, and prostate cancer by using 10 machine learning models. We applied all 10 models to each dataset to identify patterns in them. Furthermore, we use the models to diagnose risk factors that increases the chance of these diseases. All the statistical learning techniques discussed were grouped into linear and nonlinear models based on their similarities and learning styles. The models performances were significantly improved by selecting models while taking into account the bias-variance tradeoffs and using cross-validation for selecting the tuning parameter. Our results suggests that no particular class of models or learning style dominated the prognosis and diagnosis for all three medical datasets. However nonlinear models gave the best predictive performance for breast cancer data. Linear models on the other hand gave the best predictive performance for heart disease data and a combination of linear and nonlinear models for the prostate cancer dataset. Full article
Show Figures

Figure 1

11 pages, 1676 KiB  
Article
Modeling and Estimating Volatility of Day-Ahead Electricity Prices
by Sherzod N. Tashpulatov
Mathematics 2021, 9(7), 750; https://doi.org/10.3390/math9070750 - 31 Mar 2021
Cited by 3 | Viewed by 1938
Abstract
We model day-ahead electricity prices of the UK power market using skew generalized error distribution. This distribution allows us to take into account the features of asymmetry, heavy tails, and a peak higher than in normal or Student’s t distributions. The adequacy of [...] Read more.
We model day-ahead electricity prices of the UK power market using skew generalized error distribution. This distribution allows us to take into account the features of asymmetry, heavy tails, and a peak higher than in normal or Student’s t distributions. The adequacy of the estimated volatility model is verified using various tests and criteria. A correctly specified volatility model can be used for analyzing the impact of reforms or other events. We find that, after the start of the COVID-19 pandemic, price level and volatility increased. Full article
Show Figures

Figure 1

17 pages, 1849 KiB  
Article
Volatility Forecasting for High-Frequency Financial Data Based on Web Search Index and Deep Learning Model
by Bolin Lei, Boyu Zhang and Yuping Song
Mathematics 2021, 9(4), 320; https://doi.org/10.3390/math9040320 - 5 Feb 2021
Cited by 13 | Viewed by 6103
Abstract
The existing index system for volatility forecasting only focuses on asset return series or historical volatility, and the prediction model cannot effectively describe the highly complex and nonlinear characteristics of the stock market. In this study, we construct an investor attention factor through [...] Read more.
The existing index system for volatility forecasting only focuses on asset return series or historical volatility, and the prediction model cannot effectively describe the highly complex and nonlinear characteristics of the stock market. In this study, we construct an investor attention factor through a Baidu search index of antecedent keywords, and then combine other trading information such as the trading volume, trend indicator, quote change rate, etc., as input indicators, and finally employ the deep learning model via temporal convolutional networks (TCN) to forecast the volatility under high-frequency financial data. We found that the prediction accuracy of the TCN model with investor attention is better than those of the TCN model without investor attention, the traditional econometric model as the generalized autoregressive conditional heteroscedasticity (GARCH), the heterogeneous autoregressive model of realized volatility (HAR-RV), autoregressive fractionally integrated moving average (ARFIMA) models, and the long short-term memory (LSTM) model with investor attention. Compared with the traditional econometric models, the multi-step prediction results for the TCN model remain robust. Our findings provide a more accurate and robust method for volatility forecasting for big data and enrich the index system of volatility forecasting. Full article
Show Figures

Figure 1

25 pages, 2473 KiB  
Article
Applying Heath-Jarrow-Morton Model to Forecasting the US Treasury Daily Yield Curve Rates
by Valerii Maltsev and Michael Pokojovy
Mathematics 2021, 9(2), 114; https://doi.org/10.3390/math9020114 - 6 Jan 2021
Cited by 2 | Viewed by 3660
Abstract
The Heath-Jarrow-Morton (HJM) model is a powerful instrument for describing the stochastic evolution of interest rate curves under no-arbitrage assumption. An important feature of the HJM approach is the fact that the drifts can be expressed as functions of respective volatilities and the [...] Read more.
The Heath-Jarrow-Morton (HJM) model is a powerful instrument for describing the stochastic evolution of interest rate curves under no-arbitrage assumption. An important feature of the HJM approach is the fact that the drifts can be expressed as functions of respective volatilities and the underlying correlation structure. Aimed at researchers and practitioners, the purpose of this article is to present a self-contained, but concise review of the abstract HJM framework founded upon the theory of interest and stochastic partial differential equations in infinite dimensions. To illustrate the predictive power of this theory, we apply it to modeling and forecasting the US Treasury daily yield curve rates. We fit a non-parametric model to real data available from the US Department of the Treasury and illustrate its statistical performance in forecasting future yield curve rates. Full article
Show Figures

Figure 1

12 pages, 281 KiB  
Article
GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio
by Kei Nakagawa and Yusuke Uchiyama
Mathematics 2020, 8(11), 1990; https://doi.org/10.3390/math8111990 - 7 Nov 2020
Cited by 4 | Viewed by 2686
Abstract
There are three distinguishing features in the financial time series, such as stock prices, are as follows: (1) Non-normality, (2) serial correlation, and (3) leverage effect. All three points need to be taken into account to model the financial time series. However, multivariate [...] Read more.
There are three distinguishing features in the financial time series, such as stock prices, are as follows: (1) Non-normality, (2) serial correlation, and (3) leverage effect. All three points need to be taken into account to model the financial time series. However, multivariate financial time series modeling involves a large number of stocks, with many parameters to be estimated. Therefore, there are few examples of multivariate financial time series modeling that explicitly deal with higher-order moments. Furthermore, there is no multivariate financial time series model that takes all three characteristics above into account. In this study, we propose the generalized orthogonal (GO)-Glosten, Jagannathan, and Runkle GARCH (GJR) model which extends the GO-generalized autoregressive conditional heteroscedasticity (GARCH) model and incorporates the three features of the financial time series. We confirm the effectiveness of the proposed model by comparing the performance of risk-based portfolios with higher-order moments. The results show that the performance with our proposed model is superior to that with baseline methods, and indicate that estimation methods are important in risk-based portfolios with higher moments. Full article
20 pages, 1706 KiB  
Article
Self-Similar Models: Relationship between the Diffusion Entropy Analysis, Detrended Fluctuation Analysis and Lévy Models
by Maria C. Mariani, William Kubin, Peter K. Asante, Osei K. Tweneboah, Maria P. Beccar-Varela, Sebastian Jaroszewicz and Hector Gonzalez-Huizar
Mathematics 2020, 8(7), 1046; https://doi.org/10.3390/math8071046 - 30 Jun 2020
Cited by 5 | Viewed by 2196
Abstract
Financial and geophysical data, like many other low and high frequency time series, are known to exhibit some memory effects. These memory effects may be long or short, permanent or temporal depending on the event that is being modeled. The purpose of this [...] Read more.
Financial and geophysical data, like many other low and high frequency time series, are known to exhibit some memory effects. These memory effects may be long or short, permanent or temporal depending on the event that is being modeled. The purpose of this study is to investigate the memory effects characterized by the financial market closing values and volcanic eruption time series as well as to investigate the relation between the self-similar models used and the Lévy process. This paper uses highly effective scaling methods including Lévy processes, Detrended Fluctuation Analysis (DFA) and Diffusion Entropy Analysis (DEA) to examine long-range persistence behavior in time series by estimating their respective parameters. We use the parameter of the Lévy process (α) characterizing the data and the scaling parameters of DFA (H) and DEA (δ) characterizing the self-similar property to generate a relationship between the three (3) aforementioned scaling methods. Findings from the numerical simulations confirm the existence of long-range persistence (long-memory behavior) in both the financial and geophysical time series. Furthermore, the numerical results from this study indicates an approximate inverse relationship between the parameter of the Lévy process and the scaling parameters of the DFA and DEA (i.e., H , δ 1 α ), which we prove analytically. Full article
Show Figures

Figure 1

10 pages, 278 KiB  
Article
TPLVM: Portfolio Construction by Student’s t-Process Latent Variable Model
by Yusuke Uchiyama and Kei Nakagawa
Mathematics 2020, 8(3), 449; https://doi.org/10.3390/math8030449 - 19 Mar 2020
Cited by 8 | Viewed by 3563
Abstract
Optimal asset allocation is a key topic in modern finance theory. To realize the optimal asset allocation on investor’s risk aversion, various portfolio construction methods have been proposed. Recently, the applications of machine learning are rapidly growing in the area of finance. In [...] Read more.
Optimal asset allocation is a key topic in modern finance theory. To realize the optimal asset allocation on investor’s risk aversion, various portfolio construction methods have been proposed. Recently, the applications of machine learning are rapidly growing in the area of finance. In this article, we propose the Student’s t-process latent variable model (TPLVM) to describe non-Gaussian fluctuations of financial timeseries by lower dimensional latent variables. Subsequently, we apply the TPLVM to portfolio construction as an alternative of existing nonlinear factor models. To test the performance of the proposed method, we construct minimum-variance portfolios of global stock market indices based on the TPLVM or Gaussian process latent variable model. By comparing these portfolios, we confirm the proposed portfolio outperforms that of the existing Gaussian process latent variable model. Full article
18 pages, 1272 KiB  
Article
Long-Range Correlations and Characterization of Financial and Volcanic Time Series
by Maria C. Mariani, Peter K. Asante, Md Al Masum Bhuiyan, Maria P. Beccar-Varela, Sebastian Jaroszewicz and Osei K. Tweneboah
Mathematics 2020, 8(3), 441; https://doi.org/10.3390/math8030441 - 18 Mar 2020
Cited by 13 | Viewed by 4102
Abstract
In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series [...] Read more.
In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight. Full article
Show Figures

Figure 1

Back to TopTop