Application of Mathematical Analysis and Models to Financial Economics

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

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 57561

Special Issue Editor


E-Mail Website
Guest Editor
Department of Economics and Finance, University of Castilla-La Mancha, 02071 Albacete, Spain
Interests: term structure of interest rates; term structure of volatilities; risk management

Special Issue Information

Dear Colleagues,

In recent years, new mathematical developments have been applied in the context of financial economics. Thus, a relevant challenge is to provide a bridge between, on the one hand, new mathematical tools and, on the other hand, economics and finance issues. So, the main objective of this Special Issue of Mathematics named “Application of Mathematical Analysis and Models to Financial Economics” is the use of new mathematical approaches to economics and finance. Papers may focus on the mathematical part of the valuation of stocks, bonds and financial derivatives. The use of some factor models to manage potential financial risks and other applications in asset pricing theory and interest-rate modeling are also of interest.

We aim to provide a collection of new mathematical applications on economics and finance issues, such as interest rates, volatility modelling, factor models, risk management, derivatives, portfolio management and uncertainty in a quantitative finance context.

Prof. Dr. Francisco Jareño
Guest Editor

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Keywords

  • Derivatives
  • Factor models
  • Financial mathematics
  • Interest rates
  • Portfolio management
  • Quantitative finance
  • Risk management
  • Uncertainty
  • Volatility modelling

Published Papers (21 papers)

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Research

27 pages, 450 KiB  
Article
Pricing European and American Installment Options
by Joanna Goard and Mohammed AbaOud
Mathematics 2022, 10(19), 3494; https://doi.org/10.3390/math10193494 - 25 Sep 2022
Cited by 1 | Viewed by 1133
Abstract
This paper derives accurate and efficient analytic approximations for the prices of both European and American continuous-installment call and put options. The solutions are in the form of series in time-to-expiry with explicit formulae for the coefficients provided. Unlike other solutions for installment [...] Read more.
This paper derives accurate and efficient analytic approximations for the prices of both European and American continuous-installment call and put options. The solutions are in the form of series in time-to-expiry with explicit formulae for the coefficients provided. Unlike other solutions for installment options, no Laplace inverses are needed, and there is no need to solve complex, recursive systems or integral equations. The formulae provided fast yield and accurate solutions not just for the prices, but also for the critical boundaries. We also compare the solutions with those obtained using an existing method and show that it surpasses it delivering more correct option prices and critical stock prices. Full article
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12 pages, 1578 KiB  
Article
Reconstructing the Local Volatility Surface from Market Option Prices
by Soobin Kwak, Youngjin Hwang, Yongho Choi, Jian Wang, Sangkwon Kim and Junseok Kim
Mathematics 2022, 10(14), 2537; https://doi.org/10.3390/math10142537 - 21 Jul 2022
Cited by 1 | Viewed by 1884
Abstract
We present an efficient and accurate computational algorithm for reconstructing a local volatility surface from given market option prices. The local volatility surface is dependent on the values of both the time and underlying asset. We use the generalized Black–Scholes (BS) equation and [...] Read more.
We present an efficient and accurate computational algorithm for reconstructing a local volatility surface from given market option prices. The local volatility surface is dependent on the values of both the time and underlying asset. We use the generalized Black–Scholes (BS) equation and finite difference method (FDM) to numerically solve the generalized BS equation. We reconstruct the local volatility function, which provides the best fit between the theoretical and market option prices by minimizing a cost function that is a quadratic representation of the difference between the two option prices. This is an inverse problem in which we want to calculate a local volatility function consistent with the observed market prices. To achieve robust computation, we place the sample points of the unknown volatility function in the middle of the expiration dates. We perform various numerical experiments to confirm the simplicity, robustness, and accuracy of the proposed method in reconstructing the local volatility function. Full article
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15 pages, 4103 KiB  
Article
Dynamical Investigation, Electronic Circuit Realization and Emulation of a Fractional-Order Chaotic Three-Echelon Supply Chain System
by Qing Ding, Oumate Alhadji Abba, Hadi Jahanshahi, Madini O. Alassafi and Wen-Hua Huang
Mathematics 2022, 10(4), 625; https://doi.org/10.3390/math10040625 - 17 Feb 2022
Cited by 9 | Viewed by 1487
Abstract
This study is concerned with dynamical investigation, electrical circuit realization, and emulation of a fractional three-echelon supply chain system. In the financial realm, long-term memory effects play important roles. On the other hand, most financial systems are uncertain with unknown nonlinear dynamics. However, [...] Read more.
This study is concerned with dynamical investigation, electrical circuit realization, and emulation of a fractional three-echelon supply chain system. In the financial realm, long-term memory effects play important roles. On the other hand, most financial systems are uncertain with unknown nonlinear dynamics. However, most studies on nonlinear supply chains neither consider the fractional calculus nor take advantage of state-of-the-art emulation methods. These issues motivated the current study. A fractional-order chaotic three-echelon supply chain system is studied. At first, the system’s dynamic is studied through Lyapunov exponent and bifurcation diagrams. It is shown that a slight deferent in some parameters of the system can dramatically change the behavior of the system. Then, a real-time analog circuit is designed and implemented to investigate the system’s chaotic behavior. This way, the system’s chaotic attractors are empirically demonstrated. Finally, emulation and interpolation of the fractional-order chaotic system using the Gaussian process have been studied, and its luminous results have been presented. Full article
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15 pages, 328 KiB  
Article
The Generalized First- and Second-Price Auctions: Overbidding, Underbidding, and Optimal Reserve Price
by Ziyi Tan and Shulin Liu
Mathematics 2022, 10(3), 403; https://doi.org/10.3390/math10030403 - 27 Jan 2022
Cited by 1 | Viewed by 1832
Abstract
The paper generalizes the models of the standard first- and second-price auctions (FPA and SPA) by using the Cobb-Douglas function to evaluate bidders’ two conflicting bidding preferences for the probability of winning the item (Cpwin) and the profit conditional on [...] Read more.
The paper generalizes the models of the standard first- and second-price auctions (FPA and SPA) by using the Cobb-Douglas function to evaluate bidders’ two conflicting bidding preferences for the probability of winning the item (Cpwin) and the profit conditional on winning (Cprofit). Compared with the popular expected profit function, this function has the advantage of allowing the bidders to equally or differently value Cpwin and Cprofit from the point of view of multiple criteria decision making, and then can capture bidders’ bidding behavior in reality. Introduction of the Cobb-Douglas function into the FPA allows us to provide new interpretations for overbidding (underbidding) behavior and the dependence of the optimal reserve price on the number of bidders. Our new interpretations are all attributed to the bidders’ different preferences for Cpwin and Cprofit. In contrast, this introduction into the SPA does not matter. Our findings suggest that the seller should prefer the FPA (SPA) over the SPA (FPA) and set a lower (higher) optimal reserve price if he conjectures that the bidders have a stronger desire to win an auction (to obtain a profit). The above results help the seller to select between the two auctions and set a reserve price in practice. Full article
14 pages, 312 KiB  
Article
Capital Allocation Methods under Solvency II: A Comparative Analysis
by Pablo Durán-Santomil and Luís Otero-González
Mathematics 2022, 10(3), 303; https://doi.org/10.3390/math10030303 - 19 Jan 2022
Cited by 2 | Viewed by 3726
Abstract
The objective of this document is to analyze different methods that an insurer can use to allocate capital to his or her different lines of business or business segments under Solvency II. For this analysis, a review of the main methods developed in [...] Read more.
The objective of this document is to analyze different methods that an insurer can use to allocate capital to his or her different lines of business or business segments under Solvency II. For this analysis, a review of the main methods developed in the literature is carried out. Many of the proposed methods in the literature can only be implemented with the internal data from the company’s loss distributions. In addition to this, in some of the methods that can be applied with external data, the diversifying effect is in essence not assigned to the lines of business (LoBs) that cause it. Therefore, in this paper, we compare the results of the main methods that can be used with public data and propose a simple method of capital allocation for insurance companies, which does not require knowledge of the loss distribution of an LoB, and which allows the diversification benefit to be assigned only to the LoBs that really cause such an effect. A practical example of the differences between the different methods and the one proposed is shown for better understanding. Full article
27 pages, 376 KiB  
Article
Transmission Channels between Financial Deepening and Economic Growth: Econometric Analysis Comprising Monetary Factors
by Marina Abramova, Dmitri Artemenko and Konstantin Krinichansky
Mathematics 2022, 10(2), 242; https://doi.org/10.3390/math10020242 - 13 Jan 2022
Cited by 5 | Viewed by 1950
Abstract
Contemporary literature continues to foster discussion whether financial development is important for economic growth. In the clash of theoretical arguments, the prevailing idea is that finance exerts a direct positive influence on GDP growth. However, the presence of theoretical counterarguments and contradictory results [...] Read more.
Contemporary literature continues to foster discussion whether financial development is important for economic growth. In the clash of theoretical arguments, the prevailing idea is that finance exerts a direct positive influence on GDP growth. However, the presence of theoretical counterarguments and contradictory results of empirical studies suggest that scientists, in search of an answer about the direction and power of the net effect, should develop methods of empirical analysis, and the very mystery of the relationship between finance and growth will finally be solved exclusively empirically. In this paper, the authors contribute to the development of the ‘finance-growth’ literature by answering some existing questions concerning the transmission channels from finance to growth, relying on more recent data compared to already conducted studies. We use panel data covering the period 1995 to 2019 for 168 countries. In addition, the paper touches on the problem of studying the exogenous conditions of such channels, considering the assumption that among these conditions there may be those that hinder the impact of financial deepening on economic growth. Our focus is on monetary conditions, and in the empirical part of the study, we touch upon the problem of the influence of price stability on the operation of these transmission channels. The methods of the conducted study are based on the dynamic panel data analysis techniques (System GMM). The novelty of this paper lies in the development of the modern theory of the financial sector transmission mechanism in the economic growth context. The main result of the study is that productivity channel is the most reliable transmission channel of financial deepening to economic growth. Furthermore, the effectiveness of this channel remains virtually unaffected by inflation. The channel of capital accumulation should be considered less reliable (in terms of statistical reliability of estimates obtained), but it has turned out to be a more economically significant transmission channel. This channel is sensitive to the inflation factor in certain categories of countries. Finally, as follows from the estimates gained, the non-linearity of the “finance-growth” relationship can be explained by the non-linearity of the variable responsible for the capital accumulation channel. Full article
14 pages, 297 KiB  
Article
The Effect of the Launch of Bitcoin Futures on the Cryptocurrency Market: An Economic Efficiency Approach
by David Vidal-Tomás, Ana M. Ibáñez and José E. Farinós
Mathematics 2021, 9(4), 413; https://doi.org/10.3390/math9040413 - 20 Feb 2021
Cited by 3 | Viewed by 2640
Abstract
We analyze the economic efficiency of the cryptocurrency market after the launch of Bitcoin futures by means of the Data Envelopment Analysis and Malmquist Indexes. Our results show that the introduction of Bitcoin futures did not affect the economic efficiency of the cryptocurrency [...] Read more.
We analyze the economic efficiency of the cryptocurrency market after the launch of Bitcoin futures by means of the Data Envelopment Analysis and Malmquist Indexes. Our results show that the introduction of Bitcoin futures did not affect the economic efficiency of the cryptocurrency market. However, we observe that Bitcoin obtained the highest risk-return trade-off due to its liquidity compared to the rest of cryptocurrencies. Therefore, our paper underlines the support of investors on Bitcoin to the detriment of the rest of cryptocurrencies. Full article
16 pages, 757 KiB  
Article
Modeling of the Bitcoin Volatility through Key Financial Environment Variables: An Application of Conditional Correlation MGARCH Models
by Ángeles Cebrián-Hernández and Enrique Jiménez-Rodríguez
Mathematics 2021, 9(3), 267; https://doi.org/10.3390/math9030267 - 29 Jan 2021
Cited by 13 | Viewed by 3508
Abstract
Since the launch of Bitcoin, there has been a lot of controversy surrounding what asset class it is. Several authors recognize the potential of cryptocurrencies but also certain deviations with respect to the functions of a conventional currency. Instead, Bitcoin’s diversifying factor and [...] Read more.
Since the launch of Bitcoin, there has been a lot of controversy surrounding what asset class it is. Several authors recognize the potential of cryptocurrencies but also certain deviations with respect to the functions of a conventional currency. Instead, Bitcoin’s diversifying factor and its high return potential have generated the attention of portfolio managers. In this context, understanding how its volatility is explained is a critical element of investor decision-making. By modeling the volatility of classic assets, nonlinear models such as Generalized Autoregressive Conditional Heteroskedasticity (GARCH) offer suitable results. Therefore, taking GARCH(1,1) as a reference point, the main aim of this study is to model and assess the relationship between the Bitcoin volatility and key financial environment variables through a Conditional Correlation (CC) Multivariate GARCH (MGARCH) approach. For this, several commodities, exchange rates, stock market indices, and company stocks linked to cryptocurrencies have been tested. The results obtained show certain heterogeneity in the fit of the different variables, highlighting the uncorrelation with respect to traditional safe haven assets such as gold and oil. Focusing on the CC-MGARCH model, a better behavior of the dynamic conditional correlation is found compared to the constant. Full article
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17 pages, 366 KiB  
Article
Including Jumps in the Stochastic Valuation of Freight Derivatives
by Lourdes Gómez-Valle and Julia Martínez-Rodríguez
Mathematics 2021, 9(2), 154; https://doi.org/10.3390/math9020154 - 13 Jan 2021
Cited by 3 | Viewed by 1553
Abstract
The spot freight rate processes considered in the literature for pricing forward freight agreements (FFA) and freight options usually have a particular dynamics in order to obtain the prices. In those cases, the FFA prices are explicitly obtained. However, for jump-diffusion models, an [...] Read more.
The spot freight rate processes considered in the literature for pricing forward freight agreements (FFA) and freight options usually have a particular dynamics in order to obtain the prices. In those cases, the FFA prices are explicitly obtained. However, for jump-diffusion models, an exact solution is not known for the freight options (Asian-type), in part due to the absence of a suitable valuation framework. In this paper, we consider a general jump-diffusion process to describe the spot freight dynamics and we obtain exact solutions of FFA prices for two parametric models. Moreover, we develop a partial integro-differential equation (PIDE), for pricing freight options for a general unifactorial jump-diffusion model. When we consider that the spot freight follows a geometric process with jumps, we obtain a solution of the freight option price in a part of its domain. Finally, we show the effect of the jumps in the FFA prices by means of numerical simulations. Full article
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17 pages, 784 KiB  
Article
Fuzzy Stochastic Automation Model for Decision Support in the Process Inter-Budgetary Regulation
by Irina Yakovenko
Mathematics 2021, 9(1), 67; https://doi.org/10.3390/math9010067 - 30 Dec 2020
Cited by 2 | Viewed by 1465
Abstract
The purpose of this article is to study the theoretical foundations of the concept of fiscal decentralization, as the main path of self-development of the national economy of any country, and to develop mathematical tools that support decision-making in the aspect of “hard” [...] Read more.
The purpose of this article is to study the theoretical foundations of the concept of fiscal decentralization, as the main path of self-development of the national economy of any country, and to develop mathematical tools that support decision-making in the aspect of “hard” budget constraints. The study of the problems of fiscal policy formation in foreign countries presented in modern scientific literature has revealed that the degree of application of the concepts of “soft” and “hard” budget restrictions is an actual topic in the theory of fiscal federalism. It has been substantiated that decision-making within the framework of “soft” budget constraints (financial assistance) leads to low tax autonomy of territories and limited liability of regional and municipal authorities for the results of their financial policy. As a research hypothesis, we put forward the thesis that it is necessary to create conditions for encouraging subnational authorities to support the territorial economy by granting them the possibility to use part of the taxes collected in the respective territories. The implementation of this thesis has given rise to the problem of quantifying decisions made regarding the establishment of standards for the distribution of tax revenues between budgets of different levels of the hierarchy of the country’s budget system. In terms of solving this problem, the author has constructed mathematical models based on the use of synthesis of mathematical apparatus of the theory of stochastic automata, fuzzy algebra, and simulation. In terms of solving this problem, the author proposed the use of mathematical modeling methods. The article presents the results of constructing economic and mathematical models to support decision-making in the vertical distribution of tax revenues between budgets. The models include stochastic automata, as mathematical abstractions, describing the expedient behavior of an economic agent when choosing management alternatives for territories of different levels of economic development. The transition functions of automaton models are formally described on the basis of the synthesis of mathematical apparatus of the theories of stochastic automata operating in random environments and fuzzy sets. The expediency property of the behavior of automaton models is justified by proving the corresponding theorems. The random environment in which stochastic automata are immersed is formed by a simulation model. The article demonstrates the results of experiments carried out on models, as well as a conceptual scheme of interaction between the automaton and simulation models. Full article
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10 pages, 288 KiB  
Article
An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon
by Junkee Jeon and Geonwoo Kim
Mathematics 2020, 8(11), 2084; https://doi.org/10.3390/math8112084 - 22 Nov 2020
Cited by 2 | Viewed by 1505
Abstract
This paper studies an irreversible investment problem under a finite horizon. The firm expands its production capacity in irreversible investments by purchasing capital to increase productivity. This problem is a singular stochastic control problem and its associated Hamilton–Jacobi–Bellman equation is derived. By using [...] Read more.
This paper studies an irreversible investment problem under a finite horizon. The firm expands its production capacity in irreversible investments by purchasing capital to increase productivity. This problem is a singular stochastic control problem and its associated Hamilton–Jacobi–Bellman equation is derived. By using a Mellin transform, we obtain the integral equation satisfied by the free boundary of this investment problem. Furthermore, we solve the integral equation numerically using the recursive integration method and present the graph for the free boundary. Full article
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18 pages, 2062 KiB  
Article
Tail Dependence and Risk Spillover from the US to GCC Banking Sectors
by Faisal Alqahtani, Nader Trabelsi, Nahla Samargandi and Syed Jawad Hussain Shahzad
Mathematics 2020, 8(11), 2055; https://doi.org/10.3390/math8112055 - 18 Nov 2020
Cited by 7 | Viewed by 1661
Abstract
This study investigates the structure of the tail dependence between the United States (US) and Gulf Cooperation Council (GCC) banking sectors for the period February 2010 to July 2017. Conditional value at risk and conditional diversification benefits are calculated. The GCC banking sectors [...] Read more.
This study investigates the structure of the tail dependence between the United States (US) and Gulf Cooperation Council (GCC) banking sectors for the period February 2010 to July 2017. Conditional value at risk and conditional diversification benefits are calculated. The GCC banking sectors show lower tail dependence with the US banking sector. This is confirmed by the fact that GCC banking sectors receive higher downside risk spillover from the US banking system during downside market movements compared to upside risk spillover effects. Interestingly, an equally weighted portfolio of US and GCC banking stocks can provide relatively higher diversification benefits. These findings have implications for portfolio diversification, asset allocation and hedging strategies. Full article
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17 pages, 3037 KiB  
Article
Reverse Mortgage Risks. Time Evolution of VaR in Lump-Sum Solutions
by Iván de la Fuente, Eliseo Navarro and Gregorio Serna
Mathematics 2020, 8(11), 2043; https://doi.org/10.3390/math8112043 - 17 Nov 2020
Cited by 5 | Viewed by 2198
Abstract
In this study, we analyzed the risk faced by the reverse mortgage provider in the case of the lump-sum solution, which is increasingly becoming one of the most popular types of reverse mortgages. The risk faced by the mortgage provider was estimated by [...] Read more.
In this study, we analyzed the risk faced by the reverse mortgage provider in the case of the lump-sum solution, which is increasingly becoming one of the most popular types of reverse mortgages. The risk faced by the mortgage provider was estimated by means of a value at risk (VaR) procedure that involves a Monte Carlo simulation method and an ARMA-EGARCH assumption for modeling house price returns in the United Kingdom from 1952 to 2019. The results showed that the reverse mortgage provider faced higher risk and consequently needed to allocate more funds to meet its regulatory capital requirements in the case of relatively young borrowers, especially when they reached their life expectancy and had high roll-up rates. The risk was even higher in the case of the female population. Furthermore, care must be taken when the rental yield rate is higher than the risk-free rate, as is currently the case, as the value of the no-negative-equity guarantee (NNEG) is relatively high and results in higher value at risk (VaR) and expected shortfall (ES) values. These results have important implications in terms of policy decision making when determining the countercyclical buffer for reverse mortgages in Basel III, as well as from a managerial perspective when determining the economic capital needed to support the risk taken by the lender. Full article
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34 pages, 10504 KiB  
Article
Is There a Connection between Sovereign CDS Spreads and the Stock Market? Evidence for European and US Returns and Volatilities
by Laura Ballester and Ana González-Urteaga
Mathematics 2020, 8(10), 1667; https://doi.org/10.3390/math8101667 - 28 Sep 2020
Cited by 6 | Viewed by 2435
Abstract
This study complements the current literature, providing a thorough investigation of the lead–lag connection between stock indices and sovereign credit default swap (CDS) returns for 14 European countries and the US over the period 2004–2016. We use a rolling VAR framework that enables [...] Read more.
This study complements the current literature, providing a thorough investigation of the lead–lag connection between stock indices and sovereign credit default swap (CDS) returns for 14 European countries and the US over the period 2004–2016. We use a rolling VAR framework that enables us to analyse the connection process over time covering both crisis and non-crisis periods. In addition, we analyse the relationship between stock market volatility and CDS returns. We find that the connection between the credit and equity markets does exist and that it is time variable and seems to be related to financial crises. We also observe that stock market returns anticipate sovereign CDS returns, and sovereign CDSs anticipate the conditional volatility of equity returns, closing a connectedness circle between markets. Contribution percentages in terms of returns are more intense in the US than in Europe and the opposite result is found with respect to volatilities. Within Europe, a greater impact in Eurozone countries compared to non-Eurozone countries is observed. Finally, an additional analysis is also carried out for the financial sector, obtaining results largely consistent with those found using sovereign data. Full article
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21 pages, 1940 KiB  
Article
A Comparison of Forecasting Mortality Models Using Resampling Methods
by David Atance, Ana Debón and Eliseo Navarro
Mathematics 2020, 8(9), 1550; https://doi.org/10.3390/math8091550 - 10 Sep 2020
Cited by 17 | Viewed by 2955
Abstract
The accuracy of the predictions of age-specific probabilities of death is an essential objective for the insurance industry since it dramatically affects the proper valuation of their products. Currently, it is crucial to be able to accurately calculate the age-specific probabilities of death [...] Read more.
The accuracy of the predictions of age-specific probabilities of death is an essential objective for the insurance industry since it dramatically affects the proper valuation of their products. Currently, it is crucial to be able to accurately calculate the age-specific probabilities of death over time since insurance companies’ profits and the social security of citizens depend on human survival; therefore, forecasting dynamic life tables could have significant economic and social implications. Quantitative tools such as resampling methods are required to assess the current and future states of mortality behavior. The insurance companies that manage these life tables are attempting to establish models for evaluating the risk of insurance products to develop a proactive approach instead of using traditional reactive schemes. The main objective of this paper is to compare three mortality models to predict dynamic life tables. By using the real data of European countries from the Human Mortality Database, this study has identified the best model in terms of the prediction ability for each sex and each European country. A comparison that uses cobweb graphs leads us to the conclusion that the best model is, in general, the Lee–Carter model. Additionally, we propose a procedure that can be applied to a life table database that allows us to choose the most appropriate model for any geographical area. Full article
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27 pages, 1376 KiB  
Article
Improving the Representativeness of a Simple Random Sample: An Optimization Model and Its Application to the Continuous Sample of Working Lives
by Vicente Núñez-Antón, Juan Manuel Pérez-Salamero González, Marta Regúlez-Castillo and Carlos Vidal-Meliá
Mathematics 2020, 8(8), 1225; https://doi.org/10.3390/math8081225 - 25 Jul 2020
Cited by 3 | Viewed by 3158
Abstract
This paper proposes an optimization model for selecting a larger subsample that improves the representativeness of a simple random sample previously obtained from a population larger than the population of interest. The problem formulation involves convex mixed-integer nonlinear programming (convex MINLP) and is, [...] Read more.
This paper proposes an optimization model for selecting a larger subsample that improves the representativeness of a simple random sample previously obtained from a population larger than the population of interest. The problem formulation involves convex mixed-integer nonlinear programming (convex MINLP) and is, therefore, NP-hard. However, the solution is found by maximizing the size of the subsample taken from a stratified random sample with proportional allocation and restricting it to a p-value large enough to achieve a good fit to the population of interest using Pearson’s chi-square goodness-of-fit test. The paper also applies the model to the Continuous Sample of Working Lives (CSWL), which is a set of anonymized microdata containing information on individuals from Spanish Social Security records and the results prove that it is possible to obtain a larger subsample from the CSWL that (far) better represents the pensioner population for each of the waves analyzed. Full article
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16 pages, 2652 KiB  
Article
A New Wavelet Tool to Quantify Non-Periodicity of Non-Stationary Economic Time Series
by Vicente J. Bolós, Rafael Benítez and Román Ferrer
Mathematics 2020, 8(5), 844; https://doi.org/10.3390/math8050844 - 23 May 2020
Cited by 12 | Viewed by 3105
Abstract
We introduce a new wavelet tool, the windowed scale index, to study the degree of non-periodicity of time series. The windowed scale index is based on some recently defined tools, such as the windowed scalogram and the scale index. This novel measure is [...] Read more.
We introduce a new wavelet tool, the windowed scale index, to study the degree of non-periodicity of time series. The windowed scale index is based on some recently defined tools, such as the windowed scalogram and the scale index. This novel measure is appropriate for non-stationary time series whose characteristics change over time and, therefore, it can be applied to a wide variety of disciplines. Furthermore, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for the particular case of the Haar wavelet, reinforcing the interpretation of the windowed scale index as a useful tool to quantify non-periodicity. In addition, the applicability of this wavelet-based measure is illustrated through several examples, including an economic application which compares the non-periodicity of two major commodities in the world economy, such as crude oil and gold. Finally, we discuss the relationship between non-periodicity and unpredictability, comparing the windowed scale index with the sample entropy. Full article
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22 pages, 2343 KiB  
Article
Nonlinear Autoregressive Distributed Lag Approach: An Application on the Connectedness between Bitcoin Returns and the Other Ten Most Relevant Cryptocurrency Returns
by María de la O González, Francisco Jareño and Frank S. Skinner
Mathematics 2020, 8(5), 810; https://doi.org/10.3390/math8050810 - 17 May 2020
Cited by 26 | Viewed by 6180
Abstract
This article examines the connectedness between Bitcoin returns and returns of ten additional cryptocurrencies for several frequencies—daily, weekly, and monthly—over the period January 2015–March 2020 using a nonlinear autoregressive distributed lag (NARDL) approach. We find important and positive interdependencies among cryptocurrencies and significant [...] Read more.
This article examines the connectedness between Bitcoin returns and returns of ten additional cryptocurrencies for several frequencies—daily, weekly, and monthly—over the period January 2015–March 2020 using a nonlinear autoregressive distributed lag (NARDL) approach. We find important and positive interdependencies among cryptocurrencies and significant long-run relationships among most of them. In addition, non-Bitcoin cryptocurrency returns seem to react in the same way to positive and negative changes in Bitcoin returns, obtaining strong evidence of asymmetry in the short run. Finally, our results show high persistence in the impact of both positive and negative changes in Bitcoin returns on most of the other cryptocurrency returns. Thus, our model explains about 50% of the other cryptocurrency returns with changes in Bitcoin returns. Full article
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12 pages, 1946 KiB  
Article
Risk Management for Bonds with Embedded Options
by Antonio Díaz and Marta Tolentino
Mathematics 2020, 8(5), 790; https://doi.org/10.3390/math8050790 - 13 May 2020
Cited by 1 | Viewed by 3927
Abstract
This paper examines the behavior of the interest rate risk management measures for bonds with embedded options and studies factors it depends on. The contingent option exercise implies that both the pricing and the risk management of bonds requires modelling future interest rates. [...] Read more.
This paper examines the behavior of the interest rate risk management measures for bonds with embedded options and studies factors it depends on. The contingent option exercise implies that both the pricing and the risk management of bonds requires modelling future interest rates. We use the Ho and Lee (HL) and Black, Derman, and Toy (BDT) consistent interest rate models. In addition, specific interest rate measures that consider the contingent cash-flow structure of these coupon-bearing bonds must be computed. In our empirical analysis, we obtained evidence that effective duration and effective convexity depend primarily on the level of the forward interest rate and volatility. In addition, the higher the interest rate change and the lower the volatility, the greater the differences in pricing of these bonds when using the HL or BDT models. Full article
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15 pages, 2923 KiB  
Article
A Liquidity Shortfall Analysis Framework for the European Banking Sector
by Oana-Maria Georgescu, Dimitrios Laliotis, Miha Leber and Javier Población
Mathematics 2020, 8(5), 787; https://doi.org/10.3390/math8050787 - 13 May 2020
Cited by 1 | Viewed by 2896
Abstract
This paper presents an analytical framework for the identification of vulnerabilities arising from the liquidity and funding profile of banks. It is composed of two pillars—estimation of liquidity needs and the counterbalancing capacity of the total liquid assets—that determine a liquidity surplus or [...] Read more.
This paper presents an analytical framework for the identification of vulnerabilities arising from the liquidity and funding profile of banks. It is composed of two pillars—estimation of liquidity needs and the counterbalancing capacity of the total liquid assets—that determine a liquidity surplus or shortfall and the drivers for a range of plausible scenarios. Granular bank-level data on the structure of liabilities, maturation profile, liquid assets quality composition, and asset encumbrance are used for that purpose, also taking into account associated commonality effects. A new liquidity metric is introduced—the distance to liquidity stress indicator (DLSI)—which measures the required stress factor for banks to become illiquid. The novelty of the approach (i.e., taking into account asset encumbrance to determine counterbalancing capacity) provides empirical evidence that asset encumbrance has a significant impact on a bank’s liquidity position, leading to the non-linear behavior of liquidity shortfalls, even in the case of linear stress factors. Full article
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25 pages, 5653 KiB  
Article
Volatility Timing: Pricing Barrier Options on DAX XETRA Index
by Carlos Esparcia, Elena Ibañez and Francisco Jareño
Mathematics 2020, 8(5), 722; https://doi.org/10.3390/math8050722 - 04 May 2020
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Abstract
This paper analyses the impact of different volatility structures on a range of traditional option pricing models for the valuation of call down and out style barrier options. The construction of a Risk-Neutral Probability Term Structure (RNPTS) is one of the main contributions [...] Read more.
This paper analyses the impact of different volatility structures on a range of traditional option pricing models for the valuation of call down and out style barrier options. The construction of a Risk-Neutral Probability Term Structure (RNPTS) is one of the main contributions of this research, which changes in parallel with regard to the Volatility Term Structure (VTS) in the main and traditional methods of option pricing. As a complementary study, we propose the valuation of options by assuming a constant or historical volatility. The study implements the GARCH (1,1) model with regard to the continuously compound returns of the DAX XETRA Index traded at daily frequency. Current methodology allows for obtaining accuracy forecasts of the realized market barrier option premiums. The paper highlights not only the importance of selecting the right model for option pricing, but also fitting the most accurate volatility structure. Full article
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