Search Results (12)

Has the mean-variance framework become obsolete? In this paper, we replace traditional variance–covariance methods of portfolio optimisation with relative Tsallis entropy and mutual information measures. Its goal is to enhance risk management and diversification in complicated finance ecosystems. We utilize the S&P 500 and Bitwise 10 cryptocurrency indices’ daily returns (2019–2024 data) and conduct our analysis to the year 2020 under extreme shocks. Many models were trained with different configurations, like mean-variance (MV), mean-entropy (ME), and mean-mutual information (MI) traders and their corresponding variants, using Sharpe’s ratio, Jensen’s alpha, and entropy value of risk (EVAR). The findings indicate that entropic models outperform conventional models in terms of diversification and, especially, extreme risk management. Because the appropriate normalization conditions often fail to be satisfied, we can informally see that after a recalibration of the effective frontier, we obtain from EVAR an accumulated resilience aspect to these rare events while also observing the great potential of entropy-based models to replicate non-linear dependencies between assets. The results show that models combining entropy and mutual information optimise the gain–loss ratio (GLR), providing stable diversification and improved risk management, while maximising returns in complex and volatile market environments. Full article

This paper proposes a novel censored autoregressive conditional Fréchet (CAcF) model with a flexible evolution scheme for the time-varying parameters, which allows deciphering tail risk dynamics constrained by price limits from the viewpoints of different risk preferences. The proposed model can well accommodate many important empirical characteristics of financial data, such as heavy-tailedness, volatility clustering, extreme event clustering, and price limits. We then investigate tail risk dynamics via the CAcF model in the price-limited stock markets, taking entropic value at risk (EVaR) as a risk measurement. Our findings suggest that tail risk will be seriously underestimated in price-limited stock markets when the censored property of limit prices is ignored. Additionally, the evidence from the Chinese Taiwan stock market shows that widening price limits would lead to a decrease in the incidence of extreme events (hitting limit-down) but a significant increase in tail risk. Moreover, we find that investors with different risk preferences may make opposing decisions about an extreme event. In summary, the empirical results reveal the effectiveness of our model in interpreting and predicting time-varying tail behaviors in price-limited stock markets, providing a new tool for financial risk management. Full article

This study addresses market concentration among major corporations, highlighting the utility of relative entropy for understanding diversification strategies. It introduces entropic value at risk (EVaR) as a coherent risk measure, which is an upper bound to the conditional value at risk (CVaR), and explores its generalization, relativistic value at risk (RLVaR), rooted in Kaniadakis entropy. Through extensive empirical analysis on both developed (i.e., S&P 500 and Euro Stoxx 50) and developing markets (i.e., BIST 100 and Bovespa), the study evaluates entropy-based criteria in portfolio selection, investigates model behavior across different market types, and assesses the impact of cryptocurrency introduction on portfolio performance and diversification. The key finding indicates that entropy measures effectively identify optimal portfolios, particularly in scenarios of heightened risk and increased concentration, crucial for mitigating negative net performances during low returns or high turnover. Bitcoin is primarily used for diversification and performance enhancement in the BIST 100 index, while its allocation in other markets remains minimal or non-existent, confirming the extreme concentration observed in stock markets dominated by a few leading stocks. Full article

The perception in pair trading is to recognize that when two stocks move together, their prices will converge to a mean value in the future. However, finding the mean-reverted point at which the value of the pair will converge as well as the optimal boundaries of the trade is not easy, as uncertainty and model misspecifications may lead to losses. To cater to these problems, this study employed a novel entropic approach that utilizes entropy as a penalty function for the misspecification of the model. The use of entropy as a measure of risk in pair trading is a nascent idea, and this study utilized daily data for 64 companies listed on the PSX for the years 2017, 2018, and 2019 to compute their returns based on the entropic approach. The returns to these stocks were then evaluated and compared with the buy and hold strategy. The results show positive and significant returns from pair trading using an entropic approach. The entropic approach seems to have an edge to buy and hold, distance-based, and machine learning approaches in the context of the Pakistani market. Full article

Large subduction-zone earthquakes generate long-lasting and wide-spread aftershock sequences. The physical and statistical patterns of these aftershock sequences are of considerable importance for better understanding earthquake dynamics and for seismic hazard assessments and earthquake risk mitigation. In this work, we analyzed the statistical properties of 42 aftershock sequences in terms of their temporal evolution. These aftershock sequences followed recent large subduction-zone earthquakes of M ≥ 7.0 with focal depths less than 70 km that have occurred worldwide since 1976. Their temporal properties were analyzed by investigating the probability distribution of the interevent times between successive aftershocks in terms of non-extensive statistical physics (NESP). We demonstrate the presence of a crossover behavior from power-law (q ≠ 1) to exponential (q = 1) scaling for greater interevent times. The estimated entropic q-values characterizing the observed distributions range from 1.67 to 1.83. The q-exponential behavior, along with the crossover behavior observed for greater interevent times, are further discussed in terms of superstatistics and in view of a stochastic mechanism with memory effects, which could generate the observed scaling patterns of the interevent time evolution in earthquake aftershock sequences. Full article

Motivated by new financial markets where there is no canonical choice of a risk-neutral measure, we compared two different methods for pricing options: calibration with an entropic penalty term and valuation by the Esscher measure. The main aim of this paper is to contrast the outcomes of those two methods with real-traded call option prices in a liquid market like NASDAQ stock exchange, using data referring to the period 2019–2020. Although the Esscher measure method slightly underperforms the calibration method in terms of absolute values of the percentage difference between real and model prices, it could be the only feasible choice if there are not many liquidly traded derivatives in the market. Full article

Assuming the importance of a “socioeconomic mosaic” influencing soil and land degradation at the landscape scale, spatial contexts should be considered in the analysis of desertification risk as a base for the design of appropriate counteracting strategies. A holistic approach grounded on a multi-scale qualitative and quantitative assessment is required to identify optimal development strategies regulating the socioeconomic dimensions of land degradation. In the last few decades, the operational thinking at the base of a comprehensive, holistic theory of land degradation evolved toward many different conceptual steps. Moving from empirical, qualitative and unstructured frameworks to a more structured, rational and articulated thinking, such theoretical approaches have been usually oriented toward complex and non-linear dynamics benefiting from progressive and refined approximations. Based on these premises, eleven disciplinary approaches were identified and commented extensively on in the present study, and were classified along a gradient of increasing complexity, from more qualitative and de-structured frameworks to more articulated, non-linear thinking aimed at interpreting the intrinsic fragmentation and heterogeneity of environmental and socioeconomic processes underlying land degradation. Identifying, reviewing and classifying such approaches demonstrated that the evolution of global thinking in land degradation was intimately non-linear, developing narrative and deductive approaches together with inferential, experimentally oriented visions. Focusing specifically on advanced economies in the world, our review contributes to systematize multiple—sometimes entropic—interpretations of desertification processes into a more organized framework, giving value to methodological interplays and specific interpretations of the latent processes underlying land degradation. Full article

Measures of directed information are obtained through classical measures of information by taking into account specific qualitative characteristics of each event. These measures are classified into two main categories, the entropic and the divergence measures. Many times in statistics we wish to emphasize not only on the quantitative characteristics but also on the qualitative ones. For example, in financial risk analysis it is common to take under consideration the existence of fat tails in the distribution of returns of an asset (especially the left tail) and in biostatistics to use robust statistical methods to trim extreme values. Motivated by these needs in this work we present, study and provide simulations for measures of directed information. These measures quantify the information with emphasis on specific parts (or events) of their probability distribution, without losing the whole information of the less significant parts and at the same time by concentrating on the information of the parts we care about the most. Full article

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The objective of the paper is to lay down an alternative framework for modeling dynamics. An important information about the dynamics of a stock’s price is scale invariance. By imposing the scale invariant symmetry, we arrive at choosing the logarithm of the stock’s price as the proper variable to model. The dynamics of stock log price is derived using two pieces of information, the continuity of motion and the directionality constraint. The resulting model is the same as the Geometric Brownian Motion, GBM, of the stock price which is manifestly scale invariant. Furthermore, we come up with the dynamics of probability density function, which is a Fokker–Planck equation. Next, we extend the model to value the European Options on a stock. Derivative securities ought to be prices such that there is no arbitrage. To ensure the no-arbitrage pricing, we derive the risk-neutral measure by incorporating the risk-neutral information. Consequently, the Black–Scholes model and the Black–Scholes-Merton differential equation are derived. Full article

An Entropic Dynamics of exchange rates is laid down to model the dynamics of foreign exchange rates, FX, and European Options on FX. The main objective is to represent an alternative framework to model dynamics. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. Entropic Dynamics is an application of entropic inference, which is equipped with the entropic notion of time to model dynamics. The scale invariance is a symmetry of the dynamics of exchange rates, which is manifested in our formalism. To make the formalism manifestly invariant under this symmetry, we arrive at choosing the logarithm of the exchange rate as the proper variable to model. By taking into account the relevant information about the exchange rates, we derive the Geometric Brownian Motion, GBM, of the exchange rate, which is manifestly invariant under the scale transformation. Securities should be valued such that there is no arbitrage opportunity. To this end, we derive a risk-neutral measure to value European Options on FX. The resulting model is the celebrated Garman–Kohlhagen model. Full article

Micellar systems consisting of a surfactant and an additive such as an organic salt or an acid usually self-organize as a series of worm-like micelles that ultimately form a micellar network. The nature of the additive influences micellar structure and properties such as aggregate lifetime. For ionic surfactants such as sodium dodecyl sulfate (SDS), CMC decreases with increasing temperature to a minimum in the low-temperature region beyond which it exhibits the opposite trend. The presence of additives in a surfactant micellar system also modifies monomer interactions in aggregates, thereby altering CMC and conductance. Because the standard deviation of β was always lower than 10%, its slight decrease with increasing temperature was not significant. However, the absolute value of Gibbs free enthalpy, a thermodynamic potential that can be used to calculate the maximum of reversible work, increased with increasing temperature and caffeic acid concentration. Micellization in the presence of caffeic acid was an endothermic process, which was entropically controlled. The enthalpy and enthropy positive values resulted from melting of “icebergs” or “flickering clusters” around the surfactant, leading to increased packing of hydrocarbon chains within the micellar core in a non-random manner. This can be possibly explained by caffeic acid governing the 3D matrix structure of water around the micellar aggregates. The fact that both enthalpy and entropy were positive testifies to the importance of hydrophobic interactions as a major driving force for micellization. Micellar systems allow the service life of some products to be extended without the need to increase the amounts of post-harvest storage preservatives used. If a surfactant is not an allowed ingredient or food additive, carefully washing it off before the product is consumed can avoid any associated risks. In this work, we examined the influence of temperature and SDS concentration on the properties of SDS–caffeic acid micellar systems. Micellar properties can be modified with various additives to develop new uses for micelles. This allows smaller amounts of additives to be used without detracting from their benefits. Full article

This paper considers risks of the investment portfolio, which consist of distributed mortgages and sold European call options. It is assumed that the stream of the credit payments could fall by a jump. The time of the jump is modeled by the exponential distribution. We suggest that the returns on stock are variance-gamma distributed. The value at risk, the expected shortfall and the entropic risk measure for this portfolio are calculated in closed forms. The obtained formulas exploit the values of generalized hypergeometric functions. Full article