Quantitative Finance

We analyze social and economic systems with a hierarchical structure and show that for such systems, it is possible to construct thermostatistics, based on the intermediate Gentile statistics. We show that in social and economic hierarchical systems there are elements that obey the Fermi-Dirac statistics and can be called fermions, as well as elements that are approximately subject to Bose-Einstein statistics and can be called bosons. We derive the first and second laws of thermodynamics for the considered economic system and show that such concepts as temperature, pressure and financial potential (which is an analogue of the chemical potential in thermodynamics) that characterize the state of the economic system as a whole, can be introduced for economic systems.

This book, which is in Spanish, provides detailed descriptions, including over 550 mathematical formulas, for over 150 trading strategies across a host of asset classes (and trading styles). This includes stocks, options, fixed income, futures, ETFs, indexes, commodities, foreign exchange, convertibles, structured assets, volatility (as an asset class), real estate, distressed assets, cash, cryptocurrencies, miscellany (such as weather, energy, inflation), global macro, infrastructure, and tax arbitrage. Some strategies are based on machine learning algorithms (such as artificial neural networks, Bayes, k-nearest neighbors). We also give: source code for illustrating out-of-sample backtesting with explanatory notes; around 2,000 bibliographic references; and over 900 glossary, acronym and math definitions. The presentation is intended to be descriptive and pedagogical. ----- Este libro proporciona descripciones detalladas, que incluyen más de 550 fórmulas matemáticas, para más de 150 estrategias de trading para una gran cantidad de clases de activos y estilos de trading. Esto incluye acciones, opciones, bonos (renta fija), futuros, ETFs, índices, commodities, divisas, bonos convertibles, activos estructurados, volatilidad (como clase de activos), bienes inmuebles, activos en distress, efectivo, criptomonedas, misceláneos (como clima, energía, inflación), macro global, infraestructura y arbitraje impositivo. Algunas estrategias se basan en algoritmos de aprendizaje automático (como redes neuronales artificiales, Bayes, k vecinos más cercanos). El libro también incluye código para backtesting fuera de la muestra con notas explicativas; cerca de 2,000 referencias bibliográficas; más de 900 términos que comprenden el glosario, acrónimos y definiciones matemáticas. La presentación pretende ser descriptiva y pedagógica.

With the advent of Web 2.0, various types of data are being produced every day. This has led to the revolution of big data. Huge amount of structured and unstructured data are produced in financial markets. Processing these data could help an investor to make an informed investment decision. In this paper, a framework has been developed to incorporate both structured and unstructured data for portfolio optimization. Portfolio optimization consists of three processes: Asset selection, Asset weighting and Asset management. This framework proposes to achieve the first two processes using a 5-stage methodology. The stages include shortlisting stocks using Data Envelopment Analysis (DEA), incorporation of the qualitative factors using text mining, stock clustering, stock ranking and optimizing the portfolio using heuristics. This framework would help the investors to select appropriate assets to make portfolio, invest in them to minimize the risk and maximize the return and monitor their performance.

Stablecoins promise to bridge fiat currencies with the world of cryptocurrencies. They provide a way for users to take advantage of the benefits of digital currencies, such as ability to transfer assets over the internet, provide assurance on minting schedules and scarcity, and enable new asset classes, while also partially mitigating their volatility risks. In this paper, we systematically discuss general design, decompose existing stablecoins into various component design elements, explore their strengths and drawbacks, and identify future directions.

Global oil price is an important factor in determining many economic variables in the world's economy. It is generally modeled as a stochastic process and have been studied through different techniques by comparing the historic time series of demand, supply and the price itself. However, there are many historic events where the demand or supply changes are not sufficient in explaining the price changes. In such cases, it is the expectations on the future changes of demand or supply that causes heavy and quick influences on the price. There are many parameters and variables that shape these expectations, and are usually neglected in traditional models. In this paper, we have proposed a model based on System Dynamics approach that takes into account these non-traditional factors. The validity of the proposed model is then evaluated using real and potential scenarios in which the proposed model follows the trend of the real data.

In an economy which could not accommodate the full employment of its labor force, it employs some labor but does not employ others. The bipartition of the labor force is random, and we characterize it by an axiom of equal employment opportunity. We value each employed individual by his or her marginal contribution to the production function; we also value each unemployed individual by the potential marginal contribution the person would make if the market hired the individual. We then use the aggregate individual value to distribute the net production to the unemployment welfare and the employment benefits. Using real-time balanced-budget rule as a constraint and policy stability as an objective, we derive a scientific formula which describes a fair, debt-free, and asymptotic risk-free tax rate for any given unemployment rate and national spending level. The tax rate minimizes the asymptotic mean, variance, semi-variance, and mean absolute deviation of the underlying posterior unemployment rate. The allocation rule stimulates employment and boosts productivity. Under some symmetry assumptions, we even find that an unemployed person should enjoy equivalent employment benefits, and the tax rate goes with this welfare equality. The tool employed is the cooperative game theory in which we assume many players. The players are randomly bipartitioned, and the payoff varies with the partition. One could apply the fair distribution rule and valuation approach to other profit-sharing or cost-sharing situations with these characteristics. This framework is open to alternative identification strategies and other forms of equal opportunity axiom.

This work is an answer to the EIOPA 2017 report. It follows from the latter that in order to assess the potential systemic risk we should take into account the build-up of risk and in particular the risk that arises in time, as well as the interlinkages in the financial sector and the whole economy. Our main tools used to analyse the systemic risk dynamics in the European insurance sector during the years 2005-2019 are the topological indices of minimum spanning trees (MST) and the deltaCoVaR measure. We address the following questions: 1) What is the contribution to systemic risk of each of the 28 largest European insurance companies whose list includes also those appearing on the G-SIIs list? 2) Does the analysis of the deltaCoVaR of those 28 insurance companies and the conclusions we draw agree with the our claims from our latest article [Wanat S., Denkowska A. 2019]. In clear: does the most important contribution to systemic risk come from the companies that have the highest betweenness centrality or the highest degree in the MST obtained?

This paper presents a simple agent-based model of an economic system, populated by agents playing different games according to their different view about social cohesion and tax payment. After a first set of simulations, correctly replicating results of existing literature, a wider analysis is presented in order to study the effects of a dynamic-adaptation rule, in which citizens may possibly decide to modify their individual tax compliance according to individual criteria, such as, the strength of their ethical commitment, the satisfaction gained by consumption of the public good and the perceived opinion of neighbors. Results show the presence of thresholds levels in the composition of society - between taxpayers and evaders - which explain the extent of damages deriving from tax evasion.

This paper proposes a general model for synchronized crowding behavior. An order parameter is introduced to quantify the level of synchronization which is shown a function of percentage of agents in reactive state. Further, synchronization is shown to be driven by the most active agents with the highest volatility. A tipping point is identified when crowd becomes self-amplifying and unstable. By applying this model, financial bubbles, market momentum and volatility patterns are simulated.

Peru's abundant natural resources and friendly trade policies has made the country a major economic player in both South America and the global community. Consequently, exports are playing an increasingly important role in Peru's national economy. Indeed, growing from 13.1% as of 1994, exports now contribute approximately 21% of the GDP of Peru as of 2015. Given Peru's growing global influence, the time is ripe for a thorough analysis of the most important factors governing its export performance. Thus, within the framework of the augmented gravity model of trade, this paper examines Peru's export performance and attempts to identify the dominant economic factors that should be further developed to increase the value of exports. The analysis was conducted from three different aspects: (1) general economic parameters' effect on Peru's export value, (2) more specific analysis into a major specific trade good, copper, and (3) the impact that regional trade agreements have had on Peru's export performance. Our panel data analysis results for each dataset revealed interesting economic trends and were consistent with the theoretical expectations of the gravity model: namely positive coefficients for economic size and negative coefficients for distance. This report's results can be a reference for the proper direction of Peruvian economic policy so as to enhance economic growth in a sustainable direction.