Quantitative Finance

As the decade turns, we reflect on nearly thirty years of successful manipulation of the world's public equity markets. This reflection highlights a few of the key enabling ingredients and lessons learned along the way. A quantitative understanding of market impact and its decay, which we cover briefly, lets you move long-term market prices to your advantage at acceptable cost. Hiding your footprints turns out to be less important than moving prices in the direction most people want them to move. Widespread (if misplaced) trust of market prices -- buttressed by overestimates of the cost of manipulation and underestimates of the benefits to certain market participants -- makes price manipulation a particularly valuable and profitable tool. Of the many recent stories heralding the dawn of the present golden age of misinformation, the manipulation leading to the remarkable increase in the market capitalization of the world's publicly traded companies over the past three decades is among the best.

In this paper we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. This formula is useful for pricing and risk management as well as for extracting the implied volatility from quoted options. The latter is of particular importance since it indicates the risk of the underlying and it is the main component of the option's price. Further we estimate numerically the approximating error of the suggested solution and, by comparing our results in computing the implied volatility with the most common methods available in literature we discuss the challenges of this approach.

We study the fundamental differences that separate: Litecoin; Bitcoin Gold; Bitcoin Cash; Ethereum; and Zcash from Bitcoin, and draw analysis to how these features are appreciated by the market, to ultimately make an inference as to how future successful cryptocurrencies may behave. We use Google Trend data, as well as price, volume and market capitalization data sourced from this http URL to support this analysis. We find that Litecoin's shorter block times offer benefits in commerce, but drawbacks in the mining process through orphaned blocks. Zcash holds a niche use for anonymous transactions, benefitting areas of the world lacking in economic freedom. Bitcoin Cash suffers from centralization in the mining process, while the greater decentralization of Bitcoin Gold has generally left it to stagnate. Ether's greater functionality offers the greatest threat to Bitcoin's dominance in the market. A coin that incorporates several of these features can be technically better than Bitcoin, but the first-to-marketadvantage of Bitcoin should keep its dominant position in the market.

A simple but useful method of reciprocal values is introduced, explained and illustrated. This method simplifies the analysis of hyperbolic distributions, which are causing serious problems in the demographic and economic research. It allows for a unique identification of hyperbolic distributions and for unravelling components of more complicated trajectories. This method is illustrated by a few examples. They show that fundamental postulates of the demographic and economic research are contradicted by data, even by precisely the same data, which are used in this research. The generally accepted postulates are based on the incorrect understanding of hyperbolic distributions, which characterise the historical growth of population and the historical economic growth. In particular, data used, but never analysed, during the formulation of the Unified Growth Theory show that this theory is based on fundamentally incorrect premises and thus is fundamentally defective. Application of this simple method of analysis points to new directions in the demographic and economic research. It suggests simpler interpretations of the mechanism of growth. The concept or the evidence of the past primitive and difficult living conditions, which might be perhaps described as some kind of stagnation, is not questioned or disputed. It is only demonstrated that trajectories of the past economic growth and of the growth of population were not reflecting any form of stagnation and thus that they were not shaped by these primitive and difficult living conditions. The concept or evidence of an explosion in technology, medicine, education and in the improved living conditions is not questioned or disputed. It is only demonstrated that this possible explosion is not reflected in the trajectories of the economic growth and of the growth of population.

Catastrophic events, though rare, do occur and when they occur, they have devastating effects. It is, therefore, of utmost importance to understand the complexity of the underlying dynamics and signatures of catastrophic events, such as market crashes. For deeper understanding, we choose the US and Japanese markets from 1985 onward, and study the evolution of the cross-correlation structures of stock return matrices and their eigenspectra over different short time-intervals or "epochs". A slight non-linear distortion is applied to the correlation matrix computed for any epoch, leading to the emerging spectrum of eigenvalues. The statistical properties of the emerging spectrum display: (i) the shape of the emerging spectrum reflects the market instability, (ii) the smallest eigenvalue may be able to statistically distinguish the nature of a market turbulence or crisis -- internal instability or external shock, and (iii) the time-lagged smallest eigenvalue has a statistically significant correlation with the mean market cross-correlation. The smallest eigenvalue seems to indicate that the financial market has become more turbulent in a similar way as the mean does. Yet we show features of the smallest eigenvalue of the emerging spectrum that distinguish different types of market instabilities related to internal or external causes. Based on the paradigmatic character of financial time series for other complex systems, the capacity of the emerging spectrum to understand the nature of instability may be a new feature, which can be broadly applied.

Proponents of behavioral finance have identified several "puzzles" in the market that are inconsistent with rational finance theory. One such puzzle is the "excess volatility puzzle". Changes in equity prices are too large given changes in the fundamentals that are expected to change equity prices. In this paper, we offer a resolution to the excess volatility puzzle within the context of rational finance. We empirically show that market inefficiency attributable to the volatility of excess return across time is caused by fitting an improper distribution to the historical returns. Our results indicate that the variation of gross excess returns is attributable to poorly fitting the tail of the return distribution and that the puzzle disappears by employing a more appropriate distribution for the return data. The new distribution that we introduce in this paper that better fits the historical return distribution of stocks explains the excess volatility in the market and thereby explains the volatility puzzle. Failing to estimate the historical returns using the proper distribution is only one possible explanation for the existence of the volatility puzzle. However, it offers statistical models within the rational finance framework which can be used without relying on behavioral finance assumptions when searching for an explanation for the volatility puzzle.

The importance of supply chain management in analyzing and later catalyzing economic expectations while simultaneously prioritizing cleaner production aspects is a vital component of modern finance. Such predictions, though, are often known to be less than accurate due to the ubiquitous uncertainty plaguing most business decisions. Starting from a multi-dimensional cost function defining the sustainability of the supply chain (SC) kernel, this article outlines a 4-component SC module - environmental, demand, economic, and social uncertainties - each ranked according to its individual weight. Our mathematical model then assesses the viability of a sustainable business by first ranking the potentially stochastic variables in order of their subjective importance, and then optimizing the cost kernel, defined from a utility function. The model will then identify conditions (as equations) validating the sustainability of a business venture. The ranking is initially obtained from an Analytical Hierarchical Process; the resultant weighted cost function is then optimized to analyze the impact of market uncertainty based on our supply chain model. Model predictions are then ratified against SME data to emphasize the importance of cleaner production in business strategies.

Nowadays, financial data analysis is becoming increasingly important in the business market. As companies collect more and more data from daily operations, they expect to extract useful knowledge from existing collected data to help make reasonable decisions for new customer requests, e.g. user credit category, confidence of expected return, etc. Banking and financial institutes have applied different data mining techniques to enhance their business performance. Among these techniques, clustering has been considered as a significant method to capture the natural structure of data. However, there are not many studies on clustering approaches for financial data analysis. In this paper, we evaluate different clustering algorithms for analysing different financial datasets varied from time series to transactions. We also discuss the advantages and disadvantages of each method to enhance the understanding of inner structure of financial datasets as well as the capability of each clustering method in this context.

We demonstrate the existence of an empirical linkage between the nominal financial networks and the underlying economic fundamentals across countries. We construct the nominal return correlation networks from daily data to encapsulate sector-level dynamics and figure the relative importance of the sectors in the nominal network through a measure of centrality and clustering algorithms. The eigenvector centrality robustly identifies the backbone of the minimum spanning tree defined on the return networks as well as the primary cluster in the multidimensional scaling map. We show that the sectors that are relatively large in size, defined with the metrics market capitalization, revenue and number of employees, constitute the core of the return networks, whereas the periphery is mostly populated by relatively smaller sectors. Therefore, sector-level nominal return dynamics is anchored to the real size effect, which ultimately shapes the optimal portfolios for risk management. Our results are reasonably robust across 27 countries of varying degrees of prosperity and across periods of market turbulence (2008-09) as well as relative calmness (2015-16).

We present a simplistic model of the competition between different currencies. Each individual is free to choose the currency that minimizes his transaction costs, which arise whenever his exchanging relations have chosen a different currency. We show that competition between currencies does not necessarily converge to the emergence of a single currency. For large systems, we prove that two distinct communities using different currencies in the initial state will remain forever in this fractionalized state.