AN INTRODUCTION to ECONOPHYSICS Correlations and Complexity in Finance
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Correlation Risk Modeling and Management 3GFFIRS 11/21/2013 17:55:45 Page Ii
3GFLAST 11/18/2013 11:40:37 Page xviii 3GFFIRS 11/21/2013 17:55:45 Page i Correlation Risk Modeling and Management 3GFFIRS 11/21/2013 17:55:45 Page ii Founde d in 1807, John Wiley & Son s is th e oldest independ ent publ ishing company in the Uni ted States . With of fices in North America , Euro pe, Austral ia, and Asia, Wil ey is global ly committed to develop ing an d market ing print and electron ic products and services for our cu stomers ’ profess ional and personal knowle dge an d unde rstandi ng. The Wil ey Finan ce series contains books written speci fically for financ e and invest ment pr ofessionals as wel l as sophist icated indivi dual investo rs and their financial advisor s. Book topics range from portfol io managem ent to e-comm erce, risk managem ent, finan cial engineer ing, valuation , and fi nancial instrument analysis, as well as much more. For a lis t of available titles, visit our Web site at ww w.Wil eyFinance. com. 3GFFIRS 11/21/2013 17:55:45 Page iii Correlation Risk Modeling and Management An Applied Guide Including the Basel III Correlation Framework— with Interactive Correlation Models in Excel/VBA GUNTER MEISSNER 3GFFIRS 11/21/2013 17:55:45 Page iv Cover image: iStockphoto.com/logoboom Cover design: John Wiley & Sons, Inc. Copyright 2014 by John Wiley & Sons Singapore Pte. Ltd. Published by John Wiley & Sons Singapore Pte. Ltd. 1 Fusionopolis Walk, #07-01, Solaris South Tower, Singapore 138628 All rights reserved. -
Mathematical Finance
Mathematical Finance 6.1I nterest and Effective Rates In this section, you will learn about various ways to solve simple and compound interest problems related to bank accounts and calculate the effective rate of interest. Upon completion you will be able to: • Apply the simple interest formula to various financial scenarios. • Apply the continuously compounded interest formula to various financial scenarios. • State the difference between simple interest and compound interest. • Use technology to solve compound interest problems, not involving continuously compound interest. • Compute the effective rate of interest, using technology when possible. • Compare multiple accounts using the effective rates of interest/effective annual yields. Working with Simple Interest It costs money to borrow money. The rent one pays for the use of money is called interest. The amount of money that is being borrowed or loaned is called the principal or present value. Interest, in its simplest form, is called simple interest and is paid only on the original amount borrowed. When the money is loaned out, the person who borrows the money generally pays a fixed rate of interest on the principal for the time period the money is kept. Although the interest rate is often specified for a year, annual percentage rate, it may be specified for a week, a month, or a quarter, etc. When a person pays back the money owed, they pay back the original amount borrowed plus the interest earned on the loan, which is called the accumulated amount or future value. Definition Simple interest is the interest that is paid only on the principal, and is given by I = Prt where, I = Interest earned or paid P = Present value or Principal r = Annual percentage rate (APR) changed to a decimal* t = Number of years* *The units of time for r and t must be the same. -
Math 581/Econ 673: Mathematical Finance
Math 581/Econ 673: Mathematical Finance This course is ideal for students who want a rigorous introduction to finance. The course covers the following fundamental topics in finance: the time value of money, portfolio theory, capital market theory, security price modeling, and financial derivatives. We shall dissect financial models by isolating their central assumptions and conceptual building blocks, showing rigorously how their gov- erning equations and relations are derived, and weighing critically their strengths and weaknesses. Prerequisites: The mathematical prerequisites are Math 212 (or 222), Math 221, and Math 230 (or 340) or consent of instructor. The course assumes no prior back- ground in finance. Assignments: assignments are team based. Grading: homework is 70% and the individual in-class project is 30%. The date, time, and location of the individual project will be given during the first week of classes. The project is mandatory; missing it is analogous to missing a final exam. Text: A. O. Petters and X. Dong, An Introduction to Mathematical Finance with Appli- cations (Springer, New York, 2016) The text will be allowed as a reference during the individual project. The following books are not required and may serve as supplements: - M. Capi´nski and T. Zastawniak, Mathematics for Finance (Springer, London, 2003) - J. Hull, Options, Futures, and Other Derivatives (Pearson Prentice Hall, Upper Saddle River, 2015) - R. McDonald, Derivative Markets, Second Edition (Addison-Wesley, Boston, 2006) - S. Roman, Introduction to the Mathematics of Finance (Springer, New York, 2004) - S. Ross, An Elementary Introduction to Mathematical Finance, Third Edition (Cambrige U. Press, Cambridge, 2011) - P. Wilmott, S. -
Mathematics and Financial Economics Editor-In-Chief: Elyès Jouini, CEREMADE, Université Paris-Dauphine, Paris, France; [email protected]
ABCD springer.com 2nd Announcement and Call for Papers Mathematics and Financial Economics Editor-in-Chief: Elyès Jouini, CEREMADE, Université Paris-Dauphine, Paris, France; [email protected] New from Springer 1st issue in July 2007 NEW JOURNAL Submit your manuscript online springer.com Mathematics and Financial Economics In the last twenty years mathematical finance approach. When quantitative methods useful to has developed independently from economic economists are developed by mathematicians theory, and largely as a branch of probability and published in mathematical journals, they theory and stochastic analysis. This has led to often remain unknown and confined to a very important developments e.g. in asset pricing specific readership. More generally, there is a theory, and interest-rate modeling. need for bridges between these disciplines. This direction of research however can be The aim of this new journal is to reconcile these viewed as somewhat removed from real- two approaches and to provide the bridging world considerations and increasingly many links between mathematics, economics and academics in the field agree over the necessity finance. Typical areas of interest include of returning to foundational economic issues. foundational issues in asset pricing, financial Mainstream finance on the other hand has markets equilibrium, insurance models, port- often considered interesting economic folio management, quantitative risk manage- problems, but finance journals typically pay ment, intertemporal economics, uncertainty less -
Lecture 13: Financial Disasters and Econophysics
Lecture 13: Financial Disasters and Econophysics Big problem: Power laws in economy and finance vs Great Moderation: (Source: http://www.mckinsey.com/business-functions/strategy-and-corporate-finance/our-insights/power-curves-what- natural-and-economic-disasters-have-in-common Analysis of big data, discontinuous change especially of financial sector, where efficient market theory missed the boat has drawn attention of specialists from physics and mathematics. Wall Street“quant”models may have helped the market implode; and collapse spawned econophysics work on finance instability. NATURE PHYSICS March 2013 Volume 9, No 3 pp119-197 : “The 2008 financial crisis has highlighted major limitations in the modelling of financial and economic systems. However, an emerging field of research at the frontiers of both physics and economics aims to provide a more fundamental understanding of economic networks, as well as practical insights for policymakers. In this Nature Physics Focus, physicists and economists consider the state-of-the-art in the application of network science to finance.” The financial crisis has made us aware that financial markets are very complex networks that, in many cases, we do not really understand and that can easily go out of control. This idea, which would have been shocking only 5 years ago, results from a number of precise reasons. What does physics bring to social science problems? 1- Heterogeneous agents – strange since physics draws strength from electron is electron is electron but STATISTICAL MECHANICS --- minority game, finance artificial agents, 2- Facility with huge data sets – data-mining for regularities in time series with open eyes. 3- Network analysis 4- Percolation/other models of “phase transition”, which directs attention at boundary conditions AN INTRODUCTION TO ECONOPHYSICS Correlations and Complexity in Finance ROSARIO N. -
Processes on Complex Networks. Percolation
Chapter 5 Processes on complex networks. Percolation 77 Up till now we discussed the structure of the complex networks. The actual reason to study this structure is to understand how this structure influences the behavior of random processes on networks. I will talk about two such processes. The first one is the percolation process. The second one is the spread of epidemics. There are a lot of open problems in this area, the main of which can be innocently formulated as: How the network topology influences the dynamics of random processes on this network. We are still quite far from a definite answer to this question. 5.1 Percolation 5.1.1 Introduction to percolation Percolation is one of the simplest processes that exhibit the critical phenomena or phase transition. This means that there is a parameter in the system, whose small change yields a large change in the system behavior. To define the percolation process, consider a graph, that has a large connected component. In the classical settings, percolation was actually studied on infinite graphs, whose vertices constitute the set Zd, and edges connect each vertex with nearest neighbors, but we consider general random graphs. We have parameter ϕ, which is the probability that any edge present in the underlying graph is open or closed (an event with probability 1 − ϕ) independently of the other edges. Actually, if we talk about edges being open or closed, this means that we discuss bond percolation. It is also possible to talk about the vertices being open or closed, and this is called site percolation. -
From Big Data to Econophysics and Its Use to Explain Complex Phenomena
Journal of Risk and Financial Management Review From Big Data to Econophysics and Its Use to Explain Complex Phenomena Paulo Ferreira 1,2,3,* , Éder J.A.L. Pereira 4,5 and Hernane B.B. Pereira 4,6 1 VALORIZA—Research Center for Endogenous Resource Valorization, 7300-555 Portalegre, Portugal 2 Department of Economic Sciences and Organizations, Instituto Politécnico de Portalegre, 7300-555 Portalegre, Portugal 3 Centro de Estudos e Formação Avançada em Gestão e Economia, Instituto de Investigação e Formação Avançada, Universidade de Évora, Largo dos Colegiais 2, 7000 Évora, Portugal 4 Programa de Modelagem Computacional, SENAI Cimatec, Av. Orlando Gomes 1845, 41 650-010 Salvador, BA, Brazil; [email protected] (É.J.A.L.P.); [email protected] (H.B.B.P.) 5 Instituto Federal do Maranhão, 65075-441 São Luís-MA, Brazil 6 Universidade do Estado da Bahia, 41 150-000 Salvador, BA, Brazil * Correspondence: [email protected] Received: 5 June 2020; Accepted: 10 July 2020; Published: 13 July 2020 Abstract: Big data has become a very frequent research topic, due to the increase in data availability. In this introductory paper, we make the linkage between the use of big data and Econophysics, a research field which uses a large amount of data and deals with complex systems. Different approaches such as power laws and complex networks are discussed, as possible frameworks to analyze complex phenomena that could be studied using Econophysics and resorting to big data. Keywords: big data; complexity; networks; stock markets; power laws 1. Introduction Big data has become a very popular expression in recent years, related to the advance of technology which allows, on the one hand, the recovery of a great amount of data, and on the other hand, the analysis of that data, benefiting from the increasing computational capacity of devices. -
Understanding Complex Systems: a Communication Networks Perspective
1 Understanding Complex Systems: A Communication Networks Perspective Pavlos Antoniou and Andreas Pitsillides Networks Research Laboratory, Computer Science Department, University of Cyprus 75 Kallipoleos Street, P.O. Box 20537, 1678 Nicosia, Cyprus Telephone: +357-22-892687, Fax: +357-22-892701 Email: [email protected], [email protected] Technical Report TR-07-01 Department of Computer Science University of Cyprus February 2007 Abstract Recent approaches on the study of networks have exploded over almost all the sciences across the academic spectrum. Over the last few years, the analysis and modeling of networks as well as networked dynamical systems have attracted considerable interdisciplinary interest. These efforts were driven by the fact that systems as diverse as genetic networks or the Internet can be best described as complex networks. On the contrary, although the unprecedented evolution of technology, basic issues and fundamental principles related to the structural and evolutionary properties of networks still remain unaddressed and need to be unraveled since they affect the function of a network. Therefore, the characterization of the wiring diagram and the understanding on how an enormous network of interacting dynamical elements is able to behave collectively, given their individual non linear dynamics are of prime importance. In this study we explore simple models of complex networks from real communication networks perspective, focusing on their structural and evolutionary properties. The limitations and vulnerabilities of real communication networks drive the necessity to develop new theoretical frameworks to help explain the complex and unpredictable behaviors of those networks based on the aforementioned principles, and design alternative network methods and techniques which may be provably effective, robust and resilient to accidental failures and coordinated attacks. -
Critical Percolation As a Framework to Analyze the Training of Deep Networks
Published as a conference paper at ICLR 2018 CRITICAL PERCOLATION AS A FRAMEWORK TO ANALYZE THE TRAINING OF DEEP NETWORKS Zohar Ringel Rodrigo de Bem∗ Racah Institute of Physics Department of Engineering Science The Hebrew University of Jerusalem University of Oxford [email protected]. [email protected] ABSTRACT In this paper we approach two relevant deep learning topics: i) tackling of graph structured input data and ii) a better understanding and analysis of deep networks and related learning algorithms. With this in mind we focus on the topological classification of reachability in a particular subset of planar graphs (Mazes). Doing so, we are able to model the topology of data while staying in Euclidean space, thus allowing its processing with standard CNN architectures. We suggest a suitable architecture for this problem and show that it can express a perfect solution to the classification task. The shape of the cost function around this solution is also derived and, remarkably, does not depend on the size of the maze in the large maze limit. Responsible for this behavior are rare events in the dataset which strongly regulate the shape of the cost function near this global minimum. We further identify an obstacle to learning in the form of poorly performing local minima in which the network chooses to ignore some of the inputs. We further support our claims with training experiments and numerical analysis of the cost function on networks with up to 128 layers. 1 INTRODUCTION Deep convolutional networks have achieved great success in the last years by presenting human and super-human performance on many machine learning problems such as image classification, speech recognition and natural language processing (LeCun et al. -
Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations
Review Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations Andreas Mühlbacher * and Thomas Guhr Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany; [email protected] * Correspondence: [email protected] Received: 28 February 2018; Accepted: 19 April 2018; Published: 23 April 2018 Abstract: We review recent progress in modeling credit risk for correlated assets. We employ a new interpretation of the Wishart model for random correlation matrices to model non-stationary effects. We then use the Merton model in which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used, the correlations of which have a strong impact on the loss distribution, particularly on its tails. These correlations are non-stationary, which also influences the tails. We account for the asset fluctuations by averaging over an ensemble of random matrices that models the truly existing set of measured correlation matrices. As a most welcome side effect, this approach drastically reduces the parameter dependence of the loss distribution, allowing us to obtain very explicit results, which show quantitatively that the heavy tails prevail over diversification benefits even for small correlations. We calibrate our random matrix model with market data and show how it is capable of grasping different market situations. Furthermore, we present numerical simulations for concurrent portfolio risks, i.e., for the joint probability densities of losses for two portfolios. For the convenience of the reader, we give an introduction to the Wishart random matrix model. -
Careers in Quantitative Finance by Steven E
Careers in Quantitative Finance by Steven E. Shreve1 August 2018 1 What is Quantitative Finance? Quantitative finance as a discipline emerged in the 1980s. It is also called financial engineering, financial mathematics, mathematical finance, or, as we call it at Carnegie Mellon, computational finance. It uses the tools of mathematics, statistics, and computer science to solve problems in finance. Computational methods have become an indispensable part of the finance in- dustry. Originally, mathematical modeling played the dominant role in com- putational finance. Although this continues to be important, in recent years data science and machine learning have become more prominent. Persons working in the finance industry using mathematics, statistics and computer science have come to be known as quants. Initially relegated to peripheral roles in finance firms, quants have now taken center stage. No longer do traders make decisions based solely on instinct. Top traders rely on sophisticated mathematical models, together with analysis of the current economic and financial landscape, to guide their actions. Instead of sitting in front of monitors \following the market" and making split-second decisions, traders write algorithms that make these split- second decisions for them. Banks are eager to hire \quantitative traders" who know or are prepared to learn this craft. While trading may be the highest profile activity within financial firms, it is not the only critical function of these firms, nor is it the only place where quants can find intellectually stimulating and rewarding careers. I present below an overview of the finance industry, emphasizing areas in which quantitative skills play a role. -
An Application of Econophysics to the History of Economic Thought: the Analysis of Texts from the Frequency of Appearance of Key Words
Discussion Paper No. 2015-51 | July 15, 2015 | http://www.economics-ejournal.org/economics/discussionpapers/2015-51 An Application of Econophysics to the History of Economic Thought: The Analysis of Texts from the Frequency of Appearance of Key Words Estrella Trincado and José María Vindel Abstract This article poses a new methodology applying the statistical analysis to the economic literature. This analysis has never been used in the history of economic thought, albeit it may open up new possibilities and provide us with further explanations so as to reconsider theoretical issues. With that purpose in mind, the article applies the intermittency of the turbulence in different economic texts, and specifically in three important authors: William Stanley Jevons, Adam Smith, and Karl Marx. JEL B16 B40 C18 Z11 Keywords Econophysics; history of economic thought; bibliometrics; applications of statistical analysis Authors Estrella Trincado, Universidad Complutense de Madrid, Spain, [email protected] José María Vindel, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, Madrid, Spain Citation Estrella Trincado and José María Vindel (2015). An Application of Econophysics to the History of Economic Thought: The Analysis of Texts from the Frequency of Appearance of Key Words. Economics Discussion Papers, No 2015-51, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2015-51 Received July 7, 2015 Accepted as Economics Discussion Paper July 13, 2015 Published July 15, 2015 © Author(s) 2015. Licensed under the Creative Commons License - Attribution 3.0 1. INTRODUCTION The most obvious and usual way to deal with economic texts is to try to understand in an analytical way the theories put forward by the authors providing a scientific, social and economic context for that specific literature.