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arXiv2010

Wealth Distributions in Asset Exchange Models

How do individuals accumulate wealth as they interact economically? We outline the consequences of a simple microscopic model in which repeated pairwise exchanges of assets between individuals build the wealth distribution of a population. This distribution is determined for generic exchange rules --- transactions that involve a fixed amount or a fixed fraction of individual wealth, as well as random or greedy exchanges. In greedy multiplicative exchange, a continuously evolving power law wealth distribution arises, a feature that qualitatively mimics empirical observations.

physics.soc-ph↗
arXiv2010

Econophysics on Real Economy -The First Decade of the Kyoto Econophysics Group-

Research activities of Kyoto Econophysics Group is reviewed. Strong emphasis has been placed on real economy. While the initial stage of research was a first high-definition data analysis on personal income, it soon progressed to firm dynamics, growth rate distribution and establishment of Pareto's law and Gibrat's law. It then led to analysis and simulation of firm dynamics on economic network. Currently it covers a wide rage of dynamics of firms and financial institutions on complex network, using Japanese large-scale network data, some of which are not available in other countries. Activities of this group for publicising and promoting understanding of econophysics is also reviewed.

q-fin.GN↗
arXiv2010

Georg de Buquoy - Founder of Mathematical Economy with South Bohemian Roots

Georg de Buquoy, Lord de Vaux, lived in Nove Hrady, Prague and Cerveny Hradek for most of his productive life. From his extensive scientific contributions, both theoretical and experimental, we expand here the discussion of his contributions to mathematical economy. He is mainly celebrated as the first persons to define correctly net yield and describe method for its optimization, which was considered "strikingly modern" still in 1950. Buquoy's program was "systematic overview of all theorems which affect maintenance and increase of national wealth" for which he correctly defined and mathematically expressed many economic terms. The most striking feature of Buquoy's writing is that he was also a very influential economic practitioner. He governed one of the wealthiest possessions in Bohemia, and perhaps in Austria, of his time. Thus his economical thinking expands from the "political part", which is economy in modern sense, to "...sources of national wealth, or the technical part of national economy ...". The complexity of Buquoy's view has little match in modern literature namely because the extent of data sources is hardly available in modern times. The article puts Buquoy's mathematical economy contributions in context to his mathematical physics thoughts and approaches. The last direct citation of Buquoy's work comes from the year 2008.

physics.hist-ph↗
arXiv2010

Modeling total expenditure on warranty claims

We approximate the distribution of total expenditure of a retail company over warranty claims incurred in a fixed period [0, T], say the following quarter. We consider two kinds of warranty policies, namely, the non-renewing free replacement warranty policy and the non-renewing pro-rata warranty policy. Our approximation holds under modest assumptions on the distribution of the sales process of the warranted item and the nature of arrivals of warranty claims. We propose a method of using historical data to statistically estimate the parameters of the approximate distribution. Our methodology is applied to the warranty claims data from a large car manufacturer for a single car model and model year.

q-fin.GN↗
arXiv2010

Is an historical economic crisis upcoming?

In this work, the time chart of Dow Jones Industrial Average (DJIA) index is analyzed and approach of recession time term is predicted, which may be hallmark of a worldwide economic crisis. However, the methods used for the prediction will be disclosed a few years from now. On the other hand, this work will be updated by the author frequently once in every few months where no revisions will be made on the previous uploads and a timestamp will designate each part. Thus, the time evolution of the crisis can be followed and the prediction may be verified by the readers in time.

q-fin.GN↗
arXiv2010

A simple model for asset price bubble formation and collapse

We consider a simple stochastic differential equation for modeling bubbles in social context. A prime example is bubbles in asset pricing, but similar mechanisms may control a range of social phenomena driven by psychological factors (for example, popularity of rock groups, or a number of students pursuing a given major). Our goal is to study the simplest possible model in which every term has a clear meaning and which demonstrates several key behaviors. The main factors that enter are tendency of mean reversion to a stable value, speculative social response triggered by trend following and random fluctuations. The interplay of these three forces may lead to bubble formation and collapse. Numerical simulations show that the equation has distinct regimes depending on the values of the parameters. We perform rigorous analysis of the weakly random regime, and study the role of change in fundamentals in igniting the bubble.

q-fin.GN↗
arXiv2013

On the Multi-Dimensional Controller and Stopper Games

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the volatility terms of the state process. Under appropriate conditions, we show that the game has a value and the value function is the unique viscosity solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation.

math.OC↗
arXiv2010

Are large complex economic systems unstable ?

Although classical economic theory is based on the concept of stable equilibrium, real economic systems appear to be always out of equilibrium. Indeed, they share many of the dynamical features of other complex systems, e.g., ecological food-webs. We focus on the relation between increasing complexity of the economic network and its stability with respect to small perturbations in the dynamical variables associated with the constituent nodes. Inherent delays and multiple time-scales suggest that economic systems will be more likely to exhibit instabilities as their complexity is increased even though the speed at which transactions are conducted has increased many-fold through technological developments. Analogous to the birth of nonlinear dynamics from Poincare's work on the question of whether the solar system is stable, we suggest that similar theoretical developments may arise from efforts by econophysicists to understand the mechanisms by which instabilities arise in the economy.

physics.soc-ph↗
arXiv2012

On the nature of financial leverage

The article presents a translation of some widespread financial terminology into the language of decision theory. For instance, financial leverage can be regarded as an object of choice or a decision. We show how the optics of decision theory allows perceiving the recently introduced metrics of see-through-leverage, which proved to be very useful in understanding the phenomenology of the recent economic crisis. The importance for practical decision making of specification of the statistical regularity of the random phenomena at hand as well as of the rationality class of the decision maker is discussed.

q-fin.RM↗
arXiv2010

Completing CVA and Liquidity: Firm-Level Positions and Collateralized Trades

Bilateral CVA as currently implement has the counterintuitive effect of profiting from one's own widening CDS spreads, i.e. increased risk of default, in practice. The unified picture of CVA and liquidity introduced by Morini & Prampolini 2010 has contributed to understanding this. However, there are two significant omissions for practical implementation that come from the same source, i.e. positions not booked in usual position-keeping systems. The first omission is firm-level positions that change value upon firm default. An example is Goodwill which is a line item on balance sheets and typically written down to zero on default. Another example would be firm Equity. The second omission relates to collateralized positions. When these positions are out of the money in future, which has a positive probability, they will require funding that cannot be secured using the position itself. These contingent future funding positions are usually not booked in any position-keeping system. We show here how to include these two types of positions and thus help to complete the unified picture of CVA and liquidity. For a particular large complex financial institution that profited $2.5B from spread widening we show that including Goodwill would have resulted in a $4B loss under conservative assumptions. Whilst we cannot make a similar assessment for its collateralized derivative portfolio we calculate both the funding costs and the CVA from own default for a range of swaps and find that CVA was a positive contribution in the examples.

q-fin.PR↗
arXiv2012

Incomplete Continuous-time Securities Markets with Stochastic Income Volatility

In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income and can trade continuously on a finite time-interval in a money market account and a single risky security. Besides establishing the existence of an equilibrium, our main result shows that if the investors' unspanned income has stochastic countercyclical volatility, the resulting equilibrium can display both lower interest rates and higher risk premia compared to the Pareto efficient equilibrium in an otherwise identical complete market.

q-fin.GN↗
arXiv2010

How sensitive are equilibrium pricing models to real-world distortions?

In both finance and economics, quantitative models are usually studied as isolated mathematical objects --- most often defined by very strong simplifying assumptions concerning rationality, efficiency and the existence of disequilibrium adjustment mechanisms. This raises the important question of how sensitive such models might be to real-world effects that violate the assumptions. We show how the consequences of rational behavior caused by perverse incentives, as well as various irrational tendencies identified by behavioral economists, can be systematically and consistently introduced into an agent-based model for a financial asset. This generates a class of models which, in the special case where such effects are absent, reduces to geometric Brownian motion --- the usual equilibrium pricing model. Thus we are able to numerically perturb a widely-used equilibrium pricing model market and investigate its stability. The magnitude of such perturbations in real markets can be estimated and the simulations imply that this is far outside the stability region of the equilibrium solution, which is no longer observed. Indeed the price fluctuations generated by endogenous dynamics, are in good general agreement with the excess kurtosis and heteroskedasticity of actual asset prices. The methodology is presented within the context of a financial market. However, there are close links to concepts and theories from both micro- and macro-economics including rational expectations, Soros' theory of reflexivity, and Minsky's theory of financial instability.

q-fin.GN↗
arXiv2010

Fifteen Years of Econophysics Research

Econophysics is a new research field, which makes an attempt to bring economics in the fold of natural sciences or specifically attempts for a "physics of economics". The term Econophysics was formally born in Kolkata in 1995. The entry on Econophysics in The New Palgrave Dictionary of Economics, 2nd Ed., Vol 2, Macmillan, NY (2008), pp 729-732, begins with "... the term 'econophysics' was neologized in 1995 at the second Statphys- Kolkata conference in Kolkata (formerly Calcutta), India ...". The Econophysics research therefore formally completes fifteen years of research by the end of this year! The importance and proliferation of the interdisciplinary research of Econophysics is highlighted in the special issue of Science & Culture, which presents a collection of twenty nine papers (giving country wise perspectives, reviews of the recent developments and original research communications), written by more than forty renowned experts in physics, mathematics or economics, from all over the world. We present here the list of contents and the editorial. The manuscript files are available at http://fiquant.mas.ecp.fr/chakraboa for preview. This special issue will be published online at http://www.scienceandculture-isna.org/journal.htm, at the end of October 2010.

q-fin.GN↗
arXiv2010

How to predict and avert economic crisis

Our study shows that many firms would accumulate at zero output level (namely, Bankruptcy status) if a perfectly competitive market reaches full employment (namely, those people who should obtain employment have obtained employment). As a result, appearance of economic crisis is determined by two points; that is, (a). Stock market approaches perfect competition; (b). Society reaches full employment. The empirical research of these two points would lead to early warning of economic crisis. Moreover, it is a surprise that the state of economic crisis would be a feasible equilibrium within the framework of the Arrow-Debreu model. That means that we can not understand the origin of economic crisis within the framework of modern economics, for example, the general equilibrium theory.

q-fin.GN↗
arXiv2010

Entering New Markets-a Challenge in Times of Crisis

After September 2008, the advanced economies severe decline caused demand for emerging economies' exports to drop and the crisis became truly global, much deeper and broader than expected. In these times of global depression, most countries and companies are affected, some more than others. The financial crisis has turned out to be much deeper and broader than expected. Entering new markets has always been a hazardous entrepreneurial attempt, but also a rewarding one, in the case of success. The paper aims to asses the market entry risk of a company trying to make a good acquisition, to buy shares of another company, activating in a foreign country. For this purpose, the case of Electroputere S.A., the old Romanian producer of railway equipment, has been chosen. The data were collected from the records of Bucharest Stock Exchange. After two years from the acquisition, one can draw a conclusion whether the strategy of the investor was a good one or a waste of money.

q-fin.GN↗
arXiv2010

Leverage Bubble

Leverage is strongly related to liquidity in a market and lack of liquidity is considered a cause and/or consequence of the recent financial crisis. A repurchase agreement is a financial instrument where a security is sold simultaneously with an agreement to buy it back at a later date. Repurchase agreements (repos) market size is a very important element in calculating the overall leverage in a financial market. Therefore, studying the behavior of repos market size can help to understand a process that can contribute to the birth of a financial crisis. We hypothesize that herding behavior among large investors led to massive over-leveraging through the use of repos, resulting in a bubble (built up over the previous years) and subsequent crash in this market in early 2008. We use the Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles and behavioral finance to study the dynamics of the repo market that led to the crash. The JLS model qualifies a bubble by the presence of characteristic patterns in the price dynamics, called log-periodic power law (LPPL) behavior. We show that there was significant LPPL behavior in the market before that crash and that the predicted range of times predicted by the model for the end of the bubble is consistent with the observations.

q-fin.GN↗