dorsal/arxiv
View SchemaApplications of physics to finance and economics: returns, trading activity and income
| Authors | A. Christian Silva |
|---|---|
| Categories | |
| ArXiv ID | physics/0507022 |
| URL | https://arxiv.org/abs/physics/0507022 |
Abstract
This dissertation reports work where physics methods are applied to financial and economical problems. The first part studies stock market data (chapter 1 to 5). The second part is devoted to personal income in the USA (chapter 6). We first study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. For mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an exponential law. At longer times, the exponential law continuously evolves into Gaussian distribution. After characterizing the stock returns at mesoscopic time lags, we study the subordination hypothesis. The integrated volatility V_t constructed from the number of trades process can be used as a subordinator for a Brownian motion. This subordination is able to describe approximatly 85% of the stock returns for time lags that start at 1 hour but are shorter than one day. Finally, we show that the CIR process describes well enough the empirical V_t process, such that the corresponding Heston model is able to describe the log-returns x_t process, with approximately the maximum quality that the subordination allows. Finally, we study the time evolution of the personal income distribution. We find that the personal income distribution in the USA has a well-defined two-income-class structure. The majority of population (97-99%) belongs to the lower income class characterized by the exponential Boltzmann-Gibb(``thermal'') distribution, whereas the higher income class (1-3% of population) has a Pareto power-law (``superthermal'') distribution. We show that the ``thermal'' part is stationary in time.
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"abstract": "This dissertation reports work where physics methods are applied to financial\nand economical problems. The first part studies stock market data (chapter 1 to\n5). The second part is devoted to personal income in the USA (chapter 6).\n We first study the probability distribution of stock returns at mesoscopic\ntime lags (return horizons) ranging from about an hour to about a month. For\nmesoscopic times the bulk of the distribution (more than 99% of the\nprobability) follows an exponential law. At longer times, the exponential law\ncontinuously evolves into Gaussian distribution.\n After characterizing the stock returns at mesoscopic time lags, we study the\nsubordination hypothesis. The integrated volatility V_t constructed from the\nnumber of trades process can be used as a subordinator for a Brownian motion.\nThis subordination is able to describe approximatly 85% of the stock returns\nfor time lags that start at 1 hour but are shorter than one day. Finally, we\nshow that the CIR process describes well enough the empirical V_t process, such\nthat the corresponding Heston model is able to describe the log-returns x_t\nprocess, with approximately the maximum quality that the subordination allows.\n Finally, we study the time evolution of the personal income distribution. We\nfind that the personal income distribution in the USA has a well-defined\ntwo-income-class structure. The majority of population (97-99%) belongs to the\nlower income class characterized by the exponential Boltzmann-Gibb(``thermal\u0027\u0027)\ndistribution, whereas the higher income class (1-3% of population) has a Pareto\npower-law (``superthermal\u0027\u0027) distribution. We show that the ``thermal\u0027\u0027 part is\nstationary in time.",
"arxiv_id": "physics/0507022",
"authors": [
"A. Christian Silva"
],
"categories": [
"physics.soc-ph",
"q-fin.GN"
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"title": "Applications of physics to finance and economics: returns, trading activity and income",
"url": "https://arxiv.org/abs/physics/0507022"
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