Applications of physics to finance and economics: returns, trading activity and income

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.Comment: 24 pages and 45 figures. PhD thesis presented to the committee members on May 10th 2005. This thesis is based on 3 published papers with one chapter (chapter 5) with new unpublished result

Temporal evolution of the "thermal" and "superthermal" income classes in the USA during 1983-2001

Personal income distribution in the USA has a well-defined two-class structure. The majority of population (97-99%) belongs to the lower class characterized by the exponential Boltzmann-Gibbs ("thermal") distribution, whereas the upper class (1-3% of population) has a Pareto power-law ("superthermal") distribution. By analyzing income data for 1983-2001, we show that the "thermal" part is stationary in time, save for a gradual increase of the effective temperature, whereas the "superthermal" tail swells and shrinks following the stock market. We discuss the concept of equilibrium inequality in a society, based on the principle of maximal entropy, and quantitatively show that it applies to the majority of population.Comment: v.3: 7 pages, 5 figures, EPL style, more references adde

Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact

We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an exponential law. The slope of the exponential function is determined by the variance of returns, which increases proportionally to the time lag. At longer times, the exponential law continuously evolves into Gaussian distribution. The exponential-to-Gaussian crossover is well described by the analytical solution of the Heston model with stochastic volatility.Comment: 7 pages, 12 plots, elsart.cls, submitted to the Proceedings of APFA-4. V.2: updated reference

Mortgage debt and entrepreneurship

We study the link between mortgage debt and entrepreneurship using a model of occupational choice and housing tenure in a setting where loans are recourse|like in the UK and several US states. Our model shows that as long as the mortgage interest rate exceeds the risk-free rate: (i) mortgage debt diminishes the likelihood of entrepreneurship by amplifying risk aversion; and (ii) the negative relation between mortgage debt and entrepreneurship increases with income volatility. Our model also shows that the link between housing equity and entrepreneurship is ambiguously signed because of competing portfolio and wealth effects. We use the British Household Panel Survey to test and confirm the model predictions, and deal with unobservable heterogeneity employing three research designs | individual fixed effects, housing-spell fixed effects, and instrumental variables. A one standard deviation increase in leverage reduces the probability of entrepreneurship by 10-20 percen

Properties of the open cluster Tombaugh 1 from high resolution spectroscopy and uvbyCaHβ\beta photometry

Open clusters can be the key to deepen our knowledge on various issues involving the structure and evolution of the Galactic disk and details of stellar evolution because a cluster's properties are applicable to all its members. However the number of open clusters with detailed analysis from high resolution spectroscopy and/or precision photometry imposes severe limitation on studies of these objects. To expand the number of open clusters with well-defined chemical abundances and fundamental parameters, we investigate the poorly studied, anticenter open cluster Tombaugh 1. Using precision uvbyCaH$\beta$ photometry and high resolution spectroscopy, we derive the cluster's properties and, for the first time, present detailed abundance analysis of 10 potential cluster stars. Using radial position from the cluster center and multiple color indices, we have isolated a sample of unevolved probable, single-star members of Tombaugh 1. The weighted photometric metallicity from $m_1$ and $hk$ is [Fe/H] = -0.10 $\pm$ 0.02, while a match to the Victoria-Regina Str\"{o}mgren isochrones leads to an age of 0.95 $\pm$ 0.10 Gyr and an apparent modulus of $(m-M)$ = 13.10 $\pm$ 0.10. Radial velocities identify 6 giants as probable cluster members and the elemental abundances of Fe, Na, Mg, Al, Si, Ca, Ti, Cr, Ni, Y,Ba, Ce, and Nd have been derived for both the cluster and the field stars. Tombaugh 1 appears to be a typical inner thin disk, intermediate-age open cluster of slightly subsolar metallicity, located just beyond the solar circle, with solar elemental abundance ratios except for the heavy s-process elements, which are a factor of two above solar. Its metallicity is consistent with a steep metallicity gradient in the galactocentric region between 9.5 and 12 kpc. Our study also shows that Cepheid XZ CMa is not a member of Tombaugh 1, and reveals that this Cepheid presents signs of barium enrichment.Comment: 74 pages, 15 figures, 13 tables; Accepted for publication in A