255 research outputs found
Limit theorems for prices of options written on semi-Markov processes
We consider plain vanilla European options written on an underlying asset that follows a continuous time semi-Markov multiplicative process. We derive a formula and a renewal type equation for the martingale option price. In the case in which intertrade times follow the Mittag-Leffler distribution, under appropriate scaling, we prove that these option prices converge to the price of an option written on geometric Brownian motion time-changed with the inverse stable subordinator. For geometric Brownian motion time changed with an inverse subordinator, in the more general case when the subordinator’s Laplace exponent is a special Bernstein function, we derive a time-fractional generalization of the equation of Black and Scholes
A statistical analysis of product prices in online markets
We empirically investigate fluctuations in product prices in online markets
by using a tick-by-tick price data collected from a Japanese price comparison
site, and find some similarities and differences between product and asset
prices. The average price of a product across e-retailers behaves almost like a
random walk, although the probability of price increase/decrease is higher
conditional on the multiple events of price increase/decrease. This is quite
similar to the property reported by previous studies about asset prices.
However, we fail to find a long memory property in the volatility of product
price changes. Also, we find that the price change distribution for product
prices is close to an exponential distribution, rather than a power law
distribution. These two findings are in a sharp contrast with the previous
results regarding asset prices. We propose an interpretation that these
differences may stem from the absence of speculative activities in product
markets; namely, e-retailers seldom repeat buy and sell of a product, unlike
traders in asset markets.Comment: 5 pages, 5 figures, 1 table, proceedings of APFA
Feller Processes: The Next Generation in Modeling. Brownian Motion, L\'evy Processes and Beyond
We present a simple construction method for Feller processes and a framework
for the generation of sample paths of Feller processes. The construction is
based on state space dependent mixing of L\'evy processes.
Brownian Motion is one of the most frequently used continuous time Markov
processes in applications. In recent years also L\'evy processes, of which
Brownian Motion is a special case, have become increasingly popular.
L\'evy processes are spatially homogeneous, but empirical data often suggest
the use of spatially inhomogeneous processes. Thus it seems necessary to go to
the next level of generalization: Feller processes. These include L\'evy
processes and in particular Brownian motion as special cases but allow spatial
inhomogeneities.
Many properties of Feller processes are known, but proving the very existence
is, in general, very technical. Moreover, an applicable framework for the
generation of sample paths of a Feller process was missing. We explain, with
practitioners in mind, how to overcome both of these obstacles. In particular
our simulation technique allows to apply Monte Carlo methods to Feller
processes.Comment: 22 pages, including 4 figures and 8 pages of source code for the
generation of sample paths of Feller processe
Basic kinetic wealth-exchange models: common features and open problems
We review the basic kinetic wealth-exchange models of Angle [J. Angle, Social
Forces 65 (1986) 293; J. Math. Sociol. 26 (2002) 217], Bennati [E. Bennati,
Rivista Internazionale di Scienze Economiche e Commerciali 35 (1988) 735],
Chakraborti and Chakrabarti [A. Chakraborti, B. K. Chakrabarti, Eur. Phys. J. B
17 (2000) 167], and of Dragulescu and Yakovenko [A. Dragulescu, V. M.
Yakovenko, Eur. Phys. J. B 17 (2000) 723]. Analytical fitting forms for the
equilibrium wealth distributions are proposed. The influence of heterogeneity
is investigated, the appearance of the fat tail in the wealth distribution and
the relaxation to equilibrium are discussed. A unified reformulation of the
models considered is suggested.Comment: Updated version; 9 pages, 5 figures, 2 table
Tactical Voting in Plurality Elections
How often will elections end in landslides? What is the probability for a
head-to-head race? Analyzing ballot results from several large countries rather
anomalous and yet unexplained distributions have been observed. We identify
tactical voting as the driving ingredient for the anomalies and introduce a
model to study its effect on plurality elections, characterized by the relative
strength of the feedback from polls and the pairwise interaction between
individuals in the society. With this model it becomes possible to explain the
polarization of votes between two candidates, understand the small margin of
victories frequently observed for different elections, and analyze the polls'
impact in American, Canadian, and Brazilian ballots. Moreover, the model
reproduces, quantitatively, the distribution of votes obtained in the Brazilian
mayor elections with two, three, and four candidates.Comment: 7 pages, 4 figure
Development of molecular and antigenic-based rapid tests for the identification of African swine fever virus in different tissues
Emerging properties of financial time series in the “Game of Life”
We explore the spatial complexity of Conway’s “Game of Life,” a prototypical cellular automaton by means of a geometrical procedure generating a two-dimensional random walk from a bidimensional lattice with periodical boundaries. The one-dimensional projection of this process is analyzed and it turns out that some of its statistical properties resemble the so-called stylized facts observed in financial time series. The scope and meaning of this result are discussed from the viewpoint of complex systems. In particular, we stress how the supposed peculiarities of financial time series are, often, overrated in their importance
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