1,294 research outputs found
Mixtures of compound Poisson processes as models of tick-by-tick financial data
A model for the phenomenological description of tick-by-tick share prices in
a stock exchange is introduced. It is based on mixtures of compound Poisson
processes. Preliminary results based on Monte Carlo simulation show that this
model can reproduce various stylized facts.Comment: 12 pages, 6 figures, to appear in a special issue of Chaos, Solitons
and Fractal
Continuous-time statistics and generalized relaxation equations
Using two simple examples, the continuous-time random walk as well as a two
state Markov chain, the relation between generalized anomalous relaxation
equations and semi-Markov processes is illustrated. This relation is then used
to discuss continuous-time random statistics in a general setting, for
statistics of convolution-type. Two examples are presented in some detail: the
sum statistic and the maximum statistic.Comment: 12 pages, submitted to EPJ
Five Years of Continuous-time Random Walks in Econophysics
This paper is a short review on the application of continuos-time random
walks to Econophysics in the last five years.Comment: 14 pages. Paper presented at WEHIA 2004, Kyoto, Japa
A class of CTRWs: Compound fractional Poisson processes
This chapter is an attempt to present a mathematical theory of compound
fractional Poisson processes. The chapter begins with the characterization of a
well-known L\'evy process: The compound Poisson process. The semi-Markov
extension of the compound Poisson process naturally leads to the compound
fractional Poisson process, where the Poisson counting process is replaced by
the Mittag-Leffler counting process also known as fractional Poisson process.
This process is no longer Markovian and L\'evy. However, several analytical
results are available and some of them are discussed here. The functional limit
of the compound Poisson process is an -stable L\'evy process, whereas
in the case of the compound fractional Poisson process, one gets an
-stable L\'evy process subordinated to the fractional Poisson process.Comment: 23 pages. To be published in a World Scientific book edited by Ralf
Metzle
On the gap between an empirical distribution and an exponential distribution of waiting times for price changes in a financial market
We analyze waiting times for price changes in a foreign currency exchange
rate. Recent empirical studies of high frequency financial data support that
trades in financial markets do not follow a Poisson process and the waiting
times between trades are not exponentially distributed. Here we show that our
data is well approximated by a Weibull distribution rather than an exponential
distribution in a non-asymptotic regime. Moreover, we quantitatively evaluate
how much an empirical data is far from an exponential distribution using a
Weibull fit. Finally, we discuss a phase transition between a Weibull-law and a
power-law in the asymptotic long waiting time regime.Comment: 9 pages, 6 figures, submitted for a publication and under revie
Five Years of Continuous-time Random Walks in Econophysics
This paper is a short review on the application of continuos-time random walks to Econophysics in the last five years.Duration; Continuous-time random walk; Fractional calculus; Statistical finance
Correlations in the Bond-Future Market
We analyze the time series of overnight returns for the bund and btp futures
exchanged at LIFFE (London). The overnight returns of both assets are mapped
onto a one-dimensional symbolic-dynamics random walk: The `bond walk'. During
the considered period (October 1991 - January 1994) the bund-future market
opened earlier than the btp-future one. The crosscorrelations between the two
bond walks, as well as estimates of the conditional probability, show that they
are not independent; however each walk can be modeled by means of a trinomial
probability distribution. Monte Carlo simulations confirm that it is necessary
to take into account the bivariate dependence in order to properly reproduce
the statistical properties of the real-world data. Various investment
strategies have been devised to exploit the `prior' information obtained by the
aforementioned analysis.Comment: 10 pages, 5 figures, LaTeX2e, to be published in Physica
A note on intraday option pricing
Compound renewal processes can be used as an approximate phenomenological model of tick-by-tick price fluctuations. An exact and explicit general formula is derived for the martingale price of a European call option written on a compound renewal process. The option price is obtained using the direct method of indicator functions. The applicability of this result is discussed
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A note on intraday option pricing
Compound renewal processes can be used as an approximate phenomenological model of tick-by-tick price fluctuations. An exact and explicit general formula is derived for the martingale price of a European call option written on a compound renewal process. The option price is obtained using the direct method of indicator functions. The applicability of this result is discussed
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