Maurizio Serva

Multiscale behaviour of volatility autocorrelations in a financial market

We perform a scaling analysis on NYSE daily returns. We show that volatility correlations are power-laws on a time range from one day to one year and, more important, that they exhibit a multiscale behaviour.

Multiscaling and clustering of volatility

The dynamics of prices in stock markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, while the distribution of returns of the most important indices is known to be a truncated Levy, the behaviour of volatility correlations is still poorly understood. What is well known is that absolute returns have memory on a long time range, this phenomenon is known in financial literature as clustering of volatility. In this paper we show that volatility correlations are power laws with a non-unique scaling exponent. This kind of multiscale phenomenology is known to be relevant in fully developed turbulence and in disordered systems and it is pointed out here for the first time for a financial series. In our study we consider the New York Stock Exchange (NYSE) daily index, from January 1966 to June 1998, for a total of 8180 working days.

The origin of fat tailed distributions in financial time series

A classic problem in physics is the origin of fat-tailed distributions generated by complex systems. We study the distributions of stock returns measured over different time lags τ. We find that destroying all correlations without changing the τ=1d distribution, by shuffling the order of the daily returns, causes the fat tails to almost vanish for τ>1d. We argue that the fat tails are caused by the well-known long-range volatility correlations that have already been systematically studied previously. Indeed, destroying only sign correlations, by shuffling the order of only the signs (but not the absolute values) of the daily returns, allows the fat tails to persist for τ>1d.

Diffusion reproduction processes

Interesting physics emerges from studying a population of reproducing individuals. Each can be regarded as a random walker, but it can either duplicate or die. Novel features of the collective behavior are quite surprising: if individuals reproduce or die freely, the life expectation is proportional to the size of the population, and if it is kept constant, the center of mass moves in space as if it were a single walker (i.e., the diffusion constant is independent of populations size). Biology-inspired interactions are also considered.

A statistical model of an evolving population with sexual reproduction

The authors introduce a statistical model of a population with a sexual reproduction mechanism, evolving in a flat fitness landscape. They show that fluctuations in the genetic overlap between different individuals in the population vanish in the infinite-population limit, contrary to the case of asexual reproduction which exhibited spin-glass-like behaviour.

Malagasy dialects and the peopling of Madagascar

The origin of Malagasy DNA is half African and half Indonesian, nevertheless the Malagasy language, spoken by the entire population, belongs to the Austronesian family. The language most closely related to Malagasy is Maanyan (Greater Barito East group of the Austronesian family), but related languages are also in Sulawesi, Malaysia and Sumatra. For this reason, and because Maanyan is spoken by a population which lives along the Barito river in Kalimantan and which does not possess the necessary skill for long maritime navigation, the ethnic composition of the Indonesian colonizers is still unclear. There is a general consensus that Indonesian sailors reached Madagascar by a maritime trek, but the time, the path and the landing area of the first colonization are all disputed. In this research, we try to answer these problems together with other ones, such as the historical configuration of Malagasy dialects, by types of analysis related to lexicostatistics and glottochronology that draw upon the automated method recently proposed by the authors. The data were collected by the first author at the beginning of 2010 with the invaluable help of Joselinà Soafara Néré and consist of Swadesh lists of 200 items for 23 dialects covering all areas of the island.

A GENERAL METHODOLOGY TO PRICE AND HEDGE DERIVATIVES IN INCOMPLETE MARKETS

We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in repeated multiplicative games originally introduced by Kelly. As particular cases we obtain the Cox–Ross–Rubinstein and Black–Scholes in the complete markets case and the Schweizer and Bouchaud–Sornette as a quadratic approximation of our prescription. Technical and numerical aspects for the practical option pricing, as large deviation theory approximation and Monte Carlo computation are discussed in detail.

Measures of lexical distance between languages

The idea of measuring distance between languages seems to have its roots in the work of the French explorer Dumont D’Urville (1832) [13]. He collected comparative word lists for various languages during his voyages aboard the Astrolabe from 1826 to 1829 and, in his work concerning the geographical division of the Pacific, he proposed a method for measuring the degree of relation among languages. The method used by modern glottochronology, developed by Morris Swadesh in the 1950s, measures distances from the percentage of shared cognates, which are words with a common historical origin. Recently, we proposed a new automated method which uses the normalized Levenshtein distances among words with the same meaning and averages on the words contained in a list. Recently another group of scholars, Bakker et al. (2009) [8] and Holman et al. (2008) [9], proposed a refined version of our definition including a second normalization. In this paper we compare the information content of our definition with the refined version in order to decide which of the two can be applied with greater success to resolve relationships among languages.

Stochastic mechanics of a Dirac particle in two spacetime dimensions

The authors develop the stochastic mechanics of a Dirac particle interacting with an arbitrary external electromagnetic field in two-dimensional Minkowski space. Their construction provides a consistent stochastic interpretation of solutions of the true (real time) Dirac equation and, in particular, gives a stochastic description of the zitterbewegung.

Efficiency in Foreign Exchange Markets

A quantitative check of weak efficiency in US dollar/German mark exchange rates is developed using high frequency data. We show the existence of long term return anomalies. We introduce a technique to measure the available information and show it can be profitable following a particular trading rule.