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Josep Perello

Publications and source records attributed to Josep Perello.

At least 19 recordsLinked to original sources
arXiv2016

Humans display a reduced set of consistent behavioral phenotypes in dyadic games

Socially relevant situations that involve strategic interactions are widespread among animals and humans alike. To study these situations, theoretical and experimental works have adopted a game-theoretical perspective, which has allowed to obtain valuable insights about human behavior. However, most of the results reported so far have been obtained from a population perspective and considered one specific conflicting situation at a time. This makes it difficult to extract conclusions about the consistency of individuals' behavior when facing different situations, and more importantly, to define a comprehensive classification of the strategies underlying the observed behaviors. Here, we present the results of a lab-in-the-field experiment in which subjects face four different dyadic games, with the aim of establishing general behavioral rules dictating individuals' actions. By analyzing our data with an unsupervised clustering algorithm, we find that all the subjects conform, with a large degree of consistency, to a limited number of behavioral phenotypes (Envious, Optimist, Pessimist, and Trustful), with only a small fraction of undefined subjects. We also discuss the possible connections to existing interpretations based on a priori theoretical approaches. Our findings provide a relevant contribution to the experimental and theoretical efforts towards the identification of basic behavioral phenotypes in a wider set of contexts without aprioristic assumptions regarding the rules or strategies behind actions. From this perspective, our work contributes to a fact-based approach to the study of human behavior in strategic situations, that could be applied to simulating societies, policy-making scenario building and even for a variety of business applications.

physics.soc-ph↗
arXiv2009

First-passage and risk evaluation under stochastic volatility

We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain approximate forms of these probabilities which prove, among other interesting properties, the non-existence of a mean first-passage time. One significant result is the evidence of extreme deviations --which implies a high risk of default-- when certain dimensionless parameter, related to the strength of the volatility fluctuations, increases. We believe that this may provide an effective tool for risk control which can be readily applicable to real markets.

q-fin.ST↗
arXiv2008

The escape problem under stochastic volatility: the Heston model

We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless volatility. We look over these results in terms of the dimensionless normal level of volatility --a ratio of the three parameters that appear in the Heston model-- and analyze their form in several assymptotic limits. Thus, for instance, we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower depending on the value of the normal level. We compare our results with those of the Wiener process and show that the assumption of stochastic volatility, in an apparent paradoxical way, increases survival and prolongs the escape time.

q-fin.ST↗
arXiv2008

Option pricing under stochastic volatility: the exponential Ornstein-Uhlenbeck model

We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics and an Ornstein-Uhlenbeck subordinated process describing the randomness of the log-volatility. We derive an approximate option price that is valid when (i) the fluctuations of the volatility are larger than its normal level, (ii) the volatility presents a slow driving force toward its normal level and, finally, (iii) the market price of risk is a linear function of the log-volatility. We study the resulting European call price and its implied volatility for a range of parameters consistent with daily Dow Jones Index data.

q-fin.PR↗
arXiv2007

The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows

In this paper we develop a model of an order-driven market where traders set bids and asks and post market or limit orders according to exogenously fixed rules. Agents are assumed to have three components to the expectation of future asset returns, namely-fundamentalist, chartist and noise trader. Furthermore agents differ in the characteristics describing these components, such as time horizon, risk aversion and the weights given to the various components. The model developed here extends a great deal of earlier literature in that the order submissions of agents are determined by utility maximisation, rather than the mechanical unit order size that is commonly assumed. In this way the order flow is better related to the ongoing evolution of the market. For the given market structure we analyze the impact of the three components of the trading strategies on the statistical properties of prices and order flows and observe that it is the chartist strategy that is mainly responsible of the fat tails and clustering in the artificial price data generated by the model. The paper provides further evidence that large price changes are likely to be generated by the presence of large gaps in the book.

q-fin.TR↗
arXiv2007

Volatility: a hidden Markov process in financial time series

The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable and only the price is known. Diffusion theory has many common points with the research on volatility, the key of the analogy being that volatility is the time-dependent diffusion coefficient of the random walk for the price return. We present a formal procedure to extract volatility from price data, by assuming that it is described by a hidden Markov process which together with the price form a two-dimensional diffusion process. We derive a maximum likelihood estimate valid for a wide class of two-dimensional diffusion processes. The choice of the exponential Ornstein-Uhlenbeck (expOU) stochastic volatility model performs remarkably well in inferring the hidden state of volatility. The formalism is applied to the Dow Jones index. The main results are: (i) the distribution of estimated volatility is lognormal, which is consistent with the expOU model; (ii) the estimated volatility is related to trading volume by a power law of the form $σ\propto V^{0.55}$; and (iii) future returns are proportional to the current volatility which suggests some degree of predictability for the size of future returns.

physics.soc-ph↗
arXiv2007

Extreme times for volatility processes

We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major financial indices. We find in all these data sets a very similar behavior that is far from being that of a simple Wiener process. It seems necessary to include a framework like the one provided by stochastic volatility models with a reverting force driving volatility toward its normal level to take into account memory and clustering effects in volatility dynamics. We also detect in data a very different behavior in the mean first-passage time depending whether the level is higher or lower than the normal level of volatility. For this reason, we discuss asymptotic approximations and confront them to empirical results with a good agreement, specially with the ExpOU model.

physics.soc-ph↗
arXiv2007

Downside Risk analysis applied to Hedge Funds universe

Hedge Funds are considered as one of the portfolio management sectors which shows a fastest growing for the past decade. An optimal Hedge Fund management requires an appropriate risk metrics. The classic CAPM theory and its Ratio Sharpe fail to capture some crucial aspects due to the strong non-Gaussian character of Hedge Funds statistics. A possible way out to this problem while keeping the CAPM simplicity is the so-called Downside Risk analysis. One important benefit lies in distinguishing between good and bad returns, that is: returns greater or lower than investor's goal. We revisit most popular Downside Risk indicators and provide new analytical results on them. We compute these measures by taking the Credit Suisse/Tremont Investable Hedge Fund Index Data and with the Gaussian case as a benchmark. In this way an unusual transversal lecture of the existing Downside Risk measures is provided.

physics.soc-ph↗
arXiv2006

Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion

The electricity market is a very peculiar market due to the large variety of phenomena that can affect the spot price. However, this market still shows many typical features of other speculative (commodity) markets like, for instance, data clustering and mean reversion. We apply the diffusion entropy analysis (DEA) to the Nordic spot electricity market (Nord Pool). We study the waiting time statistics between consecutive spot price spikes and find it to show anomalous scaling characterized by a decaying power-law. The exponent observed in data follows a quite robust relationship with the one implied by the DEA analysis. We also in terms of the DEA revisit topics like clustering, mean-reversion and periodicities. We finally propose a GARCH inspired model but for the price itself. Models in the context of stochastic volatility processes appear under this scope to have a feasible description.

physics.soc-ph↗
arXiv2006

Market memory and fat tail consequences in option pricing on the expOU stochastic volatility model

The expOU stochastic volatility model is capable of reproducing fairly well most important statistical properties of financial markets daily data. Among them, the presence of multiple time scales in the volatility autocorrelation is perhaps the most relevant which makes appear fat tails in the return distributions. This paper wants to go further on with the expOU model we have studied in Ref. 1 by exploring an aspect of practical interest. Having as a benchmark the parameters estimated from the Dow Jones daily data, we want to compute the price for the European option. This is actually done by Monte Carlo, running a large number of simulations. Our main interest is to "see" the effects of a long-range market memory from our expOU model in its subsequent European call option. We pay attention to the effects of the existence of a broad range of time scales in the volatility. We find that a richer set of time scales brings to a higher price of the option. This appears in clear contrast to the presence of memory in the price itself which makes the price of the option cheaper.

physics.soc-ph↗
arXiv2005

Scaling and data collapse for the mean exit time of asset prices

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.

physics.soc-ph↗
arXiv2005

Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model

We study the exponential Ornstein-Uhlenbeck stochastic volatility model and observe that the model shows a multiscale behavior in the volatility autocorrelation. It also exhibits a leverage correlation and a probability profile for the stationary volatility which are consistent with market observations. All these features make the model quite appealing since it appears to be more complete than other stochastic volatility models also based on a two-dimensional diffusion. We finally present an approximate solution for the return probability density designed to capture the kurtosis and skewness effects.

cond-mat.other↗
arXiv2004

Hints for an extension of the early exercise premium formula for American options

Characterization of the American put option price is still an open issue. From the beginning of the nineties there exists a non-closed formula for this price but nontrivial numerical computations are required to solve it. Strong efforts have been done to propose methods more and more computationally efficient but most of them have few mathematical ground as to ascertain why these methods work well and how important is to consider a good approximation to the boundary or to the smooth pasting condition. We perform an extension of the American put price aiming to catch weaknesses of the numerical methods given in the literature.

cond-mat.other↗
arXiv2004

Extreme times in financial markets

We apply the theory of continuous time random walks to study some aspects of the extreme value problem applied to financial time series. We focus our attention on extreme times, specifically the mean exit time and the mean first-passage time. We set the general equations for these extremes and evaluate the mean exit time for actual data.

cond-mat.other↗
arXiv2003

Activity autocorrelation in financial markets. A comparative study between several models

We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power law which ultimately recovers the Poissonian behavior. We discuss these results in comparison with ARCH models, stochastic volatility models and multi-agent models showing that ARCH and stochastic volatility models better describe the observed experimental evidences.

cond-mat.stat-mech↗
arXiv2003

A comparison between several correlated stochastic volatility models

We compare the most common SV models such as the Ornstein-Uhlenbeck (OU), the Heston and the exponential OU (expOU) models. We try to decide which is the most appropriate one by studying their volatility autocorrelation and leverage effect, and thus outline the limitations of each model. We add empirical research on market indices confirming the universality of the leverage and volatility correlations.

cond-mat.stat-mech↗
arXiv2003

Multiple time scales in volatility and leverage correlations: An stochastic volatility model

Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or `leverage') correlations that are much shorter ranged. Different stochastic volatility models have been proposed in the past to account for both these correlations. However, in these models, the decay of the correlations is exponential, with a single time scale for both the volatility and the leverage correlations, at variance with observations. We extend the linear Ornstein-Uhlenbeck stochastic volatility model by assuming that the mean reverting level is itself random. We find that the resulting three-dimensional diffusion process can account for different correlation time scales. We show that the results are in good agreement with a century of the Dow Jones index daily returns (1900-2000), with the exception of crash days.

cond-mat.stat-mech↗