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.Comment: 9 pages, 4 figures, APFA5 Torin

Option pricing and perfect hedging on correlated stocks

We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time tau. This is accomplished by assuming that the underlying noise in the system is derived by an Ornstein-Uhlenbeck, rather than from a Wiener process. With a modified portfolio consisting in calls, secondary calls and bonds we achieve a riskless strategy which results in a closed expression for the European call price which is always lower than Black-Scholes price. We also obtain a partial differential equation for the option price and study the sensitivity to several parameters and the risk of the dynamics of the call price.Comment: 36 pages, 8 figures, 2 table

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.Comment: 4 pages, 2 figures, APFA 4 conferences contribution (13-15 november, 2003, Warsaw

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.Comment: 15 pages, 4 figure

Citizen Social Lab: A digital platform for human behaviour experimentation within a citizen science framework

Cooperation is one of the behavioral traits that define human beings, however we are still trying to understand why humans cooperate. Behavioral experiments have been largely conducted to shed light into the mechanisms behind cooperation and other behavioral traits. However, most of these experiments have been conducted in laboratories with highly controlled experimental protocols but with varied limitations which limits the reproducibility and the generalization of the results obtained. In an attempt to overcome these limitations, some experimental approaches have moved human behavior experimentation from laboratories to public spaces, where behaviors occur naturally, and have opened the participation to the general public within the citizen science framework. Given the open nature of these environments, it is critical to establish the appropriate protocols to maintain the same data quality that one can obtain in the laboratories. Here, we introduce Citizen Social Lab, a software platform designed to be used in the wild using citizen science practices. The platform allows researchers to collect data in a more realistic context while maintaining the scientific rigour, and it is structured in a modular and scalable way so it can also be easily adapted for online or brick-and-mortar experimental laboratories. Following citizen science guidelines, the platform is designed to motivate a more general population into participation, but also to promote engaging and learning of the scientific research process. We also review the main results of the experiments performed using the platform up to now, and the set of games that each experiment includes. Finally, we evaluate some properties of the platform, such as the heterogeneity of the samples of the experiments and their satisfaction level, and the parameters that demonstrate the robustness of the platform and the quality of the data collected.Comment: 17 pages, 11 figures and 4 table

A correlated stochastic volatility model measuring leverage and other stylized facts

We present a stochastic volatility market model where volatility is correlated with return and is represented by an Ornstein-Uhlenbeck process. With this model we exactly measure the leverage effect and other stylized facts, such as mean reversion, leptokurtosis and negative skewness. We also obtain a close analytical expression for the characteristic function and study the heavy tails of the probability distribution.Comment: 22 pages, 2 figures and 2 table

Scaling properties and universality of first-passage time probabilities in financial markets

Financial markets provide an ideal frame for the study of crossing or first-passage time events of non-Gaussian correlated dynamics mainly because large data sets are available. Tick-by-tick data of six futures markets are herein considered resulting in fat tailed first-passage time probabilities. The scaling of the return with the standard deviation collapses the probabilities of all markets examined, and also for different time horizons, into single curves, suggesting that first-passage statistics is market independent (at least for high-frequency data). On the other hand, a very closely related quantity, the survival probability, shows, away from the center and tails of the distribution, a hyperbolic $t^{-1/2}$ decay typical of a Markovian dynamics albeit the existence of memory in markets. Modifications of the Weibull and Student distributions are good candidates for the phenomenological description of first-passage time properties under certain regimes. The scaling strategies shown may be useful for risk control and algorithmic trading.Comment: 7 pages, 5 figure