4,366 research outputs found
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 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
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