610 research outputs found
Mean Exit Time and Survival Probability within the CTRW Formalism
An intense research on financial market microstructure is presently in
progress. Continuous time random walks (CTRWs) are general models capable to
capture the small-scale properties that high frequency data series show. The
use of CTRW models in the analysis of financial problems is quite recent and
their potentials have not been fully developed. Here we present two (closely
related) applications of great interest in risk control. In the first place, we
will review the problem of modelling the behaviour of the mean exit time (MET)
of a process out of a given region of fixed size. The surveyed stochastic
processes are the cumulative returns of asset prices. The link between the
value of the MET and the timescale of the market fluctuations of a certain
degree is crystal clear. In this sense, MET value may help, for instance, in
deciding the optimal time horizon for the investment. The MET is, however, one
among the statistics of a distribution of bigger interest: the survival
probability (SP), the likelihood that after some lapse of time a process
remains inside the given region without having crossed its boundaries. The
final part of the article is devoted to the study of this quantity. Note that
the use of SPs may outperform the standard "Value at Risk" (VaR) method for two
reasons: we can consider other market dynamics than the limited Wiener process
and, even in this case, a risk level derived from the SP will ensure (within
the desired quintile) that the quoted value of the portfolio will not leave the
safety zone. We present some preliminary theoretical and applied results
concerning this topic.Comment: 10 pages, 2 figures, revtex4; corrected typos, to appear in the APFA5
proceeding
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
Stochastic model for market stocks with strong resistance
We present several models to describe the stochastic evolution of stocks that
show some strong resistance at some level and generalize to this situation the
evolution based upon geometric Brownian motion. If volatility and drift are
related in a certain way we show that our model can be integrated in an exact
way. The related problem of how to prize general securities that pay dividends
at a continuous rate and earn a terminal payoff at maturity is solved via the
martingale probability approach.Comment: Proceedings of the conference APFA
Perpetual American options within CTRW's
Continuous-time random walks are a well suited tool for the description of
market behaviour at the smallest scale: the tick-to-tick evolution. We will
apply this kind of market model to the valuation of perpetual American options:
derivatives with no maturity that can be exercised at any time. Our approach
leads to option prices that fulfil financial formulas when canonical
assumptions on the dynamics governing the process are made, but it is still
suitable for more exotic market conditions.Comment: elsart, 12 pages, 2 figures, presented at APFA 6 conference; Revised
and condensed version: 8 page
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
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