1,721,046 research outputs found
Yuima : the project for simulation and inference of multi-dimensional stochastic differential equations
No full textMost of the theoretical results in modern finance rely on the assumption
that the underlying dynamics of asset prices, currencies exchange rates,
interest rates, etc are continuous time stochastic processes driven by
stochastic differential equations. Continuous time models are also at the
basis of option pricing and option pricing often requires Monte Carlo
methods. In turn, the Monte Carlo method requires a preliminary good model to simulate whose parameters has to be estimated from historical data.
Most ready-to-use tools in computational finance relies on pure discrete time models, like arch, garch, etc. and very few examples of software
handling continuous time processes in a general fashion are available also
in the R community.
There still exists a gap between what is going on in mathematical finance
and applied finance. The "yuima" package is intended to help in filling
this gap.
The Yuima Project is an open source and collaborative effort of several
mathematicians and statisticians aimed at developing the R package named
"yuima" for simulation and inference of stochastic differential equations.
The "yuima" package is an environment that follows the paradigm of methods
and classes of the S4 system for the R language.
In the "yuima" package stochastic differential equations can be of very
abstract type, e.g. uni or multidimensional, driven by Wiener process of fractional Brownian motion with general Hurst parameter, with or without
jumps specified as L .A Nivy noise. L Nivy processes can be specified via
compound Poisson description, by the specification of the L Nivy measure or
via increments and stable laws.
The "yuima" package is intended to offer the basic infrastructure on which
complex models and inference procedures can be built on.
In particular, the basic set of functions includes the following: 1)
Simulation schemes for all types of stochastic differential equations
(Wiener, fBm, L .A Nivy). 2) Different subsampling schemes including random
sampling with user specified random times distribution, space
discretization, tick times, etc. 3) Automatic asymptotic expansion for the
approximation and estimation of functionals of diffusion processes with
small noise via Malliavin calculus, useful in option pricing. 4) Efficient
quasi-likelihood inference for diffusion processes and diffusion processes with jumps; 5) changepoint analysis, etc.
All simulation schemes, subsampling and inference are designed to work on
both regular or irregular grid times (i.e. regular or irregular time
series). In special cases also asynchronous data and sampling schemes can
be handle
SDE : simulation and inference for stochastic differential equations
No full textStochastic differential equations SDEs are used to model continuous
time phenomena appearing in many disciplines including finance,
biology, ecology, the social sciences, etc.
In this talk we consider one dimensional SDEs driven by standard Brownian motion. We start with a quick review on simulation schemes for SDEs. These schemes are needed in the study of random dynamical systems like in
population dynamics, numerical option pricing in finance, etc.
While inference for SDEs with continuous time observation is a long
studied field, only recently the interest of the scientific community
focused on discrete time observations. The boost of this growing interest
has been ignited by the increasing availability of high frequency data, e.g. from finance.
Unfortunately, the likelihood function for these data is almost never
available in explicit form and, moreover, different sampling schemes are
possible. We review different approaches to both likelihood and
non-likelihood inference for discretely observed SDEs. In particular we will
discuss pseudo-likelihood and approximate-likelihood methods, estimating functions, generalized method of moments, non parametric estimation and model selectio
Semiparametric estimation of a functional of the drift coefficient of a dynamical system with small noise
No full text
Big data or big fail? The good, the bad and the ugly and the missing role of statistics
No full textThe so called “Big Data” are data which we think as being “big” because of their volume, their amount per unit of time and because they are un- structured. The usual sources of big data are administrative repositories, transaction data or social media and social network feeds. Someone defines big data as those data which cannot be analyzed on a desktop machine or stored on one’s hard disk. These ways of defining big data completely miss the point of view of Statistics: they seem to be tailored more to advertising campaign of SaS or storage solution rather than to Science. Moreover, recent big fails, like e.g. the famous/infamous Google Flu Trend experiment, raised a series of popular news paper articles against the validity of information contained in these data and Statistics itself, even though none of these bad practices has been conducted by statisticians. While Information Technology and Computer Science are good at efficiently retrive and manage them, these data should be soon brought back into the field of Statistics to where data belong and this Special Issues of EJASA is one important step in this direction
OPEFIMOR : option pricing and estimation of financial models in R.
No full textOPEFIMOR : option pricing and estimation of financial models in
Statistic analysis of the inhomogeneous telegrapher's process
No full textWe consider a problem of estimation for the telegrapher's process on the line, say X(t), driven by a Poisson process with non-constant rate. The finite-dimensional law of the process X(t) is a solution to the telegraph equation with non-constant coefficients. We present the explicit law (Pθ) of the process X(t) for a parametric class of intensity functions for the Poisson process. This is one rare example where an explicit law can be obtained. We propose further, an estimator for the parameter θ of Pθ and we discuss its properties as a first attempt to apply statistics to these models
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