Most financial and investment decisions are based on
considerations of possible future changes and require forecasts on
the evolution of the financial world. Time series and processes are
the natural tools for describing the dynamic behavior of financial
data, leading to the required forecasts. This book presents a
survey of the empirical properties of financial time series, their
descriptions by means of mathematical processes, and some
implications for important financial applications used in many
areas like risk evaluation, option pricing or portfolio
construction. The statistical tools used to extract information
from raw data are introduced. Extensive multiscale empirical
statistics provide a solid benchmark of stylized facts
(heteroskedasticity, long memory, fat-tails, leverage ), in order
to assess various mathematical structures that can capture the
observed regularities. The author introduces a broad range of
processes and evaluates them systematically against the benchmark,
summarizing the successes and limitations of these models from an
empirical point of view. The outcome is that only multiscale ARCH
processes with long memory, discrete multiplicative structures and
non-normal innovations are able to capture correctly the empirical
properties. In particular, only a discrete time series framework
allows to capture all the stylized facts in a process, whereas the
stochastic calculus used in the continuum limit is too
constraining. The present volume offers various applications and
extensions for this class of processes including high-frequency
volatility estimators, market risk evaluation, covariance
estimation and multivariate extensions of the processes. The book
discusses many practical implications and is addressed to
practitioners and quants in the financial industry, as well as to
academics, including graduate (Master or PhD level) students. The
prerequisites are basic statistics and some elementary financial
mathematics."
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