EAN: 9780128042489

FRACTIONAL CALCULUS AND FRACTIONAL PROCESSES WI...

Fractional Calculus and Fractional Processes with Applications to Financial Economics presents
the theory and application of fractional calculus and fractional processes to financial data.
Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the
possibility of fractional derivatives. Research on fractional calculus started in full earnest
in the second half of the twentieth century. The fractional paradigm applies not only to
calculus  but also to stochastic processes  used in many applications in financial economics
such as modelling volatility  interest rates  and modelling high-frequency data. The key
features of fractional processes that make them interesting are long-range memory 
path-dependence  non-Markovian properties  self-similarity  fractal paths  and anomalous
diffusion behaviour. In this book  the authors discuss how fractional calculus and fractional
processes are used in financial modelling and finance economic theory. It provides a practical
guide that can be useful for students  researchers  and quantitative asset and risk managers
interested in applying fractional calculus and fractional processes to asset pricing  financial
time-series analysis  stochastic volatility modelling  and portfolio optimization.

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