Abstract
The Brownian motion is the workhorse of continuous time finance theory. The log price of a financial asset is specified as a Brownian motion with constant drift and volatility. While highly tractable in theoretical applications, the Brownian motion representation assumes independent Gaussian increments and thus cannot capture the outliers and volatility cycles exhibited by typical financial returns. It is conveniently extended by considering deformations of clock time. This chapter provides the background material for a brief introduction to the continuous-time concepts, fractal processes and measures with the help of fully developed models. The background information is essential to understand the first multifractal diffusion, the multifractalmodel of asset returns (MMAR). Specifically, time deformation and multifractal measures are critical building blocks for the MMAR. Jump-diffusion models of financial prices are briefly discussed. These models are essential in obtaining endogenous discontinuities in prices and other appealing features by using equilibrium valuation. Jumps in valuations and their relation to volatility are exogenously specified.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
