Stochastic Clock and Financial Markets

Hèlyette Geman ()
Additional contact information
Hèlyette Geman: University of London

A chapter in Aspects of Mathematical Finance, 2008, pp 37-52 from Springer

Abstract: Brownian motion played a central role throughout the twentieth century in probability theory. The same statement is even truer in finance, with the introduction in 1900 by the French mathematician Louis Bachelier of an arithmetic Brownian motion (or a version of it) to represent stock price dynamics. This process was ‘pragmatically’ transformed by Samuelson in ([48, 49]; see also [50]) into a geometric Brownian motion ensuring the positivity of stock prices. More recently the elegant martingale property under an equivalent probability measure derived from the No Arbitrage assumption combined with Monroe’s theorem on the representation of semi-martingales have led to write asset prices as time-changed Brownian motion. Independently, Clark [14] had the original idea of writing cotton Future prices as subordinated processes, with Brownian motion as the driving process. Over the last few years, time changes have been used to account for different speeds in market activity in relation to news arrival as the stochastic clock goes faster during periods of intense trading. They have also allowed us to uncover new classes of processes in asset price modelling.

Keywords: Brownian Motion; Stock Price; Asset Price; Stochastic Volatility; Price Process (search for similar items in EconPapers)
Date: 2008
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-75265-3_5

Ordering information: This item can be ordered from
http://www.springer.com/9783540752653

DOI: 10.1007/978-3-540-75265-3_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().