Binomial trees as dynamical systems

Roza Galeeva

Physica A: Statistical Mechanics and its Applications, 2001, vol. 292, issue 1, 519-535

Abstract: One of the simplest and very popular techniques for pricing an option or other derivative involves constructing what is known as a binomial tree. This is a tree which represents the possible paths, that might be followed by the underlying assets price. We will view this tree as a dynamical system, which means that we specify a space, and a map acting on it. Here the space will be the space of all possible paths, and the corresponding map will be the shift on each path. Such approach reveals a dynamical nature of certain financial terms and financial principles. For example, returns along a path could be defined by a potential, and the price on each path is expressed in a very “dynamical” fashion. Using this interpretation, we introduce a new characteristic as the pressure of the potential of returns. Under the conditions of no arbitrage, the pressure has to be equal to be the interest rate. This gives a new formulation of the no arbitrage principle: the expected price has to be finite: a smaller or greater discount would give either very small (zero at the limit), or very large (at the limit infinity) price. Therefore, the presented work links the discrete models of option pricing to the thermodynamical formalism and multifractal analysis of invariant sets in dynamical systems.

Keywords: Binomial tree; Invariant measure; Potential (search for similar items in EconPapers)
Date: 2001
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437100004908
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

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:eee:phsmap:v:292:y:2001:i:1:p:519-535

DOI: 10.1016/S0378-4371(00)00490-8

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().