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Random dynamics and finance: constructing implied binomial trees from a predetermined stationary density
Author(s) -
Bahsoun Wael,
Góra Paweł,
Mayoral Silvia,
Morales Manuel
Publication year - 2006
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.663
Subject(s) - negative binomial distribution , binomial distribution , binomial options pricing model , binomial (polynomial) , stationary distribution , econometrics , mathematics , distribution (mathematics) , continuity correction , beta binomial distribution , statistical physics , computer science , mathematical economics , statistics , valuation of options , mathematical analysis , physics , markov chain , poisson distribution
We introduce a general binomial model for asset prices based on the concept of random maps. The asymptotic stationary distribution for such model is studied using techniques from dynamical systems. In particular, we present a technique to construct a general binomial model with a predetermined stationary distribution. This technique is independent of the chosen distribution making our model potentially useful in financial applications. We briefly explore the suitability of our construction as an implied binomial tree. Copyright © 2006 John Wiley & Sons, Ltd.