Random dynamics and finance: constructing implied binomial trees from a predetermined stationary density

Abstract

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 brie y explore the suitability of our construction as an implied binomial tree. Wael AbstractWe 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.

Monte Carlo and Quasi Monte Carlo Approach to Ulam's Method for Position Dependent Random Maps

“…Monte Carlo approach to Ulam's method: In Figure 5.1 (a) and 5.1 (b) we have plotted the actual density and approximate density for Monte Carlo approach to Ulam's method. [5] for this random map)…”

“…In each iteration of the process, one map from the set of maps with one position dependent probability from the set of probabilities [1] is selected and applied. There are applications of random maps in many areas of science and engineering [2]- [3]- [4]- [5]- [6]. In [2] the author applied the theory of random dynamical systems in the study of fractals.…”

“…The authors in [4] applied random maps for computing metric entropy. Random maps have application in forecasting the financial markets [5] and in economics [6].…”