Random binomial tree models and options

• Main Authors: Ganikhodjaev, Nasir, Bayram, Kamola
• Format: Article
• Language: English
• Published: Asian Network for Scientific Information 2012
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/25877/1/Journal_of_Applied_Sciences_Random_Binomial_Tree_Models_and_Options.pdf; http://irep.iium.edu.my/25877/; http://scialert.net/qredirect.php?doi=jas.2012.1978.1981&linkid=pdf
• Institution: Universiti Islam Antarabangsa Malaysia

In this study, we introduce the simplest random binomial tree model. Usual binomial tree model is prescribed by pair of numbers (u, d), where u denotes the increase rate of the stock over the fixed period of time and d denotes the decrease rate, with 0<d<1<u. We call the pair (u, d) an environment of the binomial tree model. A pair (Un, Dn), where {Un} and {Dn} be the sequences of independent, identically distributed random variables with Un>1 and 0<Dn<1<Un for all n, is called a random environment and binomial tree model with random environment is called random binomial tree model. In this paper, we define and study European call option for such models.