The Modeling of the Worth of an Asset Using a Skew Random Pricing Tree

Abstract

The binomial formula given by Cox, Ross and Rubinstein (1979) is a tool for evaluating the call option price. It is well known that the price from the binomial formula converges to the price from the Black-Scholes formula, which was given, by Black, Scholes and Merton (1973) as the number of periods (n) converges to infinity. In this paper, however, a formula for the worth of the expected returns of options and stock according to risk characteristics is derived. The knowledge of the binomial method of option pricing as well as the tree is applied herein in calculating the fair value of options. At each node of the tree, two possible outcomes are considered: an increase in the price of the underlying asset and a decrease in the price of the underlying asset. A sensitivity analysis worth of options is carried out at each node when it is affected by some policies.