Binomial tree for option valuation process derived from stochastic autonomous differential equation

In this paper we propose a multiplicative generalized binomial trees recombination associated with the autonomous equation in terms of the initial condition and the product of non-constant upwards and downwards jumps from the discretized process. We present a formal technique for finding the dynamic transition probabilities involving the first two moments of the solution to the differential equation, which incorporate the factor of growth and volatility in terms of the parameters and the underlying process along its branching. Some experimental numerical results are shown for European option pricing for lognormal process and the processes of mean reversion with additive noise and proportional noise for different expiration dates