Binomial tree for option valuation process derived from stochastic autonomous differential equation (2010)
This paper proposes a recombination in binomial trees multiplicatively generalized for the autonomous equation, in terms of the initial condition and the product between non-constant jumps up and down the discretized process. A technique is formally presented to find dynamic transition probabilities considering the first two moments of the differential equation solution process, which incorporates the growth factor and volatility in terms of the parameters and the underlying process throughout its branching. Some experimental numerical results of valuation of European options for the log – normal process and for the mean reversion processes with additive noise and proportional noise for different expiration dates are shown.