This computational mannequin makes use of an iterative process, permitting for the specification of nodes through the time between the valuation date and the choice’s expiration date. At every node, the mannequin assumes the underlying asset can transfer to certainly one of two doable costs, making a binomial tree. By working backward from the choice’s expiration worth at every closing node and making use of a risk-neutral chance at every step, the mannequin determines the choice’s theoretical worth on the preliminary node. A easy instance may contain a inventory which may both enhance or lower by a sure share at every step. The mannequin calculates the choice’s payoff at every closing node based mostly on these value actions after which works backward to find out the present possibility value.
Its energy lies in its capability to deal with American-style choices, which could be exercised earlier than expiration, in contrast to European-style choices. Moreover, it will possibly accommodate dividends and different company actions that impression the underlying asset’s value. Traditionally, earlier than widespread computational energy, this methodology offered a sensible different to extra advanced fashions just like the Black-Scholes mannequin, particularly when coping with early train options. It stays a precious device for understanding possibility pricing ideas and for valuing choices on belongings with non-standard traits.
