and is the spot price of the underlying asset at the period. Step 3: Find option value at earlier nodes Once the above step is complete, the option value is then found for each node, starting at the penultimate time step, and working back to the first node of the tree (the valuation date) where the calculated result is the value of the option. In overview: the "binomial value" is found at each node, using the risk neutrality assumption; see Risk neutral valuation. If exercise is permitted at the node, then the model takes the greater of binomial and exercise value at the node. The steps are as follows: In calculating the value at the next time step calculated—i.e. one step closer to valuation—the model must use the value selected here, for "Option up"/"Option down" as appropriate, in the formula at the node. The aside algorithm demonstrates the approach computing the price of an American put option, although is easily generalized for calls and for European and Bermudan options: Relationship with Black–Scholes Similar assumptions underpin both the binomial model and the Black–Scholes model, and the binomial model thus provides a discrete time approximation to the continuous process underlying the Black–Scholes model. The binomial model assumes that movements in the price follow a binomial distribution; for many trials, this binomial distribution approaches the log-normal distribution assumed by Black–Scholes. In this case then, for European options without dividends, the binomial model value converges on the Black–Scholes formula value as the number of time steps increases. In addition, when analyzed as a numerical procedure, the CRR binomial method can be viewed as a special case of the explicit finite difference method for the Black–Scholes PDE; see finite difference methods for option pricing. See also Trinomial tree, a similar model with three possible paths per node. Tree (data structure) Lattice model (finance), for more general discussion and application to other underlyings Black–Scholes: binomial lattices are able to handle a variety of conditions for which Black–Scholes cannot be applied. Monte Carlo option model, used in the valuation of options with complicated features that make them difficult to value through other methods. Real options analysis, where the BOPM is widely used. Quantum finance, quantum binomial pricing model. Mathematical finance, which has a list of related articles. , where the BOPM is widely used. Implied binomial tree Edgeworth binomial tree References External links The Binomial Model for