and expiration dates. Each node in the lattice represents a possible price of the underlying at a given point in time. Valuation is performed iteratively, starting at each of the final nodes (those that may be reached at the time of expiration), and then working backwards through the tree towards the first node (valuation date). The value computed at each stage is the value of the option at that point in time. Option valuation using this method is, as described, a three-step process: Price tree generation, Calculation of option value at each final node, Sequential calculation of the option value at each preceding node. Step 1: Create the binomial price tree The tree of prices is produced by working forward from valuation date to expiration. At each step, it is assumed that the underlying instrument will move up or down by a specific factor ( or ) per step of the tree (where, by definition, and ). So, if is the current price, then in the next period the price will either be or . The up and down factors are calculated using the underlying volatility, , and the time duration of a step, , measured in years (using the day count convention of the underlying instrument). From the condition that the variance of the log of the price is , we have: Above is the original Cox, Ross, & Rubinstein (CRR) method; there are various other techniques for generating the lattice, such as "the equal probabilities" tree, see. The CRR method ensures that the tree is recombinant, i.e. if the underlying asset moves up and then down (u,d), the price will be the same as if it had moved down and then up (d,u)—here the two paths merge or recombine. This property reduces the number of tree nodes, and thus accelerates the computation of the option price. This property also allows the value of the underlying asset at each node to be calculated directly via formula, and does not require that the tree be built first. The node-value will be: Where is the number of up ticks and is the number of down ticks. Step 2: Find option value at each final node At each final node of the tree—i.e. at expiration of the option—the option value is simply its intrinsic, or exercise, value: , for a call option , for a put option, Where is the strike price