trees. The DM Method gives the same results as the Black–Scholes and the binomial lattice option models, provided the same inputs and the discount methods are used. This non-traded real option value therefore is dependent on the risk perception of the evaluator toward a market asset relative to a privately held investment asset. The DM Method is advantageous for use in real option applications because unlike some other option models it does not require a value for sigma (a measure of uncertainty) or for S0 (the value of the project today), both of which are difficult to derive for new product development projects; see further under real options valuation. Finally, the DM Method uses real-world values of any distribution type, avoiding the requirement for conversion to risk-neutral values and the restriction of a lognormal distribution; see further under Monte Carlo methods for option pricing. Extensions of the method for other real option valuations have been developed such as contract guarantee (put option), Multi-Stage (compound option), Early Launch (American option), and others. Implementation The DM Method may be implemented using Monte-Carlo simulation, or in a simplified algebraic or other form (see the Range Option below). Using simulation, for each sample, the engine draws a random variable from both calculates their present values, and takes the difference. Fig. 2A. The difference value is compared to zero, the maximum of the two is determined, and the resulting value recorded by the simulation engine. Here, reflecting the optionality inherent in the project, a forecast of a net negative value outcome corresponds to an abandoned project, and has a zero value. Fig. 2B. The resulting values create a payoff distribution representing the economically rational set of plausible, discounted value forecasts of the project at time T0. When sufficient payoff values have been recorded, typically a few hundred, then the mean, or expected value, of the payoff distribution is calculated. Fig. 2C. The option value is the expected value, the first moment of all positive NPVs and zeros, of the payoff distribution. A simple interpretation is: where operating profit and launch costs are the appropriately discounted range of cash flows to time T0. The option value can also be understood as a distribution () reflecting the uncertainty of the underlying variables. DM Option Variations Algebraic lognormal form The DM real option can be considered a generalized form for option valuation. Its simulation produces a truncated present