Fuzzy pay-off method for real option valuation

# Metoda formulei de opțiuni reale

Conținutul

In many generalized option applications, the risk-free discount rate is used.

However other discount rates can be considered, such as the corporate bond rate, particularly when the application is an internal corporate product development project. The option value can be understood as the expected value of the metoda formulei de opțiuni reale of two present value distributions with an economically rational threshold limiting losses on a risk-adjusted basis.

This value may also be expressed as a stochastic distribution. The differential discount rate for R and r implicitly allows the DM Method to account for the underlying risk. 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 todayboth of which are difficult to derive for new product development projects; see further under real options valuation.

Finally, the Metoda formulei de opțiuni reale Method uses real-world values of any distribution typeavoiding the requirement for conversion to risk-neutral values and the restriction of a lognormal distribution ; [6] 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 optionMulti-Stage compound optionEarly Launch American optionand others. Using simulation, for each sample, the engine draws a random variable from both ST and XT, calculates their present values, and takes the difference.

As can be seen, the real option value can be derived directly from the fuzzy NPV, without simulation. But what is totally different is that the Datar—Mathews method is based on probability theory and as such has a very different foundation from the pay-off method that is based on possibility theory: the way that the two models treat uncertainty is fundamentally different.

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. 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. The option value is the expected value, the first moment of all positive NPVs and zeros, of the payoff distribution.

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