small that it no longer affects the overall profitability of the projects. This implies that
optimal “now or never” decisions are taken before expiry21. When the volatility of the
project becomes negligible, the reversibility component tends to zero and the remaining
lifespan of the option does not affect the optimality rule computed at the previous nodes. In
order to model business opportunities whose volatility disappears after a certain number of
years, we make use of finitely lived options.
The Cox, Ross and Rubinstein (1979) model lends itself to be employed for finitely
lived Bermudan options. It discretises both time and price changes through a recombining
symmetric binomial tree. The distribution of dividends and price changes occur at discrete
time intervals. Due to the recursive structure of the problem the solution is obtained
through iteration.
In the following we will test the model first by applying it to a new entrant operator that
decided to invest in FttH technology back in 2005; then to an established operator, which
has to decide whether to invest in NGNs on the basis of a number of educated guesses on
revenues and costs22.
4.1 - Model input parameters
The Cox et al. (1979) model requires the following parameters:
• current expected net present value of the project, denoted by NPV
• up-front investment, denotes by UI
• net cash flow lost by a one year postponement of the project
commencement date, denoted by PO (Pay Out) ;
• annualised logarithmic volatility of the project returns, denoted by VOL
(Volatility);
• risk free rate, denoted by Rf;
21 An optimal “now or never” decision is a one whose optimality remains unchanged over time.
22 Very few established operators in Europe have already began the deployment of access NGNs.
23
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