Flexible Design of Airport System Using Real Options Analysis - MIT

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12/14/2007 1.231 Planning and Design of Airport System Dai Ohama C = S ⋅ N −r T ( d ) − K ⋅ e f ⋅ N( ) 1 d 2 Where C: Theoretical value of a European call option with no dividends d d 1 2 ln = 2 ( S / K ) + ( r / 2) = d 1 − σ T σ f + σ ⋅T T N(x): Cumulative probability function for a standardized normal distribution The following formula shows the theoretical value of European put options. P = K ⋅ e −r f T ⋅ N ( − d ) − S ⋅ N( − ) 2 d 1 Where P: Theoretical value of a European put option with no dividends 3.1.2 Binomial Lattice Model Binomial Lattice Model, which is also widely used, is a more simplified discrete-time approach to valuation of options compared to the Black-Scholes Option Pricing Model. [4] It assumes that the price of the underlying asset will change to one of the only two possible values during the next period of time. Figure 3-2 shows a three-stage binomial example. Figure 3-2 Binomial Tree Representations of Changes in Underlying Asset Source: R de Neufville Lecture notes of the MIT course of ESD.71[4] In the Binomial Lattice Model, the price of an underlying asset at a certain time can change to one of the only two possibilities, which are an upward movement with multiplier u with the probability of p, and a downward movement with multiplier d with the probability of 1-q. [4] Term Project: Flexible Design of Airport System Page 8 of 22
12/14/2007 1.231 Planning and Design of Airport System Dai Ohama u = e d = e σ ΔT −σ ΔT p = 0.5 + 0.5 = 1/ u ( v / d ) ΔT 3.1.3 Monte Calro Simulation Monte Calro Simulation is an analytical method that generates the stochastic distribution of possible outcome that correspond to probability-distributed sampled inputs. [5] Because of the development of computer technology, large computer simulation such as Monte Calro Simulation can be constructed easily. Spread sheet software such as Microsoft Excel is the tool for conducting Monte Calro Simulation. 3.2 Real Options Analysis In the previous section, financial options theory including Black-Scholes option pricing model, Binomial Lattice Model, and Monte Calro Simulation were introduced. In this section, real options analysis, which was the application of financial options theory to the actual projects, is introduced. 3.2.1 Real Options Real option is the option to undertake some business decision under high uncertainty. In real options analysis, they are associated with flexibilities in designing systems or the evolution of projects. [4] Option - like flexibilities are included in systems and projects, represent opportunities to increase the value of the project through design or through management actions. [4] It is not obligation, and only when future asset price is preferable for you, you can exercise it, otherwise you don’t have to do it. This allows decision-makers to avoid downside losses as well as to obtain upside opportunities. These flexibilities are called “real” options. [4] Managers have applied real options analysis to business strategies including large-scale engineering systems. Although real options are very similar to financial options, they are different from financial options in terms of what should be assessed and the time span. [4] In financial options, the actual price such as Term Project: Flexible Design of Airport System Page 9 of 22
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