Flexible Design of Airport System Using Real Options Analysis - MIT

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]
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