Consideraciones psicológicas en el estudio de estados expandidos de

The basis inputs used to value any type of option and real option include the underlying asset value, option type, exercise price, volatility factor and others. Table 3.2 defines the

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similarities and differences between the parameters used in financial options versus typical real options. The similarities make it easier to understand and to implement option methods for real assets.

Variable Financial options Real options Symbol

Underlying asset

Stock price Net present value of the

potential investment

S

Option Type To buy (call) or sell (put) Opportunity to invest (call) or divest (put)

c, p

Exercise date Continuous right exists up to maturity (American) or right at the maturity date (European)

The same as financial options

C, P

Exercise price Fixed price at which the option holder can buy (call) or sell (put) a unit of stock

Fixed price at which the option holder can invest or sell the asset

X

Expiry date The last date of exercise (American) or the only date of exercise

(European)

The last date for possible investment (American) or the only date for possible investment (European)

T

Volatility Stock price volatility Volatility of the underlying cash flow. Volatility may be time- varying, usually with diminishing volatility. However, if the underlying cash flow follows geometric Brownian motion (GBM), then the volatility can be estimated as constant.

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Variable Financial options Real options Symbol

outflows. Dividends are considered to be leakages that can affect the

project‘s cash flow, such as royalty income, royalty fees, storage costs and lost market share to competitors. Dividend yield is

difficult to estimate with real options. Practitioners assume it to be zero.

Delta The change in the option‘s

value, corresponding to the change of price in the underlying asset

The change in the

option‘s value with a unit change in the present value of underlying cash flow series. Delta is defined mathematically as the partial differential of ∂π/∂S.

Δ

Theta The change in value of the

option corresponding to the passage of time

The same definition as in the financial option. In projects, the time horizontal may involve years. Theta is defined mathematically by the partial differential ∂π/∂t.

Θ

Gamma The change in delta with

respect to the price of an underlying asset

The change in delta with a unit change in the present value of the underlying cash flows series. It is defined mathematically by the

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Variable Financial options Real options Symbol

partial differential (∂2

π)/∂S.

Vega The change in the value of

an option corresponding to changes in the asset‘s volatility

The change in an

option‘s value with a unit change in the volatility of the present value of the underlying cash flow series. It is defined mathematically by the partial differential ∂π/∂v.

v

Rho The change in the option‘s

value corresponding to changes in interest rates

The change in the option‘s value of option corresponding to changes in the discount rate. It is defined mathematically by the partial differential ∂π/∂r.

Rho

Xi The change in the value of

option with corresponding to the change in the value of strike price

The change in the value of option with

corresponding to the change in the value of cost. It is defined by mathematical of partial differential ∂π/∂X.

Xi

Table 3.2: The key parameters of financial and real options Source: Howell et al. (2001)

Understanding the parameters in the model can help to understand real option problems and implement option methods on the real assets. The changes in option value relative to the changes in each parameter are defined by partial differential equations based on the Black– Scholes model. For example, delta is defined as the change in an option‘s value relative to each incremental change in the value of the underlying asset (S). However, although this sensitivity analysis is used extensively in financial options, it is rarely used in real option analysis.

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In order to apply the method initially developed for financial options to real options, an appropriate underlying asset must first be identified. Most financial options refer to the underlying stock price, whereas the underlying asset of a real option can be an asset, the project cash flow and the commodity price. The fundamentals of both financial and real options are similar in that both are rights (explicit for one because there are two parties and implicit for the other) but not obligations. If we can find a financial option, such as a call option, that provides sufficiently similar characteristics to an investment opportunity of a real asset, the value of this option would tell us the value of the real asset. In fact, it is difficult to obtain such options because of the unique characteristics of any project. The other method for us to find an option is that we instead have to construct a real option. In real practise, one party can construct an option and give another party the right to do something. Real options, unlike financial options, are usually not bought or sold at capital markets. In the next section, this research will illustrate the concept of real options, including the methodology for

constructing the real option.