Real options

Real options

Real options (Black-Scholes Option Pricing Model)


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Contents:

  • Terminologies
  • Types of options: (Real Options)
  • Black Scholes Option Pricing Model Formulae (Given)
  • Put Option Formulae: (Given)
  • Black Scholes Option Pricing model
  • The Greeks
  • Call delta hedge
  • Put delta hedge

Referenced syllabus: B2, B4 (d)


Terminologies

When appraising projects, the traditional NPV measure may not well incorporate the value of uncertainties, such as:

  • Timing uncertainties – the project could be deferred
  • Expanding uncertainties – the project could be expanded at a later stage, possibly in the form of making investments by stages, or to make the investment now and wait for bigger opportunities later.
  • Switching uncertainties – the project could be switched into another project

To value these uncertainties, option comes in.

Types of options: (Real Options)

Description

Option types

Option to delay

This allows the business to defer the project.

This is often found when the business has exclusive right to the product or market.

Call option

Option to expand

This allows the business to make further investments.

This is usually found that the original project NPV is negative, but by considering the expansion option value, the whole project NPV would become positive.

Call option

Option to abandon

This allows the business the right to cease the project during its life and sell its cash flows.

For example, a business may sell the venture to the investor at a specified period of time.

Put option

Option to redeploy (switch)

This allows the business the right to switch the productive assets to another project.

This is suitable when switching value is higher than the switching costs.

Put option to switch;

Call option to start the new project.


Call option and put option

  • Call option – an option to buy
  • Put option – an option to sell

Option styles

  • European style option – option can be exercised only on the expiry date. For example, Black Scholes Option Pricing model.
  • American style option - option can be exercised before the expiry date.

The whole project value

Project value= Traditional value (NPV) + Option value*

*Option value

Factors affecting option value:

Call option value

Put option value

Market price

Exercise price

Time to expiry

Volatility

Interest rate


Black Scholes Option Pricing Model Formulae (Given)

c= Call option value

Pa= Future cash flows from the investment

Pe =Project investment costs incurred

e= 2.7183 (exponential constant which is developed by scientist)

r= Risk free rate (not cost of capital)

t= Years remaining before costs incurred (for example, if the investment begins in 2 years’ time, t=2 not 24 months)

Put Option Formulae: (Given)

In Excel

Step 1 – lay out the five elements:

Pa

Pe

S (standard deviation)

r

t

Step 2 – use the Excel functions:

Functions

Command

Natural log

=LN()

Exponential (e)

=exp()

d1

=(ln(pe/pe)+(r+0.5*s^2)*t)/(s*sqrt(t))

d2

=d1-s*(sqrt(t))

Nd1

=normsdist(d1)

Nd2

=normsdist(d2)

Step 3 – show in the excel: (example):

B

C

D

E

F

1

Pa

100

d1

=((ln(C1/C2)+(C4+0.5*(C3^2)*C5)/(C3*sqrt(C5)

2

Pe

95

d2

=F1-(C3*sqrt(C5))

3

S

0.5

N(d1)

=normsdist(F1)

4

r

0.1

N(d2)

=normsdist(F2)

5

t

0.25

Call

=(C1*F3)-(C2*F4*exp(-C4*C5))

Put

=F5-B1+B2*exp(-B4*B5)

Current exam

In the exam, you do not need to learn the Excel formulae of how BSOP model is calculated. However, you can directly click ‘BSOP Calculator’ and input numbers into the ‘Variables’ cells’. The final answer is automatically generated.

Example:

Black Scholes Option Pricing model

Characteristics of Black Scholes Option Pricing model:

  • Transaction costs and taxes are zero;
  • The share pays no dividends;
  • The option has European exercise terms;
  • The short-term (risk-free) interest rate is known and constant.
  • The standard deviation of returns must be estimated and be constant over the life of the option.


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