???????????????????????????? CVE 619 Infrastructure System Development

1
???????????????????????????? CVE 619
Infrastructure System Development
8

• ??????????????????????????????????????
• ???????????????????
• ?????????????????????????????????????
• ?????????????? 1 ?????????? 2548

2

• Financial Derivatives
• (??????????????)

3
??????? ??????????????

• ??????????????????????????????????????????????????
  ??????????????????????????????????????????????????
  ??????????????? (???????????????? underlying
  asset)
• ??????????????????????????????????????????????????
  ??????????????????????????? ? ?????????? ????
  ???????? (cash price or spot price)
• ??????????????????????????????????????????????????
  ???????????????????????????????????????

4
?????????????????????????????????

• Objectives
• Risk management (???????????????????)
• Speculation (???????????)

5
???????????????????????

• ???????????????????????
• ???????????????????????????????? (forward
  commitments)
• Future
• Forward
• Swap
• ??????????????????????????????? (contingent
  claims)
• Option

6
Futures - ????????????????????????????

• ??????????????????????????????????????????????????
  ???????????????????? ?????????????????????????????
  ????????????????????????
• ???????????????????????????? ??????????????????

7
Forward - ??????????????????????????????

• ???????????? future ??????????????????????????????
  ???? (over-the-counter) ??????????????????????????
  ????????????

8
????????????????? futures ??? forward
????????
????????
???????????????????? (St)
???????????????????? (St)
X
X
St X
X St
????????????
???????????
9
Option - ????????????

• ??????????????????? (???????????????????)
  ???????????????????????????????? (???? ???)
  ???????????????? ???????????????????
  ????????????????????????
• A contract which gives its holder the right,
  without obligation, to buy (or sell) an asset at
  some pre-agreed price within a specified period
  of time

10
????????????????
?????????? (Call Option) ?????????????????????
???? ???????????????? ? ?????????????????
?????????????????

• ?????????? (Put Option)
• ????????????????????? ??? ???????????????? ?
  ????????????????? ?????????????????

11
?????????????????????????
?????????? Call option
???????????????? Underlying asset

• ????????????????? ???? CPF ????? 100 ???? ? ????
  50 ?????????? ??????????? 16 ????????? 2548

???????????? Exercise price (Strike price)
?????????? Expiration
12
?????????????????????????

• ??????????????????????? long position
• ?????????????????????? short position

13
???????????????? ?????????????????????????

• American Option ????????????????????????????????
  ????? ? ?????????????????????????????
• European Option ????????????????????????????????
  ????? ? ?????????????????????????????

14
??????????????????
??????????????????

• ??????????????????????????????????????????????? ?
  ???????????????
• ???????? ???????????????????????? (exercise
  price) ??????? 55

15
40
70
55
?????????????
15
????????????????? Option
Max (0,St X)
Max (0,St X)
Max (X St, 0)
Max (X St, 0)
16
??????????????????????????????????
????????
????????
????????????? ? ????????????
????????????? ? ????????????
X
X
Long Call
Long Put

• ??????????????????????????????????????????????????
  ????????
• ??????????????????????????????????????????????????
  ??????
• ??????????????????????????????????????

17
???????????????? (??????) ??? ???????

• ????? Option pricing theory
• ????????????????????
• Black-Scholes model
• ?????????? Numerical
• Finite differences
• Binomial
• ?????????? Simulation
• Monte Carlo simulation
• Etc.

18
???? Binomial

• ??????????????????????????????????????????????????
  ??????????????????????????????????????
  ??????????????????????????????????????????????????
  ??????????????????????
• ????????????????????????????? replicating
  portfolio
• ??????????????????? Cox, Ross and Rubinstein
  (1979)

No Arbitrage opportunities
19
No arbitrage opportunity

• ??????????????????????????? (Efficient market)
• ????????????????????????????? (???????????????????
  ???????????????) ????????????????????? (??????)
  ???????????
• ???????? overprice ???? underprice
  ?????????????????????????????? (Equilibrium)
  ????????????

20
???????????? 1

• ???????????????????????????????????????? ?????? ?
  ?????? 21 ??? ?????????????????????????????? 20
  ??? ?????????????????????????????????????????? 22
  ??? ???? 18 ???

T 0
T1
22
Max (0,2221) 1
20
18
Max (0,1821) 0
21
???????????? 2 ????????????????????????????????
??????????????????
uS0
Cu max 0, uS0-X
S0
C
dS0
Cd max 0, dS0-X
Stock price movement
Option value

• S Stock price
• u up movement factor
• d down movement factor

• X Exercise price of the option
• C Option value
• Cu Option value when price move up
• Cd Option value when price move down

22
Replicating portfolio (1)

• ???????????????????????????????????????????????
  ????????????????? (?????????????????????????)
  ????? m ????? ?????????????????
  (??????????????????????????) ????? B ?????
  ??????????????????????????????????????????????????
  ???? ????????????????

umS RB
Cu max 0, uS0-X
C
mS B
Cd max 0, dS0-X
dmS RB
R risk-free interest rate (1r)
23
Replicating portfolio (2)

24
Replicating portfolio (3)
25
??????????? 1 Call Option
??????????? call option ????????????????????????
??????????????? ? ??????????????????????? 20 ???
???????????????????????? (exercise price) 21,
???? 1 ??, rf 5 ?????????????????????? 1
????????????????????????????????????? 22 ???
??????????????? 18 ??? ??????????????????????????
?????????????
t 0
t1
uS22
CuMax (0,2221) 1
S20
dS18
CdMax (0,1821) 0
26
t 0
t1
uS22
CuMax (0,2221) 1
T 1 rf 5
S20 C?
dS18
CdMax (0,1821) 0
27
?????????????????????????????????

• ??????????????????????????????? (S)
• ???????????? (Exercise price) (X)
• ????????????????????????????????????????
  (Movement factors)
• upward movement factor (u)
• downward movement factor (d)
• ?????????????????????????????????????????
  (risk-free interest rate) (r)
• ?????????????? (T)

28
Variable CALL PUT
??????????????????????????????? -
???????????? -
??????????????
?????????????????????????????????????
??????????????????????????????????? -
????????? -
29
??????????? 2 Put Option
??????????? put option ?????????????????????????
??????? 1 ????????????????? (exercise price)
20, T 1, rf 5 ,
t 0
t1
uS22
CuMax (0,2022) 0
S20
dS18
CdMax (0,2018) 3
30
t 0
t1
uS22
CuMax (0,2022) 0
T 1 rf 5
S20
dS18
CdMax (0,2018) 2
31
Generalization (1)

• Single ? Multiple time step
• The example was single time step
• In practice, multiple step valuation is necessary
• Dividing time into multiple step improves
  accuracy of the valuation
• Matching volatility with u and d
• Discrete ? Continuous compounding interest

32
Single ? Multiple time steps
t1
t 0
t 0
t1
t 0.5
uS0
u2S0
uS0
udS0
S0
S0
dS0
dS0
d2S0
t0.25
t0.75
t0.5
t0
t1
u4S0
u2S0
u3d1S0
u2d2S0
S0
u1d3S0
d2S0
d4S0
33
Matching volatility with u and d

• Volatility of stock price is represented by
  variance or standard deviation ( )
• We must transform it into u and d factor

time per one time step
34
Discrete ? Continuous compounding interest
35
Generalized binomial approach
36
Example multiple-steps binomial

• Example
• Price 36 .40 T 90 days D t 30
  days
• Exercise 40 r 10
• u 1.1215
• d .8917
• p .5075
• (1 p) .4925

37
u 1.1215 d .8917
40.37
36
32.10
38
u 1.1215 d .8917
50.78 40.37 32.10 25.52
45.28 36 28.62
40.37 32.10
36
39
Option value max(0,50.78 40)10.78
50.78 40.37 32.10 25.52
10.78
45.28 36 28.62
40.37 32.10
0.37
36
0
0
40
Max (Option price, Option value) Max (5.60,
5.28)
10.78
5.60
50.78 40.37 32.10 25.52
(45.28 40)
45.28 36 28.62
2.91
0.37
40.37 32.10
0.19
1.51
0
36
0
0.1
0
41
Put Call Parity (1)
Payoff
Payoff

Stock price
Stock price
X
X
Put option
Share
Payoff
CALL !
Stock price
X
Portfolio
42
Put Call Parity (2)

• If you buy the share and a put option to see it
  for X, you receive the same pay off as from
  buying a call option and set money of X aside for
  exercising it
• Value of Call present value of exercise price
  Value of put Share price

43
Strategic portfolio of options(Spreads) (1)
Payoff
Sell Option B
Stock price
XA
XB
Buy option A
Bull Spreads (by calls)
44
Strategic portfolio of options(Spreads) (2)
Sell option B
Payoff
Stock price
XA
XB
Buy option A
Bull Spreads (by puts)
45
Strategic portfolio of options(Spreads) (3)
Sell option A
Payoff
Stock price
XA
XB
Buy option B
Bear Spreads (by calls)
46
Strategic portfolio of options(Spreads) (4)
Sell Option A
Payoff
Stock price
XA
XB
Buy option B
Bear Spreads (by puts)
47
Strategic portfolio of options(Spreads) (5)
Buy Option A
Sell 2 unit of Option B
Payoff
Buy option C
Stock price
XA
XC
XB
Butterfly Spreads (by calls)
48
Strategic portfolio of options(Spreads) (5)
Buy option C
Sell 2 unit of Option B
Payoff
Stock price
XA
XC
XB
Buy Option A
Butterfly Spreads (by puts)
49
Strategic portfolio of options(Spreads) (6)
Buy a call
Buy a put
Payoff
Stock price
X
Straddle (by call and put)
50

• Whats Real Options?

51
What is Real Options?

• Options
• The right, but not the obligation, to buy (or
  sell) an asset at some predetermined price within
  a specified period of time
• Real Options
• The right, but not the obligation, to take action
  with a predetermined expenses within a specified
  period of time

52
Where are they?

• Real Options are everywhere
• Real Options are embedded in almost every
  activities (both business and non-business)
• Investment
• Life
• Industrial activity
• Construction process
• Etc.

53
What Real Options help?

• Concept of real options is used for over a decade
  in investment valuation theory
• Real options fit managements intuition better
  than the traditional way of valuation (NPV)
• NPV assumes that management looks passively
  during project process
• In fact, management can actively takes valuable
  actions that can improve profitability of the
  project
• Management actions are Real Options the right
  but not obligation to take action

54
NPVs assumption
55
Cash flow diagram
Time
10
3
2
5
4
9
8
1
0
7
6
56
NPV shortfall

• NPV systematically undervalues everything because
  it fails to capture the value of flexibility
• NPV may lead to the wrong decision, if there are
  naturally embedded options in the project
• Almost all projects contains such option-like
  features

57
When options have the greatest value?
Uncertainty Likelihood of receiving new
information
High
Low
Moderate Flexibility Value High Flexibility Value
Low Flexibility Value Moderate Flexibility Value
Managerial Flexibility Ability to respond
Source Copeland and Antikarov (2001)
58
Favorable
Unfavorable
59
How can we have options?

• Naturally embedded option in many activities
• By creation

60
Variables in Real Options
Stock Options Real Options
Asset price Projects PV
Exercise price The expenses required for taking action
Time to expiration Project time
Volatility of stock price Volatility of NPV
Risk-free rate Risk-free rate
Dividend Cash out flow (optional)
61

• Real options in investment valuation

62
Types of RO in investment context

• Option to invest (deferral option)
• Option to expand (expansion option)
• Option to abandon (cancellation option)
• Option to contract down (downsizing option)
• Option to choose (mixed)
• Option to switch among mode of operation
• Compound options

63

• Option to invest

64
Option to invest

• Right without obligation to make investment
• Making investment now may not be optimum,
  considering ability to receive more information
  that will become resolved (at least partially) in
  the future
• Investment choices are not only invest or not
  to invest, but also invest now or invest
  later
• Searching for the best investment timing
• Also called Deferral option

65
Simplified example
t 0
t1
300
0.5
200
0.5
100
200
200
200
200
200
200
Time (t)
. . . . .
1
2
3
4
T infinity
Investment cost
1,600
66
Its NPV
t1
t 0
3,300
0.5
2,200
0.5
1,100
Investment cost (I) 1600 Cost of capital (r)
10
NPV
67
If we wait for a year
Investment cost (I) 1600 Cost of capital (r)
10
68
Value of waiting

• Value of waiting for new information about
  uncertainty
• 733 600 133
• This is simplified version of the value of
  option to invest

69
Value of information

• This concept utilize value of information
• The example was actually based on Decision Tree
  analysis

Value of Information 733 600 133
70
Solving with Real Options theory
t1
t1
t 0
t 0
3,300
CuMax(3,300-1600,0) 1,700
0.5
rf 5
C
2,200
0.5
1,100
CdMax(1,100-1600,0) 0
u 3,300 / 2,200 1.5 d 1,100 / 2,200 0.5
71
Value of the Option to invest

• By RO analysis,
• 888.195 600 288.195
• Which answer is more reliable?
• Same concept but different answer

72
Decision tree vs Real Options

• Both concepts are from the same root waiting for
  information that become resolved in the future is
  valuable Value of Information
• Differences
• Discount rate
• DT violates no arbitrage law
• RO analysis automatically adjusts discount rate
  according to the actual level of risk

73
Option variables
74

• Option to expand

75
Option to expand

• Manager has the right (but not obligation) to
  expand capacity of project, when project goes on
  favorably
• When project is expanded, NPV is enlarged
• The expenses required for expansion is in essence
  exercise price
• Payoff Max unexercised, expanded value -
  expenses

76
Variables in option to expand
Stock Options Option to expand
Underlying stock The Project
Asset price Projects PV
Exercise price The expenses for expansion
Time to expiration Time limitation
Volatility of stock price Volatility of PV
Risk-free rate Risk-free rate
77

• Option to abandon
• (cancellation)

78
Option to abandon

• Manager has the right (but not obligation) to
  abandon (cancel) the project , when it goes on
  unfavorably
• When project is cancel, the loss is discontinued
• We also can receive salvage value of the
  cancelled project
• Payoff Max unexercised, salvage value

79
Variables in option to abandon
Stock Options Option to expand
Underlying stock The Project
Asset price Projects PV
Exercise price Salvage value
Time to expiration Time limitation
Volatility of stock price Volatility of PV
Risk-free rate Risk-free rate
80

• Option to contract
• (downsizing)

81
Option to contract down

• Manager has the right (but not obligation) to
  contract down (downsize) the project , when it
  goes on unfavorably
• When project is downsized, the losses are
  partially reduced
• It means we have some saving (by losses
  reduction)
• Payoff Max unexercised, downsized value
  saving

82
Variables in option to abandon
Stock Options Option to expand
Underlying stock The Project
Asset price Projects PV
Exercise price Saving
Time to expiration Time limitation
Volatility of stock price Volatility of PV
Risk-free rate Risk-free rate
83

• Option to choose
• (expansion cancellation downsizing)

84
Option to choose

• Manager has the right (but not obligation) to
  expand, abandon or contract down the project ,
  according to changing uncertainties
• Manager hold a portfolio consisted of option to
  expand, option to abandon, and option to
  contract
• Payoff
• Max unexercised, expand, contract, abandon

85
Interaction of options in portfolio

• Sum of value of options in portfolio is not equal
  to value of portfolio of options
• Exercise of one option affects the others
• For example,
• Exercise of abandon option killed the other
  options
• Exercise of contract down option downsize
  magnitudes of the other options

86
Compound option

• Options whose value is contingent on the value of
  other options
• Option on Option
• Two types
• Simultaneously compound option on equity
  (stock)
• Sequentially compound phased investment, RD
  investment

87
Switching option

• Buying flexibility
• Right (without obligation) to change to better
  mode of production when environment is changed
• Change mode of production
• abandon existing mode utilize the other mode

88
Consolidation of uncertainties by Monte Carlo
Simulation
Output
Input
Process (Monte Carlo Simulation)
Uncertainty 1
Risk Model
Uncertainty 2
Uncertainty 3
89
Real options by business sectors
90
RO from risk management viewpoint (1)

• Risk is not always unfavorable
• By RO idea, more efforts should be made to
  maintain flexibility (to create options)
• How to have option?
• Identify the existing (hidden) option
• Manage to have new option

91
RO from risk management viewpoint (2)

• 4. Instead of make decision in advance
  (traditional approach), we may create alternative
  (Options) and wait until the right time

Time line
Implementing
Pre-implementation
Problem occur
92
RO from risk management viewpoint (3)

• 5.New ways of managing risks
• Risk management ? Risk utilization
• 6. Gaining of Value of Control

• Retention
• Avoidance
• Reduction
• Transfer
• Sharing
• Insurance

• Defer
• Abandon
• Expand
• Contract
• Switch
• Compound

93
Utilizing concept of real options

• Environments in real market are somehow different
  from those in financial market
• Critical issue is how to recognize and structure
  mechanism of RO in phenomenon occurred in
  everyday world
• How to match real variables with options
  variables
• Aim is to meet risk management demand -lower
  risk premium

94
Value of information
without soil information
95
Value of information
with soil information
-5,000
value of information 22,500 20,000 2,500
96
Black-Scholes model
OC S0N(d1) - XN(d2)e-rt

• OC- Call Option Price
• S0 - Stock Price
• N(d1) - Cumulative normal density function of
  (d1)
• X - Strike or Exercise price
• N(d2) - Cumulative normal density function of
  (d2)
• r - discount rate (90 day comm paper rate or risk
  free rate)
• t - time to maturity of option (as of year)
• v - volatility - annualized standard deviation of
  daily returns

97
Black-Scholes model
S0 X
v2 2
ln ( r ) t
(d1)
v t
N(d1)
32 34 36 38 40
98
Cumulative Normal Density Function
S0 X
v2 2
ln ( r ) t
(d1)
v t
(d2) d1 -
v t
99
Example Call option

• What is the price of a call option given the
  following?
• So 36 r 10 v .40
• X 40 t 90 days / 365

100
Determine input variables

• Example
• What is the price of a call option given the
  following?
• S0 36 r 10 v .40
• X 40 t 90 days / 365

S0 X
v2 2
ln ( r ) t
(d1)
v t
(d1) - .3070
N(d1) 1 - .6206 .3794
101
Determine input variables

• Example
• What is the price of a call option given the
  following?
• S0 36 r 10 v .40
• X 40 t 90 days / 365

(d2) d1 -
v t
(d2) - .5056
N(d2) 1 - .6935 .3065
102
Answer

• Example
• What is the price of a call option given the
  following?
• S0 36 r 10 v .40
• X 40 t 90 days / 365

OC S0N(d1) - XN(d2)e-rt
OC 36.3794 - 40.3065e - (.10)(.2466)
OC 1.70
103
Black-Scholes model assumptions

1. The stock underlying the call option provides no
   dividends during the call options life.
2. There are no transactions costs for the
   sale/purchase of either the stock or the option.
3. Risk-free interest rate (rf ) is known and
   constant during the options life.
4. Security buyers may borrow any fraction of the
   purchase price at the short-term risk-free rate.

(More...)
104
Black-Scholes model assumptions

1. No penalty for short selling and sellers receive
   immediately full cash proceeds at todays price.
2. Call option can be exercised only on its
   expiration date.
3. Security trading takes place in continuous time,
   and stock prices move randomly in continuous time.

105
How estimated call price changes as number of
binomial steps increases
Binomial vs. Black-Scholes
No. of steps Estimated value 1 48.1
2 41.0 3 42.1 5 41.8 10 41.4 50
40.3 100 40.6 Black-Scholes 40.5
Binomial