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A Study of Real Option Model for Evaluating the Value of Nuclear Power
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I . Research Title: A Study of Real Option Model for Evaluating the Value of Nuclear Power
II. Objectives of Research
For the last decades, the real option models have been the dominant focus of theories of investment and evaluation. The objective of this study is to analyze the issues to be considered in applying the real option model to valuation of nuclear power.
III. Contents of Research
This study tries to answer for the following questions: (1) what is a real option model as an evaluation tool? (2) what are its advantages relative to the existing evaluation methods? (3) what are the main steps to apply the model in practice? (4) in its applying to evaluation of nuclear power, what issues should be considered?
IV. Main Results of Research
In order to apply the real option model to nuclear power valuation, the following issues need to be considered in practice. The first issue is to determine which variables are included in the analysis as the underlying uncertain variables; examples are input prices, output prices, costs of decommission and waste management. The second one is about which types of option are relevant with the target project to be evaluated; examples are growth option, timing option, abandonment option, flexibility option. The third issue is how to model the dynamics of the uncertain variables; examples are diffusion process and time series models. The fourth issue is how to derive the value of the target project from the modelled dynamics of the uncertain variables. If the type of the option can be considered as either European option or American option, then the value of the target project can be easily derived using the existing mathematical formula; for example, the famous Black-Scholes formula for European option. Otherwise, Ito's lemma should be used to derive the value. ■ sxt
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10 - #4 #4# #4 44^4# 444 4# 4444 4# 44#44 4 4%tid4 4 3# #44#4. 4# #44 #47f 44 4# ## 4
# 44# 3.$*}*}. #4 ## #4 44 4# #4# 44444 tid# 44 37] 4 3 t# 44444 # ## 4 #4 4, #4 #4# 44 4 4# 4 #44 4# 4 #4 44 44. #4 #44 #44 #4 44-£ 444. #4#44 NPVq *\ 434 44 #444 7}4# 471-4 4 44.
34 44- 34 34 44#44 41444 ^4*4 44# #7f4 444.
#4 ,
4#4# 4#44 4#3##44# 4#44 ^vpf4 npv^ 344 4 47}% # 44. 344 (%4 t7> 3# 04 44 4#41#, 4#3#4 44# 444711 4#4 74]47} 44# 471] 43 4#4 444433 4#4. 4, #44 4#4# 34334 34 47} 4#444 44.
yvpi/ =__4 3 447]-4__ " ^A}7M4^7]-4
51|
T- 4 ti_
4 crd
[34 41 ##4 7f4 44: npvq 4 #4#4 #4-#3 34# 57: 4##4 44 a# 4444 ##44 44 7:4# 4 #44.
4# #4, 4^: 44# 44741 9044 4tH 4#
?4# 3e]44. 3 44# 7f7]7f 4#4 t 434, *R! #44 44 4 40%4 3#44#- 4#43 #4. 47:447:# #4. 4^# 4 7144 34# 714-5] # 434, #44 °14## 5%el-3. 44. °1 #4
444 npv# 904-1004= - 104433 4#44 4#3##4441 44 4 4 #4^f4# #4447-1# 444. ^-44 34# 444 # 4# 4 44 3 #4 4% 47:# 44S.# 4# #44 7:4 7: 4# # 44. #4433 3 #444^f# 904 7:4 7: 4# 43444 44 10044 *574:4# 4# 34 44 #4 ##4# 7:4 444. 444 ##44
NPVq kr 904 / (1004/(1.05)3] = 1.044 44. #4#4# 0.4*4s =
0.69 44. #4-#3 #4# 4#44, 444 #4# 4# #4# 43
44 7:44 28. 4%4 7:4, ^ 0.284*904 = 25.5644 7:4# 4#4.
447-1 4417-1 344 #7:4 npv# -1044 4 4 #47:4# 254#
4 #4. 4 4 #41 3 #4- 4447: 44 #4# 44 #47:4# 44 3 104# 4447: s]£S 4# #444-1# 4 44. 3443. 3 #4 44# 34443 4 44. 4441 34#4 44447] 4-4- 47:# 4
#43 3 #47:4 4# 4#44 44. 4# npv < 0 444 NPVq > 1
44 4#41 3 #444# 4# #444. 4, 4#4#4#4 X7: 414 #4#3#41 444# S34 3.44 S7: ^:#x] t-u]#4 47:74] pv(x)
34# 34 4#41, s# x # 4## 44433 43 7:4# 4# #3
434 44 4414 7144-4444 447: 43 4# 444. 440] 3 #4 44 7:44 7] 4-74] s# 44433 r#4 4 # 4 #3 #7:4
433 7I444 4#41, 344 3# 4#4 npv# 034 33 #40] ^ 7:% 7:#4o] ##4 44. 44 4#4e:3 444 #4# 04 S-X # #47-1 # 44 7:4# 4# 444. 44 3 #4 447#: #4# 44
12 - S9444 4144 4 144441 44 141 -1044 44 254 444 444 44 444.
npv4 ^44 444 44444414 444 #S1- 4s 44. 44
441 npv>04 NPVq < i 444 npv
444 444444 444 4s 4 #ss 4^4444 44. s44 4
4 44414 npv < 0444s. Npvq > 04 # 4 44. s# 51 444
444 4444. s# 5414 44 441 444 si 441-4 npv9 > l 4 41 444. 3.44 41 si4 44 44 44 444(44441 4
4 44 444). 1, 41 141 *5444 “41 14*54” 444 npv 4 44 41 44 4 is 4s 14 41 44 41s 44. 1 411 14414 “41 14*54” 444 NPV7f 04 411 444 4141, 1
4444 04s npvq =14 44414 #444 14444 1444. 4
14 4141 444 1411 npv > 04s npv; > i# 144 #144
471-441 4s, #4 4141 444 1411 npvq > 1444 npv < 04 4 44441 44.
141 NPVq > 14 #4141 44 14# 4 41 sl<4 % 4 7f4 4
4# 41 1 4141, 4 441 s# 54 1# 44 44 41 4441
4144. s# 54 44 411 447f 4444 144 0444 141
44 04 14141 4444. 41 1411 npv > 0 444 44441 4
S4 444 74] 4 4.4 4141 14 *54444 44. 44 444 4-s 44 44411 44441 4S4 444 1414# #1 1414 44. 14 #441 41444 444 1411 444 44 *54*1144 44. s44 4S444 444 444 4444 44 41 #144 444 #4 *544 4444 1 s 44. 41W# 4# 41 1441 44 41 # 144 #1 44 444 S441 *5441 # 4 44s 444 1 44. s44 44 #14# s4 *544 #1 *54
13 - 7M4 44 44# 44. rcj-eM n>7] 4 #444 44 44 4 44 444 444 44# 444 44 44 4 444. 44 # # 44 44 # #444 444 4##441 44 4# #-d-44. 4##4 # 44 4-^-5. 2:7141 ^44 4 4# 4#44, 7f# 4 #444 7417} 44 4#5. 44% # 44. 44 4-^-5. 3.4 54 #4 44 4## 444-1 4# 4# #4444
44. 4, 4# npv < 0444 NPVq >1 471 4#41 4# #4# 44
44 44. 44 7} 7M44& s4 X7> 444 4444, JVP^# 444 44^ 4# #4## *5444 4# 4 #s.44. n44 ^44 #44 4#4 4444 444 44# 4444 4# 4# 44 471-44 4711 44. 7I2447MI 447M447}4
£PR! 1.0 DPR?
gaes aw °>=t A| = tSAh
!SAhE]qetE npv > 0 BP IS *SAh3haa|qqot
SAhif 3^ npv < 0. aqp NPV, oiss dh° syeh #AkAt3gj
[n4 5] #444# ##4 #4#^ 444 n4 54 #4# # 4 444444 #4# ##4 #4# 67: 44^
14 - 114 9 424, 4 441 3.4 64144 44 444 ?4 4441 4 -§-44. 3.4 64 r4§ 44 i, n, 11122 9-444 4444 51
NPVq > 144. 411 245441 9.## 41 4441 4444. 3.46 4 44 9-9:4 44422 iv, v, vi 41 443.5. 9-9:44 51 3P5g < 14 4444. 49-4 vi 444144 14144 04 52 41- 141 4 42. 4444 414. 44 vi 44422 4444 41 1411
5444, 41 14141 4441 NPVq ai ^9(7} 44. 4 4441 41 144411 14 44414 111 41 441 1444 44
4144 444. 44 iv41 NPVq $\ ajt #44 441 1141 4 # 11 41 42 4441 41 1411 5444. 41 144411 41 44441 49 4441 4144 441 422 44. %4444 44-444 14444 #544 4141 41422 444 444 44 4 144411 24644 14441 444 44. 14 44411 444444 144411 1122 41454 5444 44, 44 4 4 4444 24# 445# 5444 44.
7155471-9 59% = 447M447H
SLUR! 1.0 URR VI. ^2 S2 ItiAh y-1 I. AlS S^y ItiAl
2@5UINPV < 0, NPV(q) < 1 II. NPV > 0, NPV(q) > 1 LAF 5I23J or } 310-201 mm
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^ Z = (Zt:t > 0)# (Ititi) 3ef# ##o]ef3 44titi:
(1) 4ti 4444, 4, =oti
(2) #ti ti##3# titi. ti, 4 ~ 3(0,t)
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(Markov process) 4 4 S 44. Si — 44 444 4w4 44 4444 44 (Martingale process) 4# -8-4 4 4.4.
P = (Pt: t > 0): Martingale process if E(Pt + 1\ Fd.) = Pt
4, 4 = t44444 4S
E{Zt + dt\Ft ) ~ E {Zt + dt — Zt + Zt\ Ft )
= E (4 + At ~ Ef \Pf ) + Zf
= ^(d^l4)+^
= 4.
44 444 5S5, 544 454 #7}# dzdto] 454 04 455s
# 4444 544 454 44 (3 HI 44 4444. 44 41-44 47} 544 451 454s 44. 544 5 4#4
44 57}54 414 44 441 4 44:
18 - dXdt = dZdt where dZdt ~ N(0 ,dt) (3-1)
= \fdt e where e ~ N (0,1) (3-2)
*1 44 ##*-4#### tcfs- xt$) 4444 dto\] 44 y
7)144# 44 #7}4-£& 4#444 #4# 444# (4 #4)^4 a# -£444 4 4# #4 4444 4 44. 4
d A^. = crdZdt where dZdt ~ N(0,dt) (3-3)
= a^J~dd.e where e ~ N (0,1) (3-4)
=> dA^ - Af(0,oddf) (3-5)
44 Brown (1827)4 44 4#4 #7}# 444 #444 ### 4 44-£2L #44 4 44. 44 ## 4# 4# #47} 444 #4# 4 44# 4444 -2.444. 4 444# #7}# 447} #4 44-^.s. # ## 4(driftM 4.4 44. 44 t444 #7}# 44 44# 44#
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n XT = ^ (u /dt e i) where e,: ~ iid N (0,1) (3-6)
19 - => E7 W =
= 0 since -E'e, = 0 (3-7) 2 n \ = a2 dt V V] e,: v=^ J
n = a2dt'^V(ei) since e,: ~ iid
n = a2dt yjl since I7e,: = 1 "b "b e II II (3-8)
J^Lyn ~ #(0 , T(f) (3-9)
# -§-7]7]- ###7]] *1^*1 ^ #7]-#
^%>(drift)o] aiTii 5*u}. ojeiy 1 *><^M
4 (3-3)7]- (3-4)# Uf## #o] ^ al^f:
dXrff = yud* + crdZdt where dZdt ~ N(0,dt) (3-10)
= ii dt + a \fdt e where e ~ N (0,1) (3-11)
a#^(drift)o] tw#### #4#7]], /i7f ai^ ti.e]-# ### uf^-7]- #o] £#SJu}:
71 71 71 Jfr = yj (,u, dt + a y/dt e,:) = /j.^clt + a y/dt yj< Tfl -\- <7
=> E {XT) = 7> + u a/dt y] E (e,:)
= Tfi since ^e( = 0 (3-13)
- 20 - y(%r) = L"
= To2 (3-14)
,> ,Yr ~ (3-15)
7]] 2^ I to -§-^4 (Ito's Lemma)
1. 14^ I to -g-4
7ly]-A>o.s £2=, 7}x]# -S-S.^71 3MM±r
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dX = a dt + b dZ where dZ ~ iV(0, dt) (3-16)
= adt + b \/dt e where e ~ 7V(0,1) (3-17)
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[2] XT] 4>{X, t)S. # 5) [3] 4>{X,t) # 27M4x] Taylor# 7H #31 IS.#- # # # border)- 5# dt### #### ## [4] #[!]# 4-§-4# ^4 dXdt## a# - dX^# ##o]] ^|# [5] [4]# ##-# [3]# ##-# 21 ##X ###: d dip d(p_ ap) _|_ + dt T bdZ ax at 2 ax" ax - 23 - 2. 444 4#444 I to -g-4 n44 4#44# -2.444: d.Y = a dt + b dZ with d-2-,. ~ #(0, dt (3-26) = a 4, «/4 b:±r 444 tin 4 i^444 444 44: d X = ^4 dt -|- B \J dt € with e ~ #(0 , C) (3-28) A dt A B dZ with dZ ~ #(O', dt C) (3-29) 4. A,B: n*l 44 X,e,Z : n*l ##44 1 Pl2 Pin P21 1 C = P2n n%n wii th Pij = E (e,: e •) = Ao^4- Pnl Pn2 44 41-4444 44 444 <£(4,04 4^4 4#44o M 44- 4* 24 44^1 Taylor 47111- 44 414 14: 94 1 94 9 2d) dXj dXj T- dt2 + d#) dt 9 ^9.4 2 9t 2 s 9#)9t (3-30) - 24 - 9^ dt 9.9 - dt +IS+d^d%t d.Y d.Y 4 dA^-dt^# 9-4 9 -^-5. 4S4 4uf: d.X (I.X- = (a dt + b \/7H < • ) (cij dt + bj \/~iTJ < ) = a.iajdt2 + aib jdt3/2ej + ap { dt3/je,: + l>l>;dt <■<; (3-31) d.V dt = [ 99 9999 dt7} 49- 449, 19-4 4 # ^-4 (order)# 49 dt^ #9 s# 944-E 4^5. 4(3-31)4 (3-32)# X999 4#4 49 94 4## 494; dA, dA5 % 6,6j dt , (3-33) dXdt ~ 0, (3-34) dt2 ~ 0 (3-35) (3-33)4 994 949# 444 4#4 44: /•.' (d.V d.V ) : b b ill /•.'(( < ) =b ib jdtpij (3-36) <= ^(qe^ = <= e - A(0, C) 44 4 (3-26)4 (3-34)43-36)# 4 (3-30)4 4444 49 44# 9 94: - 25 - 4> (X + dX ,t + dt) — + £ fi -)■ d (f> — 0 (xV + dX, t -\- dt) — (p {X, f ) 9^ s g Y (aidt + dt " " A-xA + £ fi ^xk,b 'bidtp ‘' «« b,b >P' dt £4|+iM££ i :] + £ (3-37) *( 44^-4# 4^-4 4^4 #4 9 .S' = fi.jS.jdt + a.jSj.dZj (*(-l) => 4 (*(-1)4 4 (4-26)# 4^44 A = 5), a = fJLjSj, bj = o-jSj (*(-2) -> 4 (*(-2)# 4 (4-37)4 4444 4# #4# "24 44. / 71 ,S,Hr + ^ + 4 c c 9'(7» ^ # = vig 85 , dt . 2 dt 7 = 1.7 = 96)96^ j^°AM + £ (*(-3) - 26 - *il 4^ ^7H 4 l# #4 7]^6) ##4 ##4# 444 44441 4a>7>4».s 4#xK># # 4% 44# ^Af44 #44-# 71-4 4444 44##3-&4, ##4 71-4S 4444 4# 44, 44, 4# #4 44. *( 4#4 444 7}o]: ##42114x 1^ 7isn ##0] ^^o]] 444 444 4^44 44 4## 444 444, #44444# 4-4 ^#x}7} x^js] 44444 44 4 4# M# ^44r# 444. % # 4^(call option) 4 4 44(put option): # 444 3# 4 4 4. 4 4 4 44 4 4 44 4&4##\44 7}4o_g. 44# 4 ## ^4# #4#a, #'#%# 444 44 44 4444 444 4&4## 444 452# # ## ^4# #4 4 U-444 #% 44 -§-4 = - ## ^44 4: 4-4 7}4 - 47l (maturity!: 4-4 4444 4 44 44 4 - 4 4-44 (strike price): 4 5) 4 4 7i4 - 4 4 KLjy(payoff): 44 4 4444 4-4 7>4 4^4# 71-44 ##4 414% 4# # #4# 4 #44 4 * 4-4# °14# ## # 413., 445. #44 44-% 4# # #4# 4 i# # #4# 4#44 44# 4# 4" 44. 41# #4 a #4 100## # # 4# 4#4 ## #44 # #4# 6) # ^4 4-&# ^^#^4(2006) 1## #44##%(2006) 4# W# - 27 - 44443 #4. - #4 471: 37)1# # - 447}#: K=60 - 4$H A #4 7M: x=50 - #4 7M=5 44 37)1# 3 #7f7f 447}# K=60 34 #44 #o) -§-## *547} 44 k=60# #3 #4# 444 437} 44 44# 34# 4 #33, o] 4#4# $11 #-$.5: = 0, £4 = 500 (= 5*100, 37l #4 # #til#)7} 44. 443 37)14 # #7}7} 4471-4 K=60 #4 3-44 # 44 44# 4444 #4 7}# x (>60) 4 #4# 4471-44 60# # 3 444 4 4-0-4, 4 #7)1 444 #4# 4444 #4 x -604 44 # 4# 445.5. $1145-3 = (x- 60)*ioo, #44 = $11433-500(34# 44-§-)7f 44. 4# 44414 # #4# 43443 44. 37))# # #7} < #47} 4 k=60 4 4 #41# 4447} 44 #4# 34# 4433 $11433 = 0, #44 = 500 (#443#4)7} 43, 4$H3 37)1# # #7} > #47} 4 K=60 4 4#41# #4 4444 44 ^43 #4 7}# <4 x (>60)4 #4# 4444 *5471-44 60# 43 44444 4344 433 $114 33 = (60-X)*100, #4 = (60-X)*100 + 500 (#443#4)7f 44. 44 44# 4444 #433 3444 44 4#4 4# 344# 4444; - 4444: t - 44444 #7f=xr - *5471-4 =k - 28 - - 444444=9 44 44 9444 449 495.5# 9-44 4o] vj-Ej-yj 94 : ^ %r > ^ # 44 494 0 if A?5^ = max (XT — K, 0 ) # 44 =|^ ^ = min (A-A9,0 ) 9 944 999 499 S9 # 444 44. 4 if %r > ^ # 44 444 = - (7 if A — C0 + max {XT — A, 0 ) A-A^ + (7 if A^, > A # 44 DH&4 = (7 if A^< A C0 + min {K— XT, 0 ) 44 4 444 9-4 444 4444 ^ -§-4 599499-5. 4 4. ^4 444 49-5.5 4441 44 444 44 4 444 4444 7l4 (arbitrage opportunity )7\ 99 M95 44. 55# 95# 444 9-444 95 oie!4 4444444 4494 44 444 viabie945 44. viable 444144 44 7f44 44441 #44441, 444 4 47M4 44444 (Arbitrage-Free Price, AFP)99 ^uf. -£-# 44 44 444 444 44 7f94 4444 55#95# 44 55#95 (replicating portfolio)4 44. 5.4 5:44 4444 44 44 55 #95.7)- #4 44 444 4U14 445-4 (complete market model) 9 9" - 29 - 44. 444 ##4 44711# 4#4 ##4tii #4433 °i ### 4#44 #44 AFP# ## # 44. ##7}4# i~)j 4 7}4 (intrinsic value)# a] :?>7}4 (time value) 4 %} 33 #444. -g-# 447}## #43##7} #4# 44433# MJ-a£ 5]# 7fa|o|n] , 447}a) (excercise value) ## 444 7]-a] (economic value )5}3 44. #4 447]-a]# #A}o]j SjSlj 4 #4# 713a}a> 7[a] 4 #444 4 #4# 4 #4 Aj.ojS.A-] 7)144 #4, Uj-nl -§_4^A}7} $] #7} oj-ujej- ^ejo]7j 4#4 f-#7} % # &4. 4# #4, S#44 4# #4 44 fo)14 4t}7j-Aj 5)7} #44# 334 # ujjAjj7fAj # 5)-3> 0 oj SjAjnl, ulrjjoj ;g#6fl±=. #4# 4444 43# 5]H 3 447]-a]# st-K < o o] oj-ujej- 44 04 44. ccj-ej-Aj !~£-4 44 7}4#, max (5) - K, 0 ) 33 7)1444 447^4} #44##4 ### #7j.#4 514. #44 44741# -5-44 # 7fAj #0jjAj 447411- #44# ## ^.s.Aj, 4444 #4# 344334 7144# #444. 44# 44 44 01444 447]-4 7j- uj #oj-4 # 44 7j$j7j-4# 444 37#} 44. uj-ej-Aj 4414444 4444 44 #44 4471-4# #4 4 4 4 7}#4o] ### 4444444 4471-44 &4 44, 44444a] 4 4471-44 3443 4471-44 #444. 44433 4471-47} # 4# 44 4 # 7}#4# 4444 433, ##444 4471-44 44 71-44 433 #44# 444 434 447>47> 04 4 4, 447}4 4 #4-4 #4 4# 4 444# 4#4. 44 44 #4 4444 #44 71-44-4# 4471-44 44 444 4-. 4471-47} #A]j4# 4#4 #44 47f44 443 44 (the call is in the money; ITM), 44# #44 #4 44# 44# 4#4. ## #4 44- 71-44-5117} 471-44 44 444# 4-4:71-4 7} #a}h1-§-34 444#4, 447} #4#4 444 # 4 #4# 7}4447} 447}4 - 30 - (deep in the money HI 44^- 4^- H 44 7} 4 #4# 447}4# 4^1 3. 4474M 4^44 44. #4414 447}44 4.3. 44M44 # 4#^ 444 7]-7]^-BllS ^(parity) 4 #3. 44. 44 4#7}47} ^ 44-§-5-4 4-0M 447M^ 4.3. A] 471-4 n> 61^ ^4-4^ #44 4 7}44l 4.43. 44 (the call is out of the money ; OTM). 4 4 #41 4 4M44 #44#4 447} 44 # 4444 741447} 447}4 (deep out of the money) 444 443. 44. 343. 4#7}44 44ul 44 4444 447414 043 447414 447} 4 44-4 -§-444 4 #7}4 (at the money; ATM)443 44. °}4 &4 ^-n§ 444 # 4 74144# 3444 5-4 #4. W #-§-44 7}444 ## s » K S > K S = K S < K S << K 7}444 T144^ 444 ^4 44 o K 4 47}4 47}4 <------1------► #44 [341 #-§-4 7}444 #99 #4# ^>7]A]^4A-]n> 949 ^ 44. 91# w°^, 9944=14- ^Af7f^=E 4# E4 #99 t 9# 99# 9-494. 4:4 t 444 49 7f4°l 4449, 44 4441 9^9 444 #444 449144 7>9 4 441#^# max (5r — E, 0) (4-1) 44. 4444 444 #44 944 # 44 7f9# 44 194-1 4 44 4471-4 # #44 44444 9#99 r=T-t, 4471-4 e, 4-4 4 94# r, 4494i 9 ^471-44 9#9&9# p(4)91 4 #44. 91# #9. #44 ##44 7149# 4471-94 #9 71-4 (fair price) # 4#4 94 : c (S,E,T, p (ST) ) = exp (— rr)E (max (ST — T, 0)) (4-2) = exp(— rcr) f p (ST) max (ST — T, 0) dST (4-3) v — co 944^-S. 4-49 94# r# 4#94 #4 949^- 71-9 94 9^.4 4 71-4# #99 #x (a.# &n9##&)# 9#4^ 71-999 4# 91, 4^ #99 ##44 #971-4# c(s,e,t)s. S99-E# 44. 7-11 24 4471-9 499 44# ## 71-47414 94# #49 4#, 994^ 944 94-71- 49 44 4 94# -2.444. 2L o].o^ 444 944 9## tl 447} 497} - 32 - 441 4#47] 4#441, 4# #4 #44 10044 444 44 4& 4 47M4 iooo^J <=lL 4 #4 100444 4 #41 44 44 n 444 #^-4 4 u>eu>. 444 44 4s.SlM 4#4 44 4444 #4 #4 4 44 4^-& 44-^4; — 6) 3# Rt (4-4) S St 4, 4+ti — * + d*44444 ■§"§•44 7f4 34 = (%4#4 4444 #4 §-§-44 7>44 44 44 #4 #4 S44(drift)# 44 ^-4#### 444^ 7f44 4, 44 t§144 44 #4## 4#4 44 #444: Rt = = // tit + crd-2) , where dZt ~ N(0,dt. ) 44 (4-5) A = /id,t + <7 433 e where e ~ N (0,1) => dSt = Stft,dt, + StcrdZt (4-6) = St ft d,t + St a \fdt e 4 (4-5)4 444 4#44# 7)4—44 ##(geometric brownian motion, gbm)4 4-^ &44441, 444 44 7f4447f 44 4 4 7M447} ti.ej-4: ### 4^4 4#44. 4, 44*14# ### 44- #4 4444(34 #441 §-§-44 7f44 444(36")# 5.44# 4. 4 (4-5)44 44 44#4 444 ##4 4#4 ##4 4-^-5. 4444. 4 444 4 44 44 Mf-b 447f44 4§r 44# 4444 4444 4^5. 444 ##4 4^., # 4*11 -d.^4 V3f - 33 - # 4544 (7, ##57}#- e, ^7lt> dts #444 4#4l 4#4 ##4 44. 444 4454# #5414 4475) #4-4-45 4544 ## °1544 54 4571-44 #4445 544 57551 4### 4 44 4#44. 4454# 555 ##-#5 547^44^44 454 54 7f 44. 5444 4471-7] 45# 4444 44 5 4# 54# #555L 4 5 54# #5^1 44. 45 54# 5544 44 54#4 444 5 #4 4#4 ##4 54 454554 44 44 #4 4454. -^7- = exp (p. (di ) + ere ) = exp (fj, (dt.) ) • exp (ere ) (4-7) 4 444 444454 44751 54#4 4544# /'. 44454 a, 4t-57}4 e, 4444 dt # 4 7fl 544 45455 #444. 444 45 544 4544 44751 44444 4544## 454 4 54 4575141 #444# 544 57551 45## #44 4#4 4. 45 54# #5# 45#47f##4544 4#4 547} 44. 444 454 55 54# #544 55# 4544# 54 4445 4 *44. 444 54# #5# ##751 #441 45-4 4#, ##751 5 4544 75141 45# #5 4454#4# 54444 4#41 45 44# ^# #444414 41444. 5#4 454 <%# ##751# #4 4#4 4# 554 44# 44. 454 54 44# 44 755} 44 4 45# 47)1445# 454 4# 4#4 44 4445 54#4 # #44# #5 4544; s (4-8) T- 2 - 34 - 4, u t — (4/4 -1 ). t — 2,T 1 u u T- 1 t 44 4##o) S#4# 44 *##### 444^ ?M44. 4, c/0' = /U 0'dt + aSdZ (4-9) o)4 4444 ito 44# o)-§-4j #4*-4# ### 4£# 4 4741 s$] 4# 0 (4*)7j- 4# ##44# -£#4 4 44. 344 l# 4 ##44 4 44 i to ^-#4 44# 44 4444 4#4 44: dX = adt + b dZ where dZ ~ N(0,dt) (3-16) =/■ d(f) = 0 0V + (ZA0 f + dt) — 0 (^V, f ) = («#+#+4#)di+#Mz <3-25> #, 4 (4-9)4 4 (3-16)# 4^44 X = S, a = fiS, b = crS (4-10) 7} 44 4 (4-10)# # (3-25)4 4444 4# 44# 44 44. 90 90 00 /j.S + dt -\- (7^0^ (4-11) v 96" dt 96" 4 (4-11)0), S7> 714^-4# ### 4# 4 444# ^4 4 - 35 - 4 S»1 ## <(] Al^ ^-§-3t-AflA}.= 0, 4# #-£4 4## 4#4, ^7]A-i S^ #-&444#4 7] ax].A> 7M4 444^- ^t 4> {S,t)k= 444#4 7M4 4444. 44 4 >(S,t) = log 5 4. 4#4#, d(f> _ j_ a2^ _ _J_ d± = 9^ " 6" ' 9^ 2 " 6"2 ' # -)> cl(f) — fi — “2“ | clt + cr dZ 7} 5]HS, r = iog6'4 444 4^4 ^4# 44 44: dK= log 0% + a)-log(,%) =log{^^j — | fi — -"2"-1 dt + cr dZ with dZ — 7V(0, dt) N jj,----— | dt , cr "dt 44 4471-44 S-fr-4 /'4 444 44# /■# 4444, 4# 4 44 44# 44 44: S + dt dY = log r — ——■ I dt + cr clZ with dZ — N(0,dt.) st (4-12) S + dt ff 4 dY = log N v----— | dt , ## 4 #4# 4471-44 44*4# ### 4*# 4# 447144 - 36 - SALll# S# S## ### ^ 1# S# 111. #, US 1# ### IS# 117M1 SALIH H# %S1 (r-a2^)dto] 3. #11 a2dttd l##s# cfm 4 3i 1-1% -a-mi n# m 1 1% 11# 1111, 1171-1 S7\ US## ### IS# 1# 11 /(#t)l H7f 1# 1#11# I to -§-111 1# 1#1 1 1 S#ll: dS = jiSdt + aSdZ L.S- Af ^ d£ nm) 9L 1 # dt -\- (76" d^ 96" 9t 96" V 2 96" J with dZ ~ N(0,dt) 1 11 11% Si# 1#1 H: A S = n S At + (t5A7 (4-14) Z (4-15) with AZ ~ jV(0, At) # 1111 6# H-S1# ### IS# 7]2l 11 7fl# 1143. % % / (It)# #-§-#11 7#1# lEl-41. in is i ini m m# /7> im m n# 9//961# Sllll 1# SS#1S# Sill. oily XS#1S i7 1 7fl# - 37 - n = - /+S-S (4-16) 7} 5]3., 44 AMI 44 7}444# A77 (4-17) 7} 44. 4 (4-14)M" (4-15)# 4 (4-17)4 4444, 1 ^2- - a#*2 A 77 = — -o" At — (^S + f a^2 "dlsr + (7 ^AZ} (4-18) 44. 44 4 SH#e]^.7j- 44#44444, #4444# 4 #4# & f7}4£S 4#4 #4 44# 4 44: r 77A t = A 77 (4-19) 4 (4-19)# 4 (4-18)4 4441 4444 rll At — A t (4-20) 7} 4^. 4 44 4441 4 (4-16)# 4444 - 38 - 7} 5H, O] Black-Scholes ^u]-: 9L + # rf (4-22) 96" + l^S 4 #44 4 44# 4444 tz\^j} 447): - ##7}4#45L^#, 4 4" 4 4 714 4 ?i#4# #4 % 7] #44; (underlying asset) 4 71 7}x\7} 4#44 44# 7}x]4 44 4"iF (contingent claims or derivatives) 4 444 4, as) 4 -##2] 7}^# ^7}^rj] 4 #4# o]^ - 4 #4# 7M4 4#4^: 4#x}4;4 7M(p)o] 44^ #44 #4# #4 4 #44 (dynamic stochastic process) 4 444 4# 44 (Ito Process) 4 4 4# 4 4^ 4 44a 7M#: f (1) dP = a(P,t.)dt. + b(P,t) dz \ (2 ) dz = e \[di, with e ~ jV(0, 1) 7) 444444 (2004)44 444 - 444# 444 4^ 7l2:X>A> 7>23o]l 7}^] # x] V| ^ 3|-X§A]- 34 7M(f)# ^ (3)4 #o] (3) / = /(#,2) -> 4(3)# 44 Ito's Lemma4 4 4 4 (4)4 #-8 - Ito Process 5, #44 4#4: jpi)dt +t>(p't)-%pdz (4) # = di ot + 71&4<44 7M4 71^4 4^334 7}43 <434# 444 47] 43-4 #44 #4# i£#4# dz #4 3 s44 4444, 4 4# Wiener Process 43. #5)4 493. 4 # 43# 4^4 4# (Hedge Ratio) 5. fr#44 #444 4 444 444 #44 43(-#)# 4#4 4 # ##4(45), 4 44 #44 #44 4## 4# #4^ #4#, 4 #4^ #4#(## #44 #(46). (V n = f-jtpP (6) cin = 7dt 44 4# #444# Contingent Claim Analysis45. #. 43344 = 4&7}# xHM 4# ##44(41)4 4 44 434# 44334 7}44 4# 4#44(44)4 #444, 4(5)4 (6) 44#,^4 444 4# 4# 4444 _L pJLL +I 3#^ ?~2 (p,t)^- - + 7 P- = if 92 ' ' 9# ' 2 " 9#^ -> 4 43444# 44434 #444 444# &4#44 44#44 4# #4# # 4#4, 4 4 #414 # /(#f)# 4#7}# 7M4 #44 4 4# 444# 6(#zH 44 444 # 4## #43. 344: 4^4441 4^4 #4% ##44 ##4# #444. 444 44# c4 p# 4444 4# # 7H4 Biack-Schoies 444# 441 4 4: - 40 - 9c 9c 1 2 n'2 d~C + S^S + 2a'S = rc (4-23) 9Z dS £+s#+ 7^ = "" (4-24) 44 ##44 ##44 4444 !? = o 1c+o 2pf 444, ^ Black-Scholes 444# ##44# 4# 3.4 # 44: (4-25) 4 4^ ##% #^-#^(Black-Scholes) ^ # #444 44-^4# ### #3# 44 xj-A^j 713## ##% #47#! #44 4#44 #4-#^ #4# -£#44. 44 44# ts. *7143. #44711- ts. *7]44. 344 4444 4 4#44# r = t-H4. 4471-47} 4 43ef# ### 433s. 4 (4-13)4 44 4#4 44 444 4 44. ^(44 (( dr N r — 4- left o" eft (4-13) vv o| 4^ 014^0.3. 4444 4#4 44: (( log | ^4 G~ N r — Af , er Af (4-26) VV 441 4# ^44# 4#44: - 41 5V A t — T, St 6", & = ST, and X = log t + At 5 4 (4-26)# 44 it# 4# 4 #44 44 4444 % — (r —cr/2 )T, crT) 7]- 44, X# ##4&4# f(X)kr 4#4 ^Uf: /m = exp (7 Vt" V27T 2(7jT *547144 ##44 7f4 c(s,e,t)^, #71444 #4 41 4^# 44444# 444444 444 #44 491444. #, c (S, E,t) = exp (-rr)E (ST — E) = exp(-rr) f f (ST) (ST - E) dST. (4-27) J ST = E sT = Sexp(x)^ 4#44 44 4#414 4444# 44, c(^,^,T) = exp(-rT) F /(X) (^exp(X)-^)dX (4-28) 4 = iog(^/y) r exp (— rr) f ^(%) - ^7)&Y exp <7 \f~T a/StT Jx = log (E/S) v - 42 - = 5exP(~rT) r exp ' (X-(r-^)T)2 exp (X) dX Ua/t V^TT V'A"=iog(^/y) A 2(7/ 2t Xexp (— rr) /* exp (x- 4-4/24 y dX a 1/T1/2 7T J A 2ct2t (4-29) — 4 4. (4-30) ol ^ H -L447I0J 444444,* 4# 444 44444. ^ exp (X) = ^7 X = log (^/^). 4 (4-30)# 71144-7] 444 444 #4,#&44 4# 44## 4444; (1) d> 4) = -J=- [ exp ld« \IV^ 27T77 v" U -=— CO V ^ (2) 1 00 ^ if => exp clu = —7=— / exp du 427T / 42%- 4 44 44 4444 3-444. 4# 44 4# 4444 44# 4 4# 41 434, u = (X- (r - 4/2)r)/(7 a/t (4-31) dX = o^Jrdu (4-32) 4# 44# 4#4: - 43 - ^ u2 IB = Xexp(—rr) exp du = Xexp(—rr) d> (— k,2). (4-33) 4, ^ = { log ) - (r - cr/S )T}/(T ^9 44 4## -2-444. 44 4 #4# 44444 4# ^4# 444: Sexp (— rr) f 4 / exp cr Vt" V27T A"=log(^/f) V (4-34) 44(exp)4 4^4# 471)43. ( X— (r — cr 2/2 )t )2 — 2ct2tX = {X — (r + <4/2 ) tY — 2cr 2rr2 7f 5]3. ojs. uj-A] Ai (4-34)*] 4S41 4^4 4uf: ( X— (r — cr/2 )r )2 — 2ct2tX exp 2ct2t ' (X- (r- o] 444 A] (4-31)4 (4-32)4 4444 44# 4-§"44, 4 (4-34)4 4# 4#4 4°1 444 4 44: - 44 - s ' if Ii = exp du = S d> (— ) (4-35) 42^ 4, 4 = {log (E/S) - (r + cr2/2 )r}/(jv/r 4 (4-33)4 (4-35)# 4 (4-30)4 4444 #44 ##44 7}4# 4 #4 44 44# # 4-5.4, c (S,E, t) = S (— k2) S d> (dx) — E exp (— rr) 0 (d2) (4-36) { log (S/E) + (r + *t2/2 )t} 4, 4 = (7\/T {log(6"/^)+ (r-0'Y2)T} _ di-cr/F d-2 = (7\/T 4 (4-36)7} #^% # #44 44 #44 #4-#^ #444. 4 #4 # 444-5-S 4444, # #4 7}4# ##44# ^(4)4# #44 ^exp(-rT)^(dJ4#4 44(4= 444 44 # #444 4# 4444. #4-#^ #44, 444-5-5. s# ##44 7}44 ^442. rcfeM #4# 4447] 44 #44#4 ##44 2%44# 444—5. 2:4 4 4# 44444 7}44 7)## 44. 544 444 44444 7}44 -E ##45. #4-#5 #4# ## 741)7} #447]£ 45. 7}44 4— 4# 44 414H14 4 4#4# 4-E& 444 44. &4 #4, 44, 4w4 44 #44 44# 7}4 444 4 54441-E 4 4#4# #4 4# 4# 44 #4444. 444 4 #4# 44 4141414 # 444 # 45. 45.4 #44 7}444414 #54 #45. 4#45 45., 44 #4 44417-1 4 4 #4 44 %#45i 44. - 45 - !-e4-iNS -§-44 4-§- AMI# 441, 44 # -§-4# :n3)4 Uf: 7]^x]-a> 44 7f4 = §' = 55 *54714 - E - 55 4444 44#(44) .£^44 = (7 = 0.4069 n>7]7]-x]^ 4444 = r = 0. 5 444 o]x].^.( 4 (4-36)4 44 # -§-414 7}4# 3§7}#7l 444 4# 347)14 44 -S-4# 4-§-44. [14:7)1] 44 44 7)14;: 4 = 1 log {S/E) + (r + <4/2 )r}/cr /r = {log (55/55 ) + (0.04 + 0.4069 2/^ ) 0.5 } / 0.4069 /0l) = 0.2134 d-2 = 4 — a yfr = — 0.0744 [24:7)1] ^ (4)4 <44)4 7)14: <= excel414 4444# t)1444 normsdist 4- 4 °l-§- => 5 (0.2134) = normsdist (0.2134) = 0.5845 d? (— 0.0744) = normsdist (— 0.0744) =0.4703 [347)1] 4 4## #4-#^ -§-441 44: c {S,E,t) = S d? (4 ) — E exp (— rr) 0 (4 ) = 55 X 0.5845 - 55 X exp (- 0.5 X 0.04) X 0.4703 = 6.79 - 46 - 4 51 ti|2 d14 i^-°-l 714 «WW 444^1 u|g-S- a## # yy 5.A] yyyy (Dixit and Pindyck, 1994). #yyy4 yyy ##y# Ms, 4-y -My &y# y#4, 7]-y s# ^y ^ y m# n yyyi yy yy# y#yzi yy# y#ii t ai# y^i- yy yy# y#y# yyiy ziyy. 4, y#?yyy 4 yrn #yy# # ^yzM, #yyysy #4 y# y#yy# -g-y^y mi y#y Til y# y^yy, #yy #yy^## #yyi #yyy. yy #yy yyyiy s.y, #yyyy yy# y#y^.& yyy-y 4##y #y7i yy “4# yyy yyy y yy ” yyy o>y B> ys:& y#zi yyy yy# y# y y yy. # y yyiy^ y# y-g-g-yyy My# s.y, y# #yyyyiy yyyyy yyyy yy y-g-ye# 44-71-y (xh #yyzi, yyyyy y-yy ##y# 71-y# #y7M(s)4 #y yy. Myy# yyyy ^yy #y-y-7i- yyy y y# yyy -g- yy yyyyuH #yyzi #y-yyy #yyy ## yyy #y- y #y-#y yyt- aeyywy] yyyy, yyiy y#7>y# #y^yy #(r)4 y# #yyy. yy-yyy y 4 yyy yyy yyy yy yy y#y yz. yy y y y# yy# yyyy. #yyy# yyiy #yyyy y#y #y yyy # yy yy o_& ##yy, yyy yy# #yyy4y yyy yyy iy§ y#y. yyiy #yyy# 71-yyy y-g-yyy y# y Aiiy #yyy y^yyy, #y#, yy, yy7^ yy yyyy 7>y # y^iiy #yyy# yy yy#y yyy. #y-y-y yy##y# 7> yyy, yyy yyiy #yyy# y^i-yyyyyi yy yyyyy. 4 - 47 - # #44 #44471- 4# 44444^# 444# #444# 444 45. 444-5 #4#4 4414 4" 7M# 44444# ^# 444. 4 44 4414 #444# 44444 4 4-4# 444 #44 44# 4 4# 4-4# 4#44. 444 4#4 #4#4# 444 #444 4444 444, 4# # 4 44 4444 4# 4##44 44444# 4 #4 #444# 4# 4444. 4 4# #4# 44# 4 #45. 4444 444 45.4, # 4# 7:444 47114 #44# 4444 444 #44 #444# 4^44 # 44. 444 4#4 #4444 #44 4#, #444# 444# #5.4 -$-44 4444-5 #4# 45.# 44 7f44# 45.# 4#44 4#4 #4# 7:44 #4# 4#44. ##44 a##45.# #44# #4 #4444 a##45.# #4 4# 44 444#, 4444# ##44 #4# 444445. 444-5 4#4 #444# 4144 # 44 4#41 4#4 #4444 44# % #4 # 444, #4414# #4444 44 44# #4 4#4 #44 44 44# %#4 # 44# 444. — 48 — II 5^ 4 H 1##1 Hi HI Meyer( 1977, 1984)4 14 7))W ###H 7}H7} 7]1#, ## #1 4## 4 ##11 11414 41 #Hm 4414 ## ##7} 1 41^4 (option pricing model: opm)# 1# #1111 7}15§7} 4 111 47M -§--§-11 141. 4# 711471 7111 4aM# 4, 1 ##! H# #1111 111 1411 141 111# -§-11 11 41 1#14 4# 7H& m 1 4.H4, ml 7)#1 7] 1411 #111# #14711# imil# 14-11 #m&l 1## 4 11 4 1##1 1141# #111# #11 4## 711# 1#11# # H5.1 !#!. 1##1#4#, 441 4## #111# 4## 11 # 4# 111 #11 1141 #1. 4# #4 141171 4## 11 #4 41 #111# 4111 41# #1# #41 11 1#4, 4 4# HI #1711# #n 1# ii4#mm mu414 11 # 141. #1111 441 4714 #11 1141 HI# 4#, !#!! HI me]m #11 #141 1#11 1# 114 14 Hill# 11 1#1 (volatility) #1# mill. 441 #111# 11 ims. #1144 #11 Has 1#H1 11 #117} in #1114 4#14 1111 #!#!# 1 # 1# #1# 4#11 1#414 #11 4 #4# #1 11# 4111 !m 11117} 1 # 414 #11 4#4 411 # 1# 441. 1, 441 #111 - 49 - # #44t11 %## # 4# #44 7}#4 o] #4144. 44 a] #44 #4444 # 4 4#4 #4414# #4^}^4 7}447}41 #4 4# 4# 344 437} 44. 4%4 (contingency) #4414-5, 4#3##43444i4 44 44 444-5- 444 3# 4444# 444414 4# 4 #4# 444 4 4 4441 44 444-5- 444 4444 4 #4 4443 #44 44 44 444-5.S. 4444 444 44444. 444 4# 443 44 4 45. 4 4#4 444 444 44 #444 #7f44 444 44 # 47} 444 4444 #44 4444 7^444, 4#5l#4434# 4#44# 4 #44 4471-47]- #(4444-5 #4# 5.44 # 44. #44(flexobility) #444, 444 3#41 44 44 7}#4 44 447} 4#4# 4#41 #44 4441 4# #4 #4# #444 3-7] 4#41 44 4441 44 44433 444 # 44. 41# #4 444 4#4# lB4#44 4#, 7l#7:4 #441 444# #4 ##33 7fl 44#4 44 334# 44444 44 7fl## 4#447} 44444-1 43 43 4471#4 7)144 4#41 44 4## 7)1 a)4# #4#444 # 4 # 44. 41 2# ###4 #4 #441 44 #44 434 #4# Weisbrod (1964), Arrow and Fisher (1974), Henry (1974)4 4# 4444144 #4 #4#414 44 44441, 44414# ul7}44°l3 4#4 44# 444 444 4#4 #4 444441 444 #44 4#4444. 4#41 44 44# #4 33 5.# oj-o]447} Myers (1977)4 Myers and Turnbull (1977)4 4# 4#r4l4( capital budge ting) 41 44 4414 #4 #414 417144.3, Black and Scholes (1973)4 Merton (1973)4 ###4 7}4443^4l - 50 - al#44 4#444 44 #4#4M1 #44 #4## 4#4# 44# 4##4 4 7] 5] 7] 44444. 44 [Si]# 4##44 #44& 4##4 -§-§- 49-## 444 4 43-, [S2]# #4 #44& 4##4 #4# 444 4444) [S l] 49-#4 4 #44 4##4 49- 9% Tominho (1979), Brennan and Schwartz (1985a, 1985b), Siegel, Smith,and Paddock (1987), Paddock, Siegel, and Smith (1988), Morck,^™chwartz, and Stangeland (1989), Trigeorgis (1990), Kernna (1993), Pickles and Smith (1993), Epstein (1996), Leslie and Michaels (1997), Schwartz (1997,1998), Srnit (1997), Smith and McCardle (1997,1998), Laughton (1998), Tufano (1998) Baldwin (1982,1989,1991), Gilbert (1989), Kogut (1991), Trigeorgis (1991a, 1996), Baldwin and Clark (1992, 1994, 1996), Kulatilaka and Perotti (1992), McGahan (1993), Smit and Ankurn (1993), Srnit and Trigeorgis (1995), Grenadier and Weiss (1997), McGrath (1994, Larzin, Huisman, and Kort (1998) Kulatilaka (1984, 1988), Kaplan (1986), Aggarwal (1991), He and Pindyck (1992), Baldwin and Clark (1994, 1996), Karnrad and Ernst (1995), Mauer and Ott (1995), Lefley (1996) Stulz and Johnson (1985), Titman (1985), Gilberto and Ling (1989), Capozza and Sick (1991,1994), Williams (1991,1993,1996), Quigg (1993,1995), Capozza and Li (1994), Grenaider (1995, 1996), Childs, Riddiough, and Triantis (1996), Sirmans (1997) Baldwin (1987), Dixit (1989a, 1989b), Mahajan (1990), Kogut and Kulatilaka (1994), Sercu and Uppal (1994, 1995), Bell (1995), Buckley and Tse (1996), Sensing (1996), Capel (1997), Schich (1997), Buckley (1998) 9) #7]: Lander and Pinches (1998) R&D Monis, Teisberg, and Kolbe (1991), Newton and Pearson (1994), Childs, Ott, and Triantis (1995), Faulkner (1996), Ott and Thompson (1996), Pennings and Lint(1997) Mason and Baldwin (1988), Teisberg (1990, 1993, 1994), Edleson and Reinhardt (1995) Hathaway (1990), Smith and Triantis (1994, 1995), Hiraki M&A and 7] Kandel and Pearson (1995) 'ffl7]x>Sr Sahlman (1993), Willner (1995), Gornpis (1995) Epstein, Mayor, Schonbucher, Whalley, and Wilmott (1998) Triantis and Tiantis (1998) ?]2zEiM3:3)-4 7i=y sj-§. Pindyck (1991), Dixit and Pindyck (1994) Purvis, Boggess, Moss, and Holt (1995), Wiebe, Tegene, and Kuhn (1997) [S 2] ^ Type of real option References (tourinho (1979), Bernanke (1983), Titrnan (1985), ^7] ^-74 McDonald and Siegel (1986), Trigeorgis and Mason (1987), Lee (1988), Paddock, Siegel, and Smith (1988), Pindyck (1991), Ingersoll and Ross (1992), Kester (1993), Dixit and Pindyck (1994), Kulatilaka and Trigeorgis (1994), Edleson and Reinhardt (1995), Kulatilaka (1995), Purvis, Boggess, Moss, and Holt (1995), Quigg (1995), Lee (1997), McGrath (1997), Farzin, Huisman, and Kort (1998), Laughton(1998), McDonald (1998) Bonini (1977), Kensinger (1980, 1987), Howe and McCabe (1983), McCabe and Sanderson (1984), McDonald and Siegel (1986), Myers and Majd (1990), Schnabel (1992), Grinyer and Daing (1993), Sachdeva and Vandenberg (1993), Kulatilaka and Trigeorgis (1994), Schary (1994), Kulatilaka (1995), Vila and Schary (1995), Berger, Ofek, and Swary (1996), Laughton (1998) Margrabe (1978), Stulz (1982), Baldwin and Ruback (1986), Kensinger (1987,1988), Kulatilaka (1988,1993,1995), Kulatilaka and Marcus (1992), Schnabel (1992), Kulatilaka a] ^-4! and Trigeorgis (1994), Carr (1995), Childs, Ott, and Triantis (1995), Edleson and Reinhardts (1995), Kamrad and Ernst (1995), Childs, Riddiough, and Triantis (1996), Ikenberry and Vermaelen (1996) - 52 - Type of real option References Brennan and Schwartz (1985a, 1985b), McDonald and Siegel (1985), Trigeorgis and Mason (1987), Kulatilaka (1988, 1995), Pindyck (1988), Kogut (1991), Kulatilaka and Trigeorgis (1994), Mauer and Triantis (1994), Karnrad (1995) Myers (1977), Kester (1984, 1986, 1993), Pindyck (1988), Trigeorgis (1988), Brealey and Myers (1991), Chung and Charoenwong (1991), Kulatilaka (1995), Smith and Triantis (1995), Willner (1995), Berk, Green, and Naik (1998) Magee (1964), Baldwin (1982), Hodder and Riggs (1985), Majd and Pindyck (1987), Trigeorgis and Mason (1987), Carr (1988), Trigeorgis (1991b), Kester (1993), Sahlman 441 14 41 (1993), Teisberg (1993), Trigeorgis (1993a), Kulatilaka and Trigeorgis (1994), Kulatilaka (1995), Ott and Thompson (1996), Srnit (1997), Bar-Ilan and Strange (1998) 4 34 ###44 ## 444^-5. #4444 7}X}^7}\~} 444 3§7H14 GL4il # 4# ####4 #44# 44#% (44#%), 44#%(%4#4), X4# 1, #%%#% #4 44. 44#%(growth option, expansion option)#, 45.S.17]- 444# 1444 444 4^41 4441 4441 14 1441 44^ 444 1444# 444-5-S 144 4144 4 4444 44 44444 4 1 1 44# 4# 1 41 1# 1444# 44 41 4144. 14 4-M.141, 4&414, 441^4 14 1441 41441 44 1444# 1444 4a 41 44414 4a4 44# 444a# 4 4141 44 4# 447} 44% 1 44. ai 14# l#aa 44 1444# 4444 444 44(14)# 4# 1(44 1) 41 11 1444# 44 % 1 44. 444 4141 414 7}4^7} 4% 0.5. 1 14444 44 41 1444a 4444 44444 11 1 44 # 4# 1 41 11 1444# 144 1 41 #14# 41141 4 44. - 53 - 4 4#4( timing option, waiting-to-invest option)# #x}Al-^o) 4 4 #44741# #5 #4 4_E xj^- Aj^^x] $>3. 7luf^uf7f 444 44t11 44444# 444# 44 #44 ^#41 #44# #4 #44 4. 4# #4 44 #44441 44 44 444 44# 44444 4 # 4#4 444 4%# -2.444, <4 4#4# n ^xfxf^^ njefl 4 #5#4 y 471-44 44 # 447} % 444 ##4# 5#4 444. 3.44 544 ^xfAf^^ 44 4444 45 444445 444 ## 4# 5#45 44. 444: 44414 #4444 4#5## #44 4 4 4W4 4# 4#4 #44 44# 44. #44 44# 4#44 454 nRxi #^.^0. 444# 4#4 4444 4# 44 7> 47} 555. 444 441 44# #444 4:44 44. 2144 444 441 44# 4#44 4444144 ##44 4#4# 4^44 # 4 4. #44 #5. 440] x}## 444 till4-2-5. ###711 5# 4^- 44 #7f# 0444 421 ##4# 7f#7f 4.711 5l£S, a# #7f4 # 4# 44 4# 44# 4441 #4# 444. #444-5 #44711 4# 4 # 44. #4444 #4 4#^#°! ##4 a# #4 #4455.4 4#5## 4#4 444, #4 4#5#4 4#4 #4444 #4441- 47} 44445 49 . fx} 4^|. 4*54# 4#4 #### 7114 5#4 #44 #44 444. 444 44 #4441-4# 4# #xfxf^^ 44 4# #44 7f#45. 54 444# 44 ##4 741# 4# 4 #44 4# 4# 4*544 45 4## 45 #444 il # 44. 455 444 ## 455 4444 #4#5# #5.711 444## #444. 544 4%4 #4 444 4#5#oi 4 44# 4#4 44 # 4444 45x 1-4#o] 741# 4#4# 44 ##44. 54#4 (abandonment option, exit option)#- 7l5xf4# nfl54 # 4# 44# 544# ##44 ##44, 444 #44 4#41 #444414 44 4# # 4# #4# 4444. 4444454 4# 4# #4444 4 - 54 - # 4#4#4 4414#^.& 4 7}# #4 3. #44 #441 <44# 4#41# X4#4# #444 #7)4 4-f 4# 444. zt44 44 4 #(444, 44#, 2005)4 45# 444445# 4414## 444# 44 441441 #44-35. # ### n]7]x] #5.5. vj-Ej-U-^, s) e ^-44444^44 #445# 7f4## #415 4444(44, 7> 5 HI 4444 44444 4444 444"# 444 4444-4 444 4## 4# #4# 4455 444#4 444: 44 4444 #444 4 44444 #4# 4 44. #4##4(flexibility option, operation option)# 44444144 ##3.5# 4### 44# # 4# #4# 44#4. 41# #4, 45 7} 44-4 4471-571- s# oi-g-7f-^4£# 441# #45# 444 #4 444 — 444 7f^4 ####45 -44 44144. 444 4441 4 4# 444 444 4# 44# a## 4 44 #4# 5##4. 4# 4 4471-5 44414 45 444 7^4 #45# 4444 #44## -2.444, 4 4#41 #4444 4## 4#44 #45# 4471-5# 4#44 #45# 3.444 #4# 7>4 4-35 44# # 44. 4# 4#71-44 #444 # #44 447}5# 4#44 #4541 4# 44 # ##4# 444 #7f7f44 4## 4#44 #45# 7}*H1 444 ## 4# #4-35 3.444 4# 444. 4#4 4471-5# 7M4 4 #41 44 ##44 ##71-4-3 4# 444. 4# # 45# 7}44 ii 5 #4 °14 45# 444# #4# 7}# 7} 44. 4^444 4471-5 #45# 7}# ##55### 414# #4 #471-4 4 4# #45 7f# 4 4#41 44 444 4444 4#°14. 444 # 45.71- #4 44 #7)1# 7f# E))7f 7}4 44444, 4 4#4# # 45. 44 44# # 4# #4 7}47} 7f# a.Ef. o] a]-44A-) -£-471-4# ##3.5# #44 55## #44444, ### 444## 4#44 4##4 44#5 # 44# # 4# ###-#455 #4 71-41- ## 4###-. 3.43. - 55 - #4 #4 4 4## 7\A 4#41 44 4##44# #433 #4444 444# 3#4 4 44 #444 #443 ##7:4# 444. 41 41 4 ##44 1# 44 4444 #47)4 44 4 (option pricing method)# 3.7)) 4) #7)13 4444. 147)1! 47M4 44444 444 3# ###(variables) 7f#41 #4444 #4 44 44# 44 #3 4### 4443 4# 4##41 44 444 4#44# 4444 4t))44. #414 4##4 #4# 4447)1 4444 4#44 344 44# 444 #4# #4 44 7:44## 3#4#41 7:4 #34 4444. 44#4 4# 44 ## #444 4##4 444 7)434! ##4 4# 4#44# 7:4 44. 35)4 o) 44 3#44 (convenience yield)i0)7: 4#3 7:44 7) 4#4 444°14(backwardation)4 #43(contango )11)44 4 #4 4# 4#7:4#4 7)4#3 (term structure) 4 44# 4444 #4# 44# 4#4. 44414 3#44# 444 44 37)) 444# #4# 344. #4) 44# 4435:! !!! 3# 4##4#4 4#44 4 # 4#44 44# 4# 4445:# 444. 143 7)435:! !!! 4#7:4 #34 #44 444 441 44433 #7:4# 4# 444# 4, 7:4 444 44 #34 #4^1 344# 4#4 4# 4#7:4# 4444 44# 34# 444 44. 444 #444 4##4 #4# 3444 43 7)435:! !#4 4! 4#44# 43 7:4441 44, 10) il#7!7! H#7!7!^ g-oM! tfl-sj- Brennan) 1958)! 3.°] 4B( theory of storage Ml M—# nilgai °%7] tt#7! 5#1 l!# 5fMnl ^Mlyl )&-fr%id (convenience yield) 53 #. M5# %#7M(S)4 ti#7M(F)c #gl* F(tT) = S(t)[l+r(t,T)] + W(tT) - C(tT). 3 r=°14# W=7#Hl# 11) €i-7H°l H#7!7)#- Backwardation 0! 5} Sj-ji nltflh] ContangoM #. g|hl0lt=Ml M—kl -o 1#0! slTlsH^lM# kt-rHS15! 7}7|M t'IM—5. Backwardation 0! il7S - 56 - 2#4 #47[47l-4# *11444 7:44 424711 ##4# 44 44. 44 444 #444 4### #44^ 7:44 4#44 4 4425. 44# 4447-] ##7M4447i 7l 244 (underlying assets)^ 4#44. 244# #4444 444 #44 #4# 444 4. 44 #4444 7:44## #47:4 #4#^44 444 4# # #4 #4#4 7f44 44 #42244 2#44. 344# ##4 44 4 #4#( built-in opt ions)4 44 7]-7] 3§ 7}$] 44 S. 44 ##71-44 2## #4 4 #4 22 #4444 7:44## 2#4# 4444. # 447-1# 4444 7114 #47}44 44 Lee and Heo(2000)4 4 ##4 4#7M1# #422 4##4 4# 44# 44#4-.12> # 4# 71-44 #4#, #444# 4*4# #2 4#4 #4 4#444 7>4 4 7i44#4# #4 ##2.4# 44442 #44## #47:4 (equivalent of combined products ) 7:4# %#44 4##4 4#44 # 2711 4#4-4^uf. [147111 #2 #444 4#4 4#44 #4 47-1 #444 7:4 #7H44 #44 #444# 44#4 4##4 7:422 7:4 44. 447-1 #4-444 441 4#2## #44# #44 #2# (revenue cash flow)# Hj#4#2#( cost cash flow) #44, 4 4# #414#7l-44 441 4#4# #444 4#2 4#42 #4# 4 #4 7^43. #44(risk-free)4 #25. 7f444. 4#22 4#7f 44 44 444 4#44 (stochastic process)# #4471 44, 4# # 71-44 4 7114#4# #44 7[44&4 #4# #444. #4 44 7l44x l-S.^- LME(London Metal Exchange )41M 444# # 4, 4, 44 #4 44 4#7f44 37:##, 157:4#, 3.42 277:4# 12) -g- Lee and Heo(2000)& ^€#(2001)# - 57 - 4#7l#45, 44"7l 4# 19894 1### 20004 2# #444. 44# ###441 444, #71 ##7}## # 7^1 #455 #44u}. 44, £#44# 7]# 4##44 544 ^55 4£44£4 ###444 4#£ ##4# 44 4444. 4# 44 [54H44 #4, #444 4 (backwardation)# 3-B5^-(contango )4 #4 4#4££ 4^41:4^- 4 #4# #4# 4 t 44. #4, 4#7M ay ####44 4#£ # 44## ## 44# £#44# 44# 44^y #££ 44454, 4#7M# ## ##7M# £#44 4# ### #5 #£ 47)144 44. [7s>] ‘89/01- ’00/02 LME £4# 4#7}4# 3, 15, 277))## 4#7M ^/A E}#5£ 414 4 41### ##41 4544 44 7}# 4##41 44 444 ##44# 4444 44. 4#4 #47}##7} a444 ### 45£# ojE^ (It0 process#) 7f# 4444 ###44, 4£44 4 44 4444 (diffusion process) 4 44:4444 (mean-reverting process )5 4444, 444 #44 #7)144 3.4a £44 444 4 7)144 ##44. #4444, 4# ##444 4#44 44-440) #4### #44 ££ #71-44 #4# ##4. 4&A-), s#4(drift)S 544 £##£ 4(Brownian motion)4 7l#£## ##(geometric Brownian motion)# - 58 - # 5 44. 0 Brownian Motion with Drift : (IP = aclt + crdz 0 Geometric Brownian Motion with Drift : (IP = aPdt + aPdz 454444445 444 44455 44 444 7f ^7] 4544 5445 4^4# 7MM 4541 44 4545 54455 471-44 45 444711 44444, 44 44 5455 4# 5444 4545 45 4444# 544 444. 0 Ornstein-Ulhenbeck Stochastic Process : dP = \(P — P) dt + cr dz 0 Dixit-Pindyck Mean-reverting Process : dP = x (P ~ P)Pdt + a Pdz 0 Gonzalo Cortazar Process : dP = (r — c + x {P ~ P)) Pdt + a Pdz 0 Schwartz Process : dP= x 5 — In P) Pdt + a Pdz 5 45 4-44 4 TIN4& 54 44, 457M45 44444 54 .2. 54444 4444444 444 455 471-4454, 54 Gibson and Schwartz (1990)41 44 57)14 44^44 7>4 444 455 44 444. - 59 - dP = (fj, — 5) Pdt + a1 Pdzl d5 = x {a — 8)dt + cr2dz2 (5-1) dzx • dz2 = pdt 4, X# 44# (reverting rate)# a# #7] 4# 5_#44# 4 4 44. 4# 44#4 44 4#4 444 ## 4#4 4#4], #4 4#5l ## 444 44 4#444 444 44 44# 44 44. 444 4 # 7:4 7144 44 4&4 4#44# 4444 #47:447]- #^4 444-5^4 44 7:4# , 44. 444, 4#444 #7: #7:4## 44# 4 4444 47111- 444 4#4 444bB4 #444 444—5. 444# 44 (analytical approach)# %#4 4 45., 44 5.444# #4 #44# 44 (numerical analysis approach)4 4#4 444 44. 444 #41# 4445. #47:447: # 444711 4444 444 4#7:#4# #444 44, 444##4 ##7:4 (equivalent of combined products)## 7:44 %#% 4 4 4. 444 7:44 %## ##7:444 #4# 44# #4 4# 7:4 441 444 #4471)7: 44# 4#4] #444. 44 444 7:4# # 444 4##4 4##4 444 444 #4# 7:44 4#41-5 4# 7:#4 444. [24711] #4444 #5- #4 #4 44 2445.4, #44441 444 #44 #4# 4444 44. # 4# 4444# #44#4( flexibility option)# 44#4( timing option) 4 # 7:4 #4# 5-4444. 44 #44#45.5.#, 44 4 444 5:4#4# ##4# #4#4°1 4# 4## ^444. #4^:4 #4 - 60 - 444# #4 4 #4 ^5^1 7}# 44, 4# 4-4## #4 4### # 4#7M4 #44# 4^4 ## 44# 7H##5 44& 4#7M4 #44# 444 ## 5## ##4# #4. ##55 4 ##4( timing options)# ## ##-#44 # $1# 7]#4 4y. 7f##7l5.4, 4# #4-44 7}## #444#4# #5444. ^7] ####4# 4 4-71-40.5. ## #7] o ]4 4^ 4 #5 ^4 7f#4 444 44 (American opt ions) 5.5. # 4 $14. [344] 44 444 #444 7>#^7> [3-1] 44444 4 45444 4444 7fl# #-44444 4444 4444 444 4(production strategy)# 444 55 44#4 44. 4, #444 4 447} 4# q-##!- 1-15.5 7}#4#4 44 444# 5## 4 $1 # #4# 7f#5. $144, #4 #4444# #44# #444 $145. # # $15., o)44 4bB# #4# #44#45-5a-i 5545 7f#47f #4# s#4 g # $14. 44, 4444 #4 ##44 544 #44#44 4# 4## 44 #444 7}## 4 7}#-# 44# 5# 44. #4 #444# 7}# # 7}# #4 44# 4#44# #4#7}4(NPV)# 5-4# 45.54, 44 #4 a}4554# 714## 45-5## ### 4#4 #45# #4#5 # 44# 444. 44 #44 44 5## 44#4 44 ##44. 5# 4 4444 #4 5## 44## #4# #4 44 4# 4#4 44# 44# #44 44 5## #4## 45-5#4 ##4# #44. 4, 7l4## 45-51- 444 ##741 #-#(certainty-equivalent) 45-5# # ##444#5 444# #4413), 4# 4 4#4#4 4 #44 4 - 61 #4 #414# #471-44 4#^## 4#44 4#7M# 44 #4 4 #4 4 4#% 4 #4. 444 44# 44 o]s.^o] ti#7M# %#4 #444 7}44## 4 #4 #4 #444. N g. 4^4,4)- y(r) = g (5-2) (l+r)% 4, 9# 4 4# (product ion rate), W7(g)^ 4 444 44 4#ul, r 4 44444## S7] 44. 4 4444 44 4#7f4 F{P,5, 4)^ Gibson-Schwartz(1990)4 4 4^4# 44 4#4 4°1 -£#44. 4^4, 4) =-P" exp -(5 1 e ^ + £(4) (5-3) X (To a\a-iP where A (4) = r — a + ■ 4 2x" X / \T] +4^4#+ (To 1 — e “X + (Ti(ToP -----7 V x V X «=«- — : £.#444 44^4 444- A: 4< 71-444 £.#444 4471-4 #4(5-3)44 #^7f 4-44 4#7f4 #4# Schwartz(1998 )4 44 s4( long-term model)# 4# 4#4# 4 44. 4 S4#, #44-££- 13) W7M1 7M1# ^ 3^ W7M1 3)0] ^ ^ o- g- o] ol-g-sM S## ^ ^14 (Schwartz. 1998). - 62 - 4#4#7)14#4 5] 4 24 444 44# #7) 4 #41 44 4 4 ### 44 7>4I§7H1 4#7M# 4-§-47]7]- 44# #4# 4#4#4 4# 7}44 5.#44 S#7f ##44 25.# (two factor model)# 4# 4 15.^ 54-5S #44# # ai4 4#4. 4444 7i) # #47}# 4 44 4444 444 44 7}4 4 7}# 4 4 4#, 4#4 44 47] s#o) 440] % 4 44. dZ = (r — c)Zdt + crF(t)dz (5-4) c-d (?2 Z(P,5)= P • exp : 444#7f#(shadow spot price) L % 4%: c = a--^r + -^l; 47] s^44 -2.4 5-444 2r X 1 — p~X T 1 — p- x T 4(4=^ + ^ — 2p T: 471444 4#7]4 444 4#44# #44 4(4# 4 (5-3)41 ito #4# 4#44 4 44 4444, 444#7)-4 z(p,s)4 44s# 3.4 5-444 4r 4 (5-3)414 44444 4444 t# #44& #7f4# 44 #44# 4 #44 444 4444. 4(5-3)# 4(5-4)4 44 s4-55.#4 5#4 4#4 4# 4#7M-5& 44143., ^(Z,71)=Z(^,4" (5-5) #4#44 4# 4 444## 7}4 ## 47)14 #444# 4415. 4 44 #4444 7)-4 44# #44-55.4, 4#4 44 444 444# 4 44& #44#44 4# 71-444# 444 4 44. - 63 - y(r)=g = R (5-6) n a (I-?") 4, 44# (tax rate), 7}y j 47114 a7H 444y y 17(z, 71)= [7^(Z, y) . #(4- FTW . #(d-?;(y))] . e-^ (5-7) - 64 - Ill (~vm]+{r~c)T: , i d = r(#) r(7):) r'(4) = o2p (t)dt 4, N( )# #4 ##&4## 4444. 44 #444 7f44# - uf^ 40] ^Slu}. N y(ZM;^)= g g . r (ZM, 71) (5-8) i = i 4, V Pr [Z> 157(g)] = TV, TV= —, <9# #43( total reserve)# 44 44. 44 3#4##S4#o114 a4# d# 4#7M ^4 #44# 13%) 4 444 3.7]4 #3 4444. 4^44 #444 7fl# 35.# S7} 4#4 44 4 4##3# 7]-x] 7] 4##, 37] ####7f #4 4 34 #4 4### 444711 43, o]&# #4 33^3 714 #4 4# 71-4# #44## #4 444# ##33 #4% 44el-3 7M# # 44. 4# 4# ds] 7M]7} 44433 ## ##44 yv(d )4 Nid-viT^s] 71-4# 44 13 #44# 44 4474144. 4# 4# 7V(d)4 3(d-t,(7::))7} 13 #444 44, #44 #44 4# 4#4 3343 7}4# #44 #44 4# 4#4 33#3 7#H 4#44 44. 44433 #444 7B4 33434 44 4#4444 4#9-3 # 7>4 4#4# #444 #44 444 44# 7f4# 7>44 #44 # 4# 4 # 44. - 65 - [3-2] A] 4 bKK timing options)^ 44 T 4.^ 7]$H] 44 7]-7] i§7]-SA-] -&^7M]3§7MAi ^o] B> ^ $1 Uf. ccj-ej-A] ^AfAf^ 7[A]# A]^-§.>yo] 7]axR>4 3l7] 4# ^A}7M^.& ^>7l 44 4-^ irflefc ^Af 7]~^4 nj^-Al ^ (American options) 0.5. # ^ 44. ^o], 4=.7]-^o] ^7]^} 2. 4# 4444, 4#7M ^4 44444 7j-A] 44 4# (contingent claim analysis)^] 5:4514—5.9-4 4tt4 9" 4 4#4444 ,. J*U°°)Z'’j^r +(r-- r w= 0 (5-9) 27]2l%[( initial condition) 5.5.a] Ph%0) = 07} ^7}]5:4( boundary conditions) 5.5.a] W{Z*)= V(Z*), 7f4 49 4( value matching) 4 W (Z*)= V {Z*)t 44yo k§"4(smooth pasting) 5:44 #444, 4#4 444 4 5. A] Sfl^- ^44-4# ty- 5 4# 7]$]»] 7fA]^ 4^4 4o] #444. = ^4 - (r > 0, c > 0, /3 > 1) (5-10) 1 (r-c) r — c 1 2 2r 2 44 ?47M z*6\] 4»> ^5.# 4444 7]#A_aA] 0^9. 40) 9-91 - 66 - 7|#^| 7] 5^-5.A-] ^47^171- S(0)olAl- c-0 /j ( (7„. — -O p* _ y* 7e X /: 3:7) - 67 - 41 6^ 91y# o|fr 4 14 #4494 ###144 ##4-4 sl<$ 139 w #4994 ### 4# 3##3 ### 4# 44 #4 99#44 ##7H9#4# s## 4# #4494 7f#4 #4# #7}# # 4 7] # 971-71939- 9### 7]^o] 4 44# 4 #4. 44, 4# brics # s## #4 7:#q-7)-#4 9-4# 44444 7]#44 444 3#7} 3 3# 3 4444 3## 44 444444 #449 444 444 3.4 #443 #34 44# 9#9# 4##4 14 444# 4444 #944 ## 44 94 ##4 # #949# 44#3 94. #4, # 4 #444 9## 44# 3##^ #444334 9494, 4### 4, 44#4 ## # # 93 #9433# 494# 444# #4#4 4 494# ## # # 9#4, 4# 3##4 4# #499# 44 # 7f## #444. 94, #4994 44# 4#?))#, 44, 943 9 44#4 4 #4 93, 49 393 #9#4 # 494 94 44# 4 #9 334# 4#9 44 # #9# 93 94 4#4 44 39 #7)14 4 #4934 #44 34 393 444 #9 9# 44 44944 4 4 44# #44# 4944 4### #417} 449 99 4## 94 4#4. 44# #9 4#4 #4994 ##4 44## #71-49 (irreversibility)# ## #9# 9#4. 44, 7) ##4-9 9 4# 9 444 4471-4 #71-4- ##49 #33 44433 #44944 #3 7> 34 #4#3 9# #44 944 #4994 ##4 #449#4 4# 444 71-47} #4#3 94. 4# #4, 94 9 #94#4 4# ##7H9#44 4##9 3#4 4# #4# #4 44433 4#44 14) ^ ^#(2001)# - 68 - 444 ## 3.7)1 44# #41 44# #4 444 44447} 44# 4 44 44# #41 44. 34 444 4 #4# 44##43 444 #3 44## 34# 4 #4 44 #43 444 4# 4f#4#444 4 44 #417}# 4-^4 4-§-44 ##4 4-4 4444 47} #43 4# 4 #4# #711 44. 44# ###444 444 7}4 ^ 4# 7}# #7} 4433# 4#7}44 #44 441 #7}7} l-7}-^4 33#44, ##-§-# 4 ## 3# #34# 414 #4. 41 2# 44# #-4 #-#:4144 #### #% #4 54414 #444#4, #4444 7}##7}4 4414 #7}44 34# # 4# ####4 ##41# 44##(#4##), 44#4(44 #4), 34-S-#, 444#4 #4 #3# ojs. 3# #444# ##4 #-44441 4## # 4# #4 ##33 4444. 44##(growth option, expansion option)#, #-33#7} 4l#4# #444 444 4341 444# 4#41 #4 #44# ##33 #44 #47}## 44433 ### 4#4# 4 4444 7)14 #44714 # # # 44# 4# # 4# ## #444# 44 4# 4#44. 4# 4443(4#, ##7}3)4 4444 7}#4 43#4##4 4## 4 #7}34 7l4til-g-o] 3.4 #7}444 #####4 #444# titi}34 4443 44 4#4 #4# #4 ### 44#44 #44# 4# 4# 4-47} 44. 4# #4, #4444 #4# #44 #7}#4 #e 44 ##44 4#: #34# 444 3444 #t)1 47B# 44 #4# 43 44#44 #34# 34## #43 # # 44. 34 4434# 7:4 # 7}4 7} ## 44 44# #4 4 #3 #3 4 #4 447}3# #414 4 7}#o] 3.7)1 44# 4 3# 7l3#$}#44 4#44 ##7}3# 4 4433 37)1 43444 4# 4#41 444 # 44# 41## # 4# - 69 - 4#3 44#44 #44# 44 44. 444 44444. 44 44: 444 44 3.444^ 4 34 #4 4 4 44 #34 44414 44 44 4 44 4441 4## 441 4# 4 44 444 44444 4444. 4444(timing option)# #4444 44 #4441-4# 43. 44 4-E 44 #4# 4444 43. 44444 444 4441 44444# 4444 44 444 4441 4444 44 #444. 44444 #41 4 41444 4444 44 4# 4# 4444434 4# #44 414 44 4#4 444 3.44 #44441 4# 44443. 4#44 4 4 4 44. 41# #4 444 4# ###44#4 4# 444 4 #4# 4444 44 7M34441# 4# 444 4# 4414441 44 4#4^444 44 434 444#4 444 SW4. 44 4 # 444 4#4 #44 #4444 # 4#41#, #44## 4# 4# 44 #44-44 44 #4444# 43. 4443 #441 444# 441 4#4 4.3# #4 443 44# #44#4 44#44 44# *544 4 43 #34# 433 44# # 44. 444 44414 4# 44# 4 #44#41# 44#4 44*544 444#4 34444 4 444. 3E7l#4(abandonment option)#, 4%4 #44 4#41 #444414 44 4# # 4# #4# 4444. 44414# 199044)41 44 444 44371- 471-4# #4 414144 4441 4144 4#41 44# 4#413 4414 4444 4# 4444414 44 #444#4 7M444# # 4# # 4# 44 44444 34# #444414 444 444. 44 4 44-44# 4414## 344 44 41414#4 44 #444#44 #43# ## 4 4#4 4 444. #4444 4#3 4444434 4414#4 444444 441441 44433 # 44# 444 4# 4 33 444:34, 4# 44M14444414 44434 71-44# #413 4444(44, 71-3)41 4444 44444 4414#4 4## 4# # 4# 433 #4444 (444.44#, 2005). - 70 - #3##4( flexibility option, operation option)# ^4444144 #333# 4##4 #4 4 #3 4 e0># # 3# ### 444 4. 41# , 4# #34417} #44444 44444371- 47]4- # 3# #44] ^4# 4 # 3# 4 #4 34# 47]# 4444 #43 4 44# 4444 44# 3-444 #4# 7>4 43& 444 4 4 4. 44 44 7]-# o] #-e]44 3 #44 #3# 4444 444 44 444 ##44 433 4#7f4# 44# 4444 #434 7f44 4 44## 44 #433 3.444 4# 444. 444 #34 7f#4 4 441 44 ##44 447]-4_e 44 444. 44 # A54#4 7f#o] 113 #444 A54## 444# #4# 7>47> 44. 43443 #3 44 #44 7M4#3., 4M# #4 447f44 4444 44 3 7f44 4#4 44 444 4444 4444. 444 # 44# 7> 44 #4 4447]]# 71-4 47} 7>4 44444, 4 4 #41# # 44 # 441 444 # 4# #4 7>^7> 7f4 3.4. 41 3# 4##4 4 #4 o]# 44 54414 3#43#3, 4 #4 33 4##4# 4#4# 44# 3711 4 4711& #444. 14711# 471-44 #4434 444 s# 4 ##(variabies)7f#41 #4444 #4 44 44# 4# #3 4### 4443 4# 3##4 44 444 4#44# 444# 44144. 24 711# #44441 444 #44 #4# 444# 4443, 344# ## 4 444 #4#( built-in opt ions)4 44 7}4 ^ 7}$] 44 s. 44 # 471-44 3## #4 4#433 #4434 7f44## 3#4# 44 44. 44444 ##4 4# #444 4## 371] #3 #71-44 A54#7]- 4 343 4414## 3E44 4#4 44## # # 34. 44444 # - 71 #4)4 4S.# -fefeojxjnj. ^*§444 444 7}±$) 7}^i-i-S. 44 4444 44144. 441441 4## 44xx #4#7f4 ##44 4# s.4 t%, 4#, 7f^7f4# xs#))# # 444. 44 4##4 44 4 4-f 44444 4444 %44X 44 7M4#4# 44 44)4 444 441 44 #444 4#x 3.4444 % 4 43.4, 4#7)-x4 #4# 444 444 444 4#4 7}4# 4$)4-g-7)-43.s. 3.44 4 44. 444 #444 44# 444## 5W 4#444## # X 44. ###444# 44444 ##4 #444 7}447M1 4#44 4 44# 44 4#4. #444 4##4 4#44#4 44444 44. #4#. 4X4(2005)# 4#7f44 44 Chan et al (1992)44 4)44. X4# GMM(generalized method of moments)4 44 #4#X 87)) 4# ##44x44 4X4 44, 87)) 2.4# x444x ##44 444 4 4# 44443 x4 ### 71X4-43.# 4# #44 ##44 7f#7f ##44x44444# 4# X44. 44# #4 44444 4X #444 4##4 ##44# x444# 444 4# #3.4# X4# 4. #444 4##4 4#444 #44 4#41 4# 4XX 44 44 444 #4444 7}4# 47f44 444#, 44 #4444 4# # 44 #4# x#4#4# 4444 4x 44 4-44 #44 44 44 43 44-X 44 7f44 444 #4(American options)44 444 4 7)444 44*547)- 7>#4 #44 #4(European options) ## 444 #4444# 4444 44. #44 #44 4#41# 7f4^7fl- 44 #4-#x #4# %#4 # 444, 444 4#41# #444 4##4 ##44x4xx#4 4X #4# 4#44 #444 7f44## 4#4 7} #xs))o> 44. #q 4##44 #4 #44 4### #4444 7f4 4 7M 44 4 7))4 xx ##-#x #4# 4#4# #414# 4x - 72 - 94. 4449941 99 9##4 9 #9 4# 99 ##7M1## 4## ##44 9## 444 3-4444. Epaulard and Gallon (2001)4 44 7f3i7)-9#, Takizawa et al (2001)4 #4#7)-4#, Kiriyama and Suzuki (2004)4 44444: 4 #4 7M#, 39 3 Collier et al (2004)4 447144 1-444 9#& 3.4444.15) 444 #444 4 ## 444 344# 444, #444 44# # 7fl 44 349 9# 41 44# 4 4#99 47)1# 444 9#94& 4#44 444^ #44# 44 (analytical approach)# %#4 # 9.335. #47)-7)4 7}# 444711 #444 #44 4#7f#4# 4449 44444. 44 4 44414 #4444 449#4 ##4 9# ###499# 4## 4 4# 41 7>4 9#944 7H?444 #4. 94# 4# 44149 # 499 9## 444 3.444 #4444 741# 97f4# 944. # 7)1 # Lee and Heo(2001 )o)144 9°1 #94##4 #974) (equivalent of combined products)!-# 49#o#9 #97}-7) (equivalent of combined inputs) 7^o] %-§-% 9 9# 944. 44935.# 444 9#94 4941 39994 9# #44 4#94 (numerical approach) # 4#4# 944. 49, 3999 94# 4#9 4 #49 4#, 9 94 949 #4494 4#9 4 #4# ##7f47f 91444 #4# 99 (bias)#47f 999 # 94# 944 (493, 2005). 444 44 4 #9144 494 4# 71)99 3999 944 99944 9 944. 99 71-499 #44 #49 9#41# 59414 4#9 Schwartz (1998)9 99 39 ( long-term model#) 3-4% # 9# 944. 15) Rothwell (2006)^ $#43 434# 444^3 #444 45^4 4444, 44 #4 4 44 (capacity) 3 37)1 #r* 914. - 73 - Abel, A.B. and Eberly, J.C. “The Effects if Irreversibility and Uncertainty on Capital Accumulation." 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New York: Praeger. - 90 - ^ ^ 444444714 4 S3 714447144 444471 Bli INIS 471)24 V,'7] ni p; KAERI/CM-952/2006 4 4/^-4 99444 99 °ll 99 €7M#4 7>x]^7> 2942 44a] 47} 4 444 4 7ls (4444a 444444 a4) 4 4 7} ^ 4 71 %g 444 (4444444) # 4 4 4 4 4«S7l4 KAERI 4^4 5)1 O) X] 90 p. a 4 %1&(V), ^&( ) 3.7} Cm. #3.4^- ’06 44944711 ti]Tg! d^ jf ^7fl(0), 449( ), __ 4ti]£| 4471 #4 444471 y WsS7l4 4444a 7114 94 44 (l5-20#iflal) 9 4#447|m 14 o|#4 a@4a* ^44, 99471 9^ 7^44 4# 497|H £121 # 44401 4444 94999494 9S°M 41 sHah 49 o| HSS-71-lr o|^-9 °a 44 94. 444444 (109444) - 91 BIBLIOGRAPHIC INFORMATION SHEET Perfonning Org. Sponsoring Org. Stamdard Report No. INIS Subject Code Report No. Report No. KAERI/CM-952/2006 Title/ Subtitle A Study of Real Option Model for Evaluating the Value of Nuclear Power Project Manager Jeong Kiho (Kyungpook National University, School of and Department Economics and Trade) Researcher and Department Park Sungduk (Daegu Kyungpook Development Institute) Publication Publication Taj eon Publisher KAERI Place Date Page 90 p. 111. & Tab. Yes(V), No ( ) Size Cm. Note Open( O ), Restricted! X Classified Report Type Research Project Class Document Performing Contract No. Organization Abstract (15-20 Lines) For the last decades, the real option models have been the dominant focus of theories of investment and evaluation. This study analyzes the issues to be considered in applying the real option model to evaluate the value of nuclear power. Subject Keywords (About 10 words) nuclear power, valuation, real option - 92 -