REAL OPIONS SUPER LAICE SOLVER Dr. Johnathan Mun, MBA
Real Options SLS Real Options Valuation, Inc Real Options Valuation, Inc Dr. Johnathan MunReal Options Valuation, IncCEO Dr. Johnathan Mun e-mail Real Options Valuation, Inc Admin@RealOptionsValuation.com 005-0 by Dr. Johnathan Mun Microsoft / USA: www.realoptionsvaluation.com CHINA: www.real-consulting.com.cn
Real Option SLS Real Option SLS SLS SLS Lattice Maker SLS Excel SLS ROV Strategy ree Real Option SLS SLS, MSLS MNLS SLSMSLSMNLSLattice MakerSLS Excel Excel Excel Wiley Finance 005 Wiley 004 CRA Wiley006 3
SLS SLS SLSMSLS SLS Lattice Maker SLS Excel Excel SLS, MSLS SLS SLS A B / 4
C Black & Scholes Black & Scholes Black & Scholes Black-Scholes D E F 5
SLS Real Option SLS SLSMSLSMNLSLattice MakerSLS Excel SLS SLS MSLS Lattice Maker Excel Risk Simulator Real Option Valuation Excel Monte Carlo SLS Excel Excel SLS MSLS Excel SLS MSLS SLS Excel SLS Wiley 005Wiley 006 004FAS3 Wiley 004 Wiley 005 00 SLS 005 SLS SLS ROA SLS ROA 6
SLS Windows XPVista, Windows 7 Excel XP, Excel 003, Excel 007, Excel 00 NE Framework.0 GB 50MB Windows Excel Windows SLS 000.50.000 50 NE Framework.0 CD dotnetfx0.exe CD www.realoptionsvaluation.com.cn/attachments/dotnetfx0.exe SLS.NE.0.NE. CD www.realoptionsvaluation.com.cn SLS Real Option SLS 4 www.realoptionsvaluation.com.cn D E F 7
SLS SLS Real Options Valuation Real Option SLS SLS Lattice Maker Real Options Valuation Real Option SLS SLS SLS Excel : SLS SLS 8
SLS SLS I SLS 00 5 00 5% 0% Alt-R 00 3.3975 Black-Scholes 000 : SLS Black-Scholes 000 000 3 3.487 A 9
3: SLS 00 MaxAsset-Cost0 MaxAsset-CostOptionOpen 4 4 3.3975 OptionOpen 4 MaxAsset-CostOptionOpen MaxAsset-Cost0 0
4: Excel 0 I 5 0 000 0 SLS 0 0 0 0 0 0 SLS 6 Excel SLS
000 0-400 OptionOpen 400 OptionOpen 350 0 0 3 SLS OptionOpen 0 00 SLS 5 $00 $50 0 $00 5 $50 5 6 0 00 SLS -0-0 -30 3-40 4-50 5-60 6-70 7-80 8-90 9-00 0
Assumptions Intermediate Computations PV Asset Value ($) $00.00 Stepping ime (dt) 0.0500 Implementation Cost ($) $00.00 Up Step Size (up).06 Maturity (Years) 5.00 Down Step Size (down) 0.9779 Risk-free Rate (%) 5.00% Risk-neutral Probability 0.5504 Dividends (%) 0.00% Volatility (%) 0.00% Results Lattice Steps 00 Auditing Lattice Result (0 steps) 3.9 Option ype European Super Lattice Results) 3.40 erminal Equation Intermediate Equation Intermediate Equation (Blackouts) Option Valuation Audit Sheet Underlying Asset Lattice 5.06.9 9.59 9.59 6.94 6.94 4.36 4.36 4.36.83.83.83 09.36 09.36 09.36 09.36 06.94 06.94 06.94 06.94 04.57 04.57 04.57 04.57 04.57 0.6 0.6 0.6 0.6 0.6 00.00 00.00 00.00 00.00 00.00 00.00 97.79 97.79 97.79 97.79 97.79 95.63 95.63 95.63 95.63 95.63 93.5 93.5 93.5 93.5 9.44 9.44 9.44 9.44 89.4 89.4 89.4 87.44 87.44 87.44 85.5 85.5 83.6 83.6 8.77 79.96 Option Valuation Lattice 45.33 4.8 40.35 39.96 37.97 37.58 35.66 35.7 34.87 33.43 33.04 3.64 3.7 30.88 30.49 30.09 9.8 8.80 8.4 8.0 7.8 6.79 6.4 6.0 5.64 5.5 4.87 4.49 4. 3.73 3.40 3.03.65.8.90.5.6 0.90 0.53 0.6 9.79 9. 8.86 8.50 8.4 7.77 7.8 6.93 6.58 6. 5.45 5.0 4.76 4.4 3.7 3.38 3.05.09.77.45 0.58 0.7 9.9 8.89 7.9 6.74 5: SLS 3
6: 0 SLS 4
SLSMSLS MSLS SLS MSLS MSLS 3D MSLS SLS MSLS MSLS 8: SLS MSLS Real Options Valuation Real Option SLS Real Option SLS 9 MSLS 5
9: MSLS 0 500 8000 500 30% MSLS 767 67 67 Phase $5M Phase $80M Exit.. $00M Exit Year 0 Year Year 0: 6
MNLS Real Option SLS MNLS MNLS : 50 00-7
5 0 00,000 5,000 $30.73 $9. $9.7 $9.77 $9.78 $9. $9.50 $9.75 $9.78 $9.78 : - - -- 8
SLS Lattice Maker Lattice Maker Excel ExcelXP003 007 Lattice Maker Monte Carlo SLS Excel 00 : Lattice Maker 9
SLS Excel Excel SLS, MSLS SLS Excel Excel Excel Excel SLS,MSLS 3 SLS Real Options Valuation Real Option SLS Excel 4 SLS SLS Excel Excel 3: SLS 0
4: SLS Excel Excel 4 B8 0 3 MSLS SLS Excel 5 SLS Excel MSLS MSLS 3 MSLS A4 H6 A4 H7 6 Monte Carlo
MULIPLE SUPER LAICE SOLVER (MULIPLE ASSE & MULIPLE PHASES) Maturity (Years) 5.00 MSLS Result $34.080 Blackout Steps 0-0 Correlation* Underlying Asset Lattices Custom Variables Lattice Name PV Asset Volatility Name Value Starting Steps Underlying 00.00 5.00 Salvage 00.00 3 Salvage 90.00 Salvage 80.00 0 Contract 0.90 0 Expansion.50 0 Savings 0.00 0 Option Valuation Lattices Lattice Name Cost Riskfree Dividend Steps erminal Equation Intermediate Equation Intermediate Equation for Blackout Phase3 50.00 5.00 0.00 50 Max(Underlying*Expansion-Cost,Underlying,Salvage) Max(Underlying*Expansion-Cost,Salvage,@@) @@ Phase 0.00 5.00 0.00 30 Max(Phase3,Phase3*Contract+Savings,Salvage,0) Max(Phase3*Contract+Savings,Salvage,@@) @@ Phase 0.00 5.00 0.00 0 Max(Phase,Salvage,0) Max(Salvage,@@) @@ Note: his is the Excel version of the Multiple Super Lattice Solver, useful when running simulations or when linking to and from other spreadsheets. Use this sample spreadsheet for your models. You can simply click on File, Save As to save as a different file and start using the model. *Because this is an Excel solution, the correlation function is not supported and is linked to an empty cell. 5: SLS Excel 6:
SLS Excel SLS Real Options Valuation Real Option SLS SLS Excel Excel SLS Excel SLS 7 Excel Excel Excel SLS Excel SLS OK 7 Excel B B7 VBA Excel 5 SLS Real Option SLS.0 0 3
7: Excel 4
50 -Black-Scholes delta-gamma 8 800 ROV Risk Modeler ROV Valuator Real Options Valuation, Inc. ODBC Oracle, SAP, Access, Excel, CSV 800 ROV Modeling oolkit ROV 8 5
Single Asset SLS 8A Options SLS Plain Vanilla Call Option I Options SLS 8A (A) (B) (C) 0 00 0 0, 30, 40,, 80, 90, 00 (D) (E)(F) (G) 0 (H) (I) (J) (K) (M) (L) (N) 5 5000 5 5000 (O) (Q)(P) 6
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ABS, ACOS, ASIN, AAN, AAN, CEILING, COS, COSH, EXP, FLOOR, LOG, MAX, MIN, REMAINDER, ROUND, SIN, SINH, SQR, AN, ANH, RUNCAE, IF SLS SLS SLS MSLS SLS & AND() OR()Asset>0 Cost<0ORAsset>0Cost< 0 Asset>0&Cost<0ANDAsset>0Cost< 0 3 3 35 3 5 35-7 3567 35-6 356 5-7 567 5-0 579 5-4 3 587 5-6 3 5 5-6 3 5 a-za-z _ $ a-za-z0-9_$ { } myvariable MYVARIABLE_myVariable, myvariable$myvariable 0 9 000000345 0.3.0.00.3.9.5.934.3E33.5E-50.E-43.E+3.5e-5 o o - -3 o ^ o *, / o +, - o =, <>,!=, <, <=, >, >= o &, SLS o MAX (Asset-Cost,0) o MAX (Asset-Cost,OptionOpen) o 35 o + 4 * + 4 * 36 / 48 o 3 + ABS(-3) 33
o 3* MAX (,,3,4) MIN(,,3,4) o SQR(3) + ROUND(3) * LOG() o IF(a > 0, 3, 4) 3 a > 0, 4 o ABS+3 o MAX(a + b, c, MIN(d,e), a > b) o IF(a > 0 b < 0, 3, 4) o IF(c <> 0, 3, 4) o IF(IF(a <= 3, 4, 5) <> 4, a, a-b) o MAX({My Cost } - { My Cost }, {Asset} + {Asset3}) 34
DCF 000 Monte Carlo 5 000 5 5 9000 3000 9000 9000 9000 5 5 9 548 000 548 548 9000 548 3000 9000 000 0 3 6000 3 6000 6680 6680 3000 35
45 000 500 5 000 5% SLS 00 35 0% 5000 5000 4500 40% 5% 4500 4000 583 5000 9 0 0 36
9: 37
Option Valuation Audit Sheet Assumptions Intermediate Computations PV Asset Value ($) $0.00 Stepping ime (dt) 0.5000 Implementation Cost ($) $90.00 Up Step Size (up).934 Maturity (Years) 5.00 Down Step Size (down) 0.8380 Risk-free Rate (%) 5.00% Risk-neutral Probability 0.57 Dividends (%) 0.00% Volatility (%) 5.00% Results Lattice Steps 0 Auditing Lattice Result (0 steps) $5.48 Option ype Custom Super Lattice Result (0 steps) $5.48 User-Defined Inputs Name salvage Value 90.00 Starting Step 0 erminal: Max(Asset, Salvage) Intermediate: Max(Salvage, @@) 70.93 Underlying Asset Lattice 589.03 493.59 493.59 43.6 43.6 346.59 346.59 346.59 90.43 90.43 90.43 43.37 43.37 43.37 43.37 03.94 03.94 03.94 03.94 70.89 70.89 70.89 70.89 70.89 43.0 43.0 43.0 43.0 43.0 0.00 0.00 0.00 0.00 0.00 0.00 00.56 00.56 00.56 00.56 00.56 84.6 84.6 84.6 84.6 84.6 70.6 70.6 70.6 70.6 59.7 59.7 59.7 59.7 49.58 49.58 49.58 4.55 4.55 4.55 34.8 34.8 9.7 9.7 4.45 0.49 70.93 Option Valuation Lattice 589.03 493.59 493.59 43.6 43.6 346.59 346.59 346.59 90.43 90.43 90.43 43.43 43.37 43.37 43.37 04.30 04.06 03.94 03.94 7.07 7.6 7.5 70.89 70.89 46.0 45.36 44.6 43.77 43.0 5.48 4.77 3.88.77. 0.00 09.3 08.49 07.4 05.93 03.0 97.95 97.3 96.03 94.57 90.00 9.44 90.88 90.3 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 0: 00 SLS 0 5.48 00 5.45 Max(Asset, Salvage) Max(Salvage,OptionOpen) OptionOpen OptionOpen 38
4.5054 5.458 : 00 39
: 00 5.5 3 5 00 0-50 50 0 OptionOpen 3 40
3: 00 4 5 4 90 0 95 00 5 0 0 90 40 95 6 0-0 AB ENER 4
4: 4
5 0% 0.9 0 Monte Carlo 30% 5 5 5% 5 0% 5 0 7 5 0 0 7 0 90%+5 95 0 0 0 7 7 0 0% 9 0 0 5 0 5% 45% 0 43
30% 7500 00 SLS 44 5 7500 5 5000 057 000 5% 0% SLS 59 5% 59 000 5 0 6 00 7 5 4 0 80 00 4 8 44
5: 0 45
6: 00 46
7: 47
8: 48
400 Monte Carlo 35% 5 5 7% 50 9 6 3873 0 8873 400M-50M=550M 638.73M-550M=88.73M % 30 4.9% 550 3 5000 35% 5% SLS 5495 5000 495.34% 49
34 / 0 55% 000 5000 0% 0 5% SLS 00 7 000 0.75% 750 / 3 33 9: 00 50
30: 5
3: 5
3: 53
33: 54
34 34: 35 36 37 36 55
35: 56
36: 57
37: 58
38 39 39 38: 59
39: 60
40 SLS 0 4.4 0.68 40-0 3% 0-80 SLS 40: SLS 6
SLS MSLS 4 4 6.768 4.87.0 6.89 4: SLS 4 MSLS 43 MSLS 6
4: MSLS 43: MSLS 63
MSLS 44 PI PII 44: 44 500 8000 3 6 9.7 30% 5% 45 00 767 500-500 -8500 67 67 767 67 +500 67 8500 8% 5% 500 0 64
7%30% 45: MSLS 65
MSLS 46 MSLS NPV 47 MSLS -500 4.78 00 47 500 4.78 0 5% 8% 0 0 0 46: 66
47: MSLS 67
48 MSLS 49 48: 49: MSLS 68
49 MSLS Phase 3: : Max(Underlying*Expansion-Cost,Underlying,Salvage) : Max(Underlying*Expansion-Cost,Salvage,OptionOpen) : 50 Phase : : Max(Phase3,Phase3*Contract+Savings,Salvage,0) : Max(Phase3*Contract+Savings,Salvage,OptionOpen) : 30 Phase : : Max(Phase,Salvage,0) : Max(Salvage,OptionOpen) : 0 69
SLS 49 MSLS SLS SLS SLS MSLS MSLS 0-3 3-6 0-0 MSLS IF,AND,OR, MAX 70
50 MSLS 0 5 50: MSLS 5: MSLS 7
/ 000 5000 5 0 00,000 5,000 $30.73 $9. $9.7 $9.77 $9.78 $9. $9.50 $9.75 $9.78 $9.78 5 5 3.99 53 0 SLS MSLS MNLS 5: 7
53: 0 73
MNLS 54 54: 55 MR < > 8.6 8.76 3.99 3.4 = > 74
55A: 75
55B: MNLS 76
56 56: 57 57: 58 MNLS 77
0%.5 MSLS / 58: 78
59 60 59: 60: 6 MNLS -- - + 79
6: 80
6 7.397 4.47 90 90 6 75% 4.34 5% 3.4 5% 0.0 63 0 90 4.9 00 4.58 6 63 OptionOpen OptionOpen Barrier 8
6: 8
63: 83
>> 64 OptionOpen OptionOpen 84
64: 85
65: 86
66 66 SLS OptionOpen OptionOpen SLS 66: 87
67 0-39 EIE (IEV) E Max(Stock-Strike,0) IE Max(Stock-Strike,0,OptionOpen) IEV OptionOpen 49.73 67 ESO Valuation oolkit 68ESO Valuation oolkit Real Options Valuation 004 FAS 3 004 FAS 3 ESO Dr. Johnathan Mun 67: SLS 88
68: ESO Valuation oolkit 89
69 00 E IE IEV.85 0.85 0 00 ESO oolkit 70 69: SLS 90
70: ESO 9
7 ESO oolkit 7 9. 7: SLS 9
7: ESO oolkit 93
73 ESO oolkit 74 73: SLS 94
74: ESO 95
A A BSM 500 000 000 030 A Black-Scholes $7.0 Convergence in Binomial Lattice Steps $7.0 $7.00 Option Value $6.90 $6.80 $6.70 Black-Scholes $6.60 $6.50 0 00 000 0000 Lattice Steps Black-Scholes.336 5-.795 0-.093 0-.3 50-.87 00-.33 000-.336 A: 96
B GARCH / B B 5.58% P P 0% 35% P 365 50 P 4 P P B 0 5 5 DCF 5 0 97
(X) 0 $00 $5 $5/$00=.5 ln($5/$00) = 0.3 $95 $95/$5 = 0.76 ln($95/$5) = -0.744 3 $05 $05/$95 =. ln($05/$95) = 0.00 4 $55 $55/$05=.48 ln($55/$05) = 0.3895 5 $46 $46/$55= 0.94 ln($46/$55) = -0.0598 B: volatility n n x i x 5.58% i N X x X B ///Real Option SLS/ B A G I3 LN(G3/G4) J3 SDEV(I3:I54)*SQR(5) 004 5 J3 5 L8 AVERAGE(J3:J54) J54 SDEV(I54:I05)*SQR(5) 05 003 5 5 Monte Carlo Risk Simulator 98
B: B 00, 00, 300, 400, 500 0.08% 00, 00, 400, 800, 600 0% 00, 00, 00, 00, 00, 00 75.93% 0% EBIDA 99
5% EBIDA 0% $00, $00, $300, $400, $500 EBIDA 0%$0, $0, $30, $40, $50 0.08% DCF B 3 00 00 00% 00-50% 5%00%-50% 5% 00 00 5% 00 00.0 00% 00 90 0.9.0-0% Geometric Average PERIODS Period End Value Period End Value Period n End Value... Period Start Value Period Start Value Period n Start Value 00 00.0 00 00 00
3 S ( t ) t e S n n 3 4 n( x x ) 0 (n ) 00 00 3 n n-l n-l 4 n volatility n i 5 $0 $0 $30 x i x t t / / 5 0
B3 0 0 X ln n i n i 0 PVCFi PVCFi PVCFi i Monte Carlo 0 0 $00 $5 $95 3 $05 4 $55 5 $46 $00 ( 0.) $5 ( 0.) $95 ( 0.) $05 ( 0.) $55 ( 0.) $46 ( 0.) 0 3 4 5 $00.00 $3.64 $78.5 $78.89 $05.87 $90.65 $5 ( 0.) $95 ( 0.) $05 ( 0.) $55 ( 0.) $46 ( 0.) 0 3 4 $5.00 $86.36 $86.78 $6.45 $99.7 $567.56 $54.3 B3 X ln($54.3/$567.56) = 0.0985 X Monte Carlo X X Monte Carlo X 0
X ln n i n i0 CF CF CF3 CFN PVCF... i 0 N ( D) ( D) ( D) ( D) ln CF0 CF CF CFN PVCFi... 0 ( D) ( D) ( D) ( D) D CF Monte Carlo Monte Carlo X B4 Excel DCF 46 48 5% 0% 5% DCF 5% 5% H9 H0 NPV Black-Scholes (S)()() (X)() 0 0 00% 00%000% Black-Scholes ln( S / X ) ( r / ) r ln( S / X ) ( r / ) Call S Xe B4 5 55 5 0 00 5 0 Excel 53 Excel D54 X LN(SUM(E5:H5)/SUM(D53:H53)) DCF X X N 03
B4: 0 NPV 0 0 DCF DCF DCF X X 0 0 NPV DCF X 04
3 0 DCF EBIDA DCF 03 GARCH GARCH GARCH GARCH GARCH GARCH GARCH(p,q) p q GARCH GARCH (,) y t x t t t t (y t )(x t )( t ) t ( t )()( t- ) ( t- ) GARCH GARCH GARCH B5 GARCH (,) t 05
B5: GARCH () B6 B7 X Y B6 B6 B7 X B6 Y 06
Stock prices ime B6: Frequency Probability (area under the curve) = Stock price B7: NPV NPV NPV 5000 0% B8 Volatility Inverse of Mean the Percentile Mean Percentile Value $50M $00M Volatility Inverse (0.90) $00M $50M.85 $00M 39.0% 07
Excel NORMSINV(0.9) 0% NPV 5000 $50M $00M $50M Volatility 39.0% Inverse (0.0) $00M.85 $00M Frequency Best Case Scenario $50M 0% probability Expected NPV $00M NPV of Project 90th percentile B8: NPV 5000 50% 5000 50% 39.0% NPV 5000 0% Excel B9 B0 B9: Excel 08
B0: Excel B9 NPV B0 Excel NPV 35% 90%NPV 4485 0% NPV () DCF NPV 0 B B 986 3 004 B 0.58%90 8.06% 37% 36% 3 09
Z Z x x Z (*) x * Z Volatility Inverse of Mean the Percentile Mean Percentile Value Excel NORMSINV 350 Distribution of Microsoft Stock Prices 300 50 Frequency 00 50 00 50 0 $0.08 $3.4 $6.77 $0. $3.46 $6.80 $0.4 $3.49 $6.83 $30.7 $33.5 $36.86 $40. $43.55 $46.89 $50.4 Bin B: Microsoft ( 986) 0
Distribution of Microsoft Stock Log Returns 50 00 Frequency 50 00 50 0-7.64% -6.05% -4.46% -.87% -.8% -9.69% -8.0% -6.5% -4.9% -3.33% -.74% -0.5%.44% 3.03% 4.6% Log Returns 6.% 7.80% 9.39% 0.98%.57% 4.6% 5.75% 7.34% 8.93% More B: Microsoft ( RO ) D/E RO D E EQUIY
C Black & Scholes Black-Scholes Black-Scholes S $ X $ r % ln( S / X ) ( r / ) r ln( S / X ) ( r / ) Call S Xe Put Xe r ln( S / X ) ( r / ) ln( S / X ) ( r / ) S
3 Black & Scholes Black-Scholes q S $ X $ r % q % q r X S Xe q r X S Se Call r q ) / ( ) / ln( ) / ( ) / ln( q r X S Se q r X S Xe Put q r ) / ( ) / ln( ) / ( ) / ln(
Black & Scholes S S $ X $ r % q % CF i i rt rt * S CF e CFe... CF e rtn n S n i CF e rti i Call S * e Put Xe q r ln( S * / X ) ( r q / ) r ln( S * / X ) ( r q / ) Xe ln( S * / X ) ( r q / ) q ln( S * / X ) ( r q / ) S * e 4
5 S $ X $ r % q % / ) ( ) / ln( ) / ( ) / ln( / ) ( ) / ln( ) / ( ) / ln( t t t r q X S Xe q r X S Xe t t r q X S Se q r X S Se Option Value r r q q
6 ( C and P )(X C and X P ) Excel S $ X $ r % q % I Z (Z Z ) I t t t r q X I e X t t r q X I Ie t t t q r X I e X t t q r X I Ie P P P P t r P P P P t q C C C C t r C C C C t q P P C C ) )( / ( ) / ln( ) )( / ( ) / ln( ) )( / ( ) / ln( ) )( / ( ) / ln( 0 ) ( ) ( ) ( ) ( I t t q r I S d ) / ( ) / ln( and t d d C C C q r X S y ) / ( ) / ln( and P P P q r X S y ) / ( ) / ln( t / C and P t / ) ; ; ( ) ; ; ( ) ; ; ( ) ; ; ( P r P q C r C q y d e X y d Se y d e X y d Se Option Value P P C C
7 S $ r % q % I X ($) X ($) t () () I ) ( ) )( / ( ) / ln( ) ( ) )( / ( ) / ln( ) ( ) ( t t q r X I e X t t q r X I Ie X t r t q I ) / ( ) / ln( / ; ) / ( ) / ln( ; ) / ( ) / ln( / ; ) / ( ) / ln( ; ) / ( ) / ln( t t t q r I S e X t t t t q r I S q r X S e X t t t q r I S q r X S Se on call Call rt r q
8 S $ X $ r % t () () q % ) )( ( ) ( ) )( / ( ) ln(/ ) )( / ( ) ln(/ t t t q r e Se t t q r e Se Call t r qt t q qt ) ( ) )( ( ) )( / ( ) ln(/ ) )( / ( ) ln(/ t t q r e Se t t t q r e Se Put t q qt t r qt X%( + X).0 ( X)
Black-Scholes S $ X $ r % b % q % Call Se ( br) ln( S / X ) ( b / ) r ln( S / X ) ( b / ) Xe Put Xe r ln( S / X ) ( b / ) ( br) ln( S / X ) ( b / ) Se b = 0: b = r q: b = r: b = r r*: Black-Scholes Black-Scholes 9
F F F S X ($) F ($) r (%) q (years) (%) % Call Fe Put Xe r r ln( F / X ) ( / ) r ln( F / X ) ( / ) Xe ln( F / X ) ( / ) r ln( F / X ) ( / ) Fe 0
S $ X $ r % % q % q (%) ; ) / ( ) / ln( ; ) / ( ) / ln( ; ) / ( ) / ln( ; ) / ( ) / ln( q r X S q r X S e X q r X S q r X S e S Call r q ; ) / ( ) / ln( ; ) / ( ) / ln( ; ) / ( ) / ln( ; ) / ( ) / ln( q r X S q r X S e S q r X S q r X S e X Put q r
D SLS Windows XP, Vista, Windows 7, and beyond Excel XP or Excel 003 or Excel 007.NE Framework.0 or later () GB 80MB (Windows XP, Excel XP, Excel 003,.NE Framework.0,, 56MB 30MB ) NE Framework.0 CD dotnetfx0.exe CD www.realoptionsvaluation.com.cn/attachments/dotnetfx0.exe SLS NE Framework.0.NE.0 works.ne. CD www.realoptionsvaluation.com.cn SLS Real Option SLS 0 Real Options SLS Real Options SLS Excel SLS. Real Options SLS (Real Options Valuation, Real Options SLS, Real Options SLS).. Real Options SLS ID SLS 0 3.. Functions & Options Valuator FINGERPRIN 8 4. www.realoptionsvaluation.com 5. admin@realoptionsvaluation.com. SLS Real Options SLSReal Options Valuation Real Options SLSReal Options SLS. Real Options SLS SLS 3.. & NAME KEY
E. Windows XP, Vista, Windows 7. Excel 003, Excel 007 Excel 00.3.4 I I.4 Microsoft.NE.0 Microsoft.Net Framework.0..NE Framework.0 Real Option SLS..0 : Microsoft.NE Framework.0.NE Framework.0..NE Framework.0 CD dotnetfx0.exe CD www.realoptionsvaluation.com/download SLS.0 Software Microsoft.Net Framework.0 3
: www.realoptionsvaluation.com/downloads.ne Framework.0. 3 3:.NE Framework.0.3 4 4
4:.NE Framework.0.4 5.6 6.6.5 5:.NE Framework.0 5
6: Microsoft.5 6 www.realoptionsvaluation.com/downloads Microsoft Installer 3. 7 7: www.realoptionsvaluation.com.cn/downloads Microsoft 6
8: Microsoft 8 Windows Installer 9 9: Windows Installer 0. dotnetfx0.exe.ne Framework.0.6 7
0: Microsoft Installer : Microsoft Installer 8
: Microsoft Installer.6.NE Framework.0 3 4 3: Microsoft.NE Framework.0 9
4: Microsoft.NE Framework.0 Real Option SLS 3. CD 5 www.realoptionsvaluation.com/downloads SLS 5: Real Option SLS 3. 6 7 8 9-0 30
6: Real Option SLS 7: Real Option SLS 8: Real Option SLS 3
9: Real Option SLS 0: SLS 3
F Real Options SLS Real Options SLS Excel SLS 6. Real Options SLS (Real Options Valuation, Real Options SLS, Real Options SLS) 7.. Real Options SLS ID SLS 0 8.. Functions & Options Valuator FINGERPRIN 8 9. www.realoptionsvaluation.com 0. admin@realoptionsvaluation.com 4. SLS Real Options SLSReal Options Valuation Real Options SLSReal Options SLS 5. Real Options SLS SLS. & NAME KEY 33