Real Options "in" Projects and Systems Design ... - Title Page - MIT

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70Then, using Ito’s lemma (see Appendix 3A) to get:d ln S2σ= ( µ − ) dt + σdz2Equation 3-3From this equation, the variable lnS follows a generalized Wiener process, the change inlnS between 0 and t is normally distributed, so that S has a lognormal distribution.Lognormal Properties of stock priceIn general, a lognormal distribution probability density function is as follows:f1x1−(lnx−µ)22( x)= ⋅ ⋅ e2σtEquation 3-4σ 2πtbut the following will show a more intuitive explanation of the lognormal distribution of thestock prices. See Figure 3-5 for the shape of lognormal density function.The lognormal distribution of price means the logarithm of the price has a normaldistribution. To illustrate, if a stock is priced at $100 per share and prices have a normaldistribution, the distribution of prices is the familiar bell-shaped curve centered at $100,but if the prices have a lognormal distribution, then it is the logarithm of the price whichhas a bell-shaped distribution about ln(100) = 4.605. The logarithm of the prices isequally likely to be 5.298 or 3.912, i.e., 4.605 ± 0.693 corresponding to prices of $200 and$50, respectively. If the lognormal probability density curve is plotted as a function of
71price rather than as a function of the logarithm of price, the curve will appear positivelyskewed with tails more nearly depicting the observed behavior of stock prices.Lognormal Density0.450.40.350.30.250.20.150.10.0500 1 2 3 4 5 6 7 8Figure 3-5 Lognormal DensityLognormality arises from the process of return compounding, in other words, thelognormal property of stock prices applies when the return rate earned on a stockbetween time 0 and t is continuously compounded. It is important to distinguish thecontinuously compounded rate of return and the annualized return with no compounding1 S S0as ( ) .t St−03.3. Options Valuation ToolsThe first model to calculate options value is the Black-Scholes formula, which issometimes regarded as arcane. Interests in option pricing, however, has picked up inrecent years as more powerful computers can aid very sophisticated model building.
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Real Options "in" Projects and Syst
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4Committee Member: Dr. David H. Mar
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6Table of Contents:Acknowledgements
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84.4.3. Binomial Tree______________
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108.7. Contributions and Conclusion
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12Figure 5-3: Scenario tree _______
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14Table 6-12 Sources of options val
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16fFC s∆F sthiH sh tThe ratio of
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18X styyY jYYjAverage flow from sit
Page 20 and 21: 201.1. The problemWith the recognit
Page 22 and 23: 22The first thread - engineering sy
Page 24 and 25: 24The second thread - options theor
Page 26 and 27: 26The third thread - mathematical p
Page 28 and 29: 28especially the difference between
Page 30 and 31: 30every area in a more and more det
Page 32 and 33: 32made between forecasts of the lev
Page 34 and 35: 34memory (whereas modern computers
Page 36 and 37: 36model and presented a multiple-yi
Page 38 and 39: 38such designs exist) by simply rec
Page 40: 40mathematical properties of maximi
Page 43 and 44: 43that incorporates important perfo
Page 45 and 46: 45Dixit and Pindyck (1994) stressed
Page 47 and 48: 47The real options “in projects
Page 49 and 50: 491980s, Merck began to use simulat
Page 51 and 52: 51that the integrated approach (the
Page 53 and 54: 53blurs the exercise condition, bec
Page 55 and 56: 55Goldberg and Read (2000) found th
Page 57 and 58: 57In general, real options “in”
Page 59 and 60: 59- And, mathematical programming,
Page 61 and 62: 61Example of a stock call option:Jo
Page 63 and 64: 63or $300. Arbitrage opportunities
Page 65 and 66: 659 × 0.25 =2.25Regardless of whet
Page 67 and 68: 67∆Z = ε ∆twhere ε denotes a
Page 69: 69standard deviation of 1.0. It fol
Page 73 and 74: 73The stock price process is the on
Page 75 and 76: 75Equation 3-9 is the Black-Scholes
Page 77 and 78: 7710,000 Trials Frequency Chart90 O
Page 79 and 80: 79The two are equal whenorS0ux− f
Page 81 and 82: 81S uuS uf uuS f u S udfS df udf dS
Page 83 and 84: 83Figure 3-10 Decision Tree for Opt
Page 85 and 86: 85the Black-Scholes formula is $1.9
Page 87 and 88: 87The expected growth of the stock
Page 89 and 90: 89option, the holder has the right
Page 91 and 92: 91Boston expects to receive a cash
Page 93 and 94: 93the value of a European put on a
Page 95 and 96: 95Chapter 4 Real Options“The clas
Page 97 and 98: 97In addition to understanding the
Page 99 and 100: 99gas. The development was unsucces
Page 101 and 102: 101But if we employ Real Options th
Page 103 and 104: 103Option to switch (e.g.,outputs o
Page 105 and 106: 105The fifth step, by comparing the
Page 107 and 108: 107Real Options "in" ProjectsReal O
Page 109 and 110: 109- 5 and 3.5 billion dollars resp
Page 111 and 112: 111Real options “on” projectsVa
Page 113 and 114: 1134.3.4. A Case Example on analysi
Page 115 and 116: 115Step 1: Table 4-6 illustrates th
Page 117 and 118: 11710EXPECTED NPV ($, MILLIONS)50-5
Page 119 and 120: 119PROBABILITY1.00.90.80.70.60.50.4
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1214.4.1. Black-Scholes FormulaAs d
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123and buy the real options to earn
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125computationally prohibitive to c
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1274.5. Some Implications of Real O
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129Value of flexibility Appropriate
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1314.6.2. What is the definition of
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133- It aims at an expected value o
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135Chapter 5 Valuation of Real Opti
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137uncertain environment. Specifica
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139assuming steady state, i.e. all
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141modify this standard simulation
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143Table 5-1: Decision on each node
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145The objective function is to get
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1475.3.2. Stochastic mixed-integer
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149q⎛ R ⎞1⎜ ⎟qR = ⎜ ...
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151Table 5-4: Stochastic programmin
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153The real options timing model fo
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1555.4. A case example on satellite
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157Table 5-6 Evolution of demand fo
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1595.4.3. ParametersWe consider thr
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161Year 0 Year 2.5 Year 5 Year 7.5
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163scenario trees based on better s
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165The total length of the river is
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167Project 1 or 3. A shallow gradie
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169Table 6-5: Stream flow for Proje
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171The reservoir cost coefficient a
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173Q in,tQ in,tProject CSite 3Site
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175k t= (60Sec/ Min)× (60Min/ Hour
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177Reservoir cost: α ( Vss) = FCs+
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179[Power plant cost curve]δ 1 is
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181Complete formulation of the scre
Page 183 and 184:
183Table 6-9 List of Parameters for
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185Step 1. The important uncertain
Page 187 and 188:
187From the tornado diagram, we und
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189design feature where we consider
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191Table 6-13 List of design variab
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193Table 6-15 List of Parameters fo
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195A Realization Path of Electricit
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197Case II: there is enough water t
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199where the average head*Astis cal
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201Ball©. All designs from the scr
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203options sees Table 6-17. This is
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205XX= Q + Y ∑ Ri31 in,131 j331 i
Page 207 and 208:
207Objective functionThe objective
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209According to the screening model
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211The hydropower benefit coefficie
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213Table 6-19 List of parameters fo
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215time to build and gradually incr
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217example, at year 20, if the pric
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219from 1 to 8. The hydropower bene
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221Our planning horizon is three st
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2235 6 7 82s= R2s= R2sR2sR =1 23sR3
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225yrsIndicating whether or not the
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227The overall expected net benefit
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229contingency plan is to build Pro
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231Table 6-26 Different water flow
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233Chapter 7 Policy Implications -O
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235excess water when water is more
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237The options methodology develops
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2397.2.2. Organizational Wisdom to
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241success. In the bank, the author
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243method. Sensitivity analysis wit
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245Chapter 8 Summary and Conclusion
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2478.2. Real options “in” proje
Page 249 and 250:
249Note the difference between real
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251Carlo simulation model to value
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2538.3.1. Options identificationFor
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255can catch upside of the uncertai
Page 257 and 258:
257where r is the drift rate (in th
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259A joint realization of the probl
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261Note there is an exercise in sce
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263The real options decision variab
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265development case example, we sim
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267The standard deviation of the co
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269reservoir fixed cost is less und
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271time series of the water flow co
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273Table 8-8 Configurations set Y f
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275Table 8-9: Results for real opti
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277inconvenient features and high c
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279Year 0 Year 2.5 Year 5 Year 7.5
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281Following is a report on the com
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283can be found in Chapter 6, whose
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285This dissertation has successful
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2878.7. Contributions and Conclusio
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289ReferencesAberdein, D. A. (1994)
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291Copeland, T.E. and Antikarov, V.
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293Jacoby, H.D. and Loucks, D. (197
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295Mason, S.P. and Merton, R.C. (19
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297Schoenberger, C. R. (2000) “Si
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299AppendicesAppendix 3A: Ito’s L
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301p;Binary variablesX(i,j);X.l('4'
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303Appendix 5B: GAMS Code for Ameri
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305n5 non-antipativity constraint 5
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3072 0.50 1.51 4.57 7.5 4.573 0.50
Page 309 and 310:
309R(q,i,s)RTD(q,i,s)P1(q,i)P2(q,i)
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311na28na29na30na31na32na33na34na35
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313na26(s)..na27(s)..R('14','3',s)
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315Table DeltaF(s,t)1 21 0 02 0 03
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317EquationsObjBeneCostCont1Cont2Co
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319Appendix 6B: GAMS code for the t
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3213 -63.6 63.6;Scalars f /0.226/;P
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323Hydro1Hydro2Budget;*costs and be
Page 325 and 326:
325Scalars es /0.7/;Scalars Kt /15.
Page 327 and 328:
327VariablesXstiq(s,t,i,q)Pstiq(s,t
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329f)*Rsiq(s,i,'1') )))))*0.001 + P
Page 331 and 332:
331Appendix 6D: GAMS code for real
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3331 2 31 9600 9600 96002 0 0 03 95
Page 335 and 336:
335Rsiq.l('1','3','4') = 0;Rsiq.l('
Page 337:
337Cont1(i,q).. Xstiq('3','1',i,q)
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