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two values of the stock price that might occur. This procedure would provide a widerrange of possible stock prices for a given time period.Using indefinitely small periods, we would finally arrive at a situation where the stockprice changes continuously, generating a continuum of possible prices. In theirfamous publication of 1973, Black, Merton and Scholes derived an equation thatallows us to value options that have a constantly changing underlying asset (this is theusual case for assets such as stocks). The so-called Black-Scholes model can beconsidered as the ―continuous-time version‖ of the binomial tree.The Black-Scholes model is based on the following assumptions:Firstly, it can value European options only (where the option is exercised at a fixeddate); secondly, the assets do not pay dividend; thirdly, the volatility of the underlyingasset is constant; fourthly, the value of the underlying asset is log normally distributed;and finally, the interest rates are constant.For valuing a call option, the equation is defined as follows:Value of the call option C = SN(d1)-Ee-rt(d2)Where:N(d1): cumulative normal probability density function (i.e. the probability that anormally distributed random variable will be less that, or equal to d)S: current value of the underlying asset (current stock price)E: exercise price (it is discounted to the presence with the continuously compoundedrisk-free interest rate, i.e. by multiplication with e-rt )Page | 22
t: years to expirationr: annual risk-free rate of returnv: standard deviation per year of rate of return on stock2.3.5 Compound OptionIn the real world, real options are often compound options. Also known as option onoption, a compound option is like a standard option, but its underlying asset is antherstandard option. And the values of compound options are extremely sensitive to thevolatility of volatility. The valuation of compound option is first analysed of Analyticformulas by Geske (1979), and then by Hodges and Selby (1987) and Rubinstein(1991). A compound option can be simultaneous, or sequential.There are four types of compound options: Call on a call, Put on a call, Call on a putand Put on a put. And the third type, a call on a put, gives the holder the right to buy aput option. In this case, on the first exercise date, the holder of the compound optionis allowed to pay the first strike price and receive a put option. The put option givesthe holder the right to sell the underlying asset for the second strike price on thesecond exercise date.Consider under a Black-Scholes environment (that is: the underlying asset is follow alognormal random walk, the risk-free interest rate is used as the discount rate and theunderlying asset price is expected to appreciate at the same risk-free rate, and allow arisk-neutral valuation.2.3.6 Monte Carlo SimulationMonte-Carlo simulation is also known simply as simulation. Suppose we know howto value a derivative if only we knew the cash flows, and we know the cash flows arerandom while we have a model for the random effects. Then these components can beput together to create a valuation method.Page | 23
Page 1 and 2: APPLICATION OF REAL OPTIONS VALUATI
Page 3 and 4: Table of ContentsAbstract .........
Page 5 and 6: List of TablesTable 5.1: Value of O
Page 7 and 8: Chapter One— IntroductionAs one o
Page 9 and 10: Then, in Chapter 4, the case study
Page 11 and 12: and we will have the right to take
Page 13 and 14: project, to get its salvage value,
Page 15 and 16: The option to switch:If assets have
Page 17 and 18: 2.2 Advantages of Real Option Valua
Page 19 and 20: In the case of pharmaceutical R&D,
Page 21 and 22: delayed in time. Undertaking one pr
Page 23 and 24: Figure 2.2: Advantages and disadvan
Page 25 and 26: smallest possible payoff of zero, w
Page 27: options applications is the binomia
Page 31 and 32: Chapter Three— Apply Real options
Page 33 and 34: on Howell et al (2001).3.1.1 Precli
Page 35 and 36: approved.3.2 real options valuation
Page 37 and 38: Figure 3.3: Comparison of a call op
Page 39 and 40: applying the principals of activity
Page 41 and 42: that has occurred in the past. Depe
Page 43 and 44: Chapter Four— Case StudyFor this
Page 45 and 46: 4.3 DavanrikLAB Pharmaceuticals ori
Page 47 and 48: efficacious for depression only, a
Page 49 and 50: Chapter Five— Case Study Analysis
Page 51 and 52: figure below:Figure 5.3: NPV of Dav
Page 53 and 54: Merck & Co (10%), which gives $2338
Page 55 and 56: approval and other issues. Therefor
Page 57 and 58: of $345m at year 0 (which is $672.3
Page 59 and 60: project turns out to be unprofitabl
Page 61 and 62: these three options, the risk-free
Page 63 and 64: ewrite as, noting all the costs (in
Page 65 and 66: Figure 5.10: Valuation of Option A
Page 67 and 68: Figure 5.12: Valuation of Option A
Page 69 and 70: Figure 5.13 Valuation of Compound r
Page 71 and 72: $ in millionmillion to $113.97 mill
Page 73 and 74: Chapter Six— Limitations and conc
Page 75 and 76: discovery projects, arrives in a di
Page 77 and 78: References1. Amram M & Kulatilaka N
Page 79 and 80:
31/08/2006, available at: http://ho
Page 81 and 82:
46. T rigeorgis L . (1995), ―M et
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