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1 Options

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2 Options Financial Options There are Options and Options - Financial options - Real options

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3 Options Financial Options A financial option gives its owner the right (but not the obligation) to purchase or sell an asset at a fixed price at some future date. Puts Calls Strike price/Exercise price American/European

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4 Table 20.1 Option Quotes for Amazon.com Stock

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5 Options Financial Options Option Pricing Binomial - Two state single period - Law of one price - Replicating portfolio Call option, SP 50, No dividend, Stock will either rise by 10 or fall by 10 Risk free rate is 6%

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6 Options Financial Options/Pricing Stock Bond Call 60 1.06 max (60-50,0) = 10 0 1 Stock 50 Bond 1 40 1.06 max (40 -50,0) = 0 60 = up and 40 = down S = Share price and t = number of shares and B = investment in the bond. SP = 50

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7 Options Financial Options/Pricing Value of portfolio containing the stock and the bond must = the value of the portfolio in each state. 60St + 1.06B = 10 40St + 1.06B = 0 So St =.5 And B = - 18.8679 60 x.5 - 1.06 x 18.8679 = 10 40 x.5 – 1.06 x 18.8679 = 0

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8 Options Financial Options/Pricing Generalising we get St = C u – C d and B = C d – S d t S u – S d 1+r f This gives us the replicable portfolio The Call option price then follows C = St + B or 50x.5 – 18.8679(1) = 6.13

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9 Options Financial Options/Pricing But what about multi period models? Strike price of 50, R f = 6% 0 1 2 Periods 50 30 40 60 40 20

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10 Options Financial Options/Pricing We start at the end and work back 1 2 50 60 40 Max(60 -50,0) = 10 Max 40 -50,0) = 0 This is the same as before therefore St =.5 and B = -18. 87 and the call value at time 1 is 6.13

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11 Options Financial Options/Pricing What if share dropped to 30 in the next period (period 1)? 30 40Max (40 – 50, 0) = 0 20 Max (30 – 50, 0) = 0 The option is worthless in both states so no portfolio value

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12 Options Financial Options/Pricing Now move back a period 0 1 40 Stock Call 50 6.13 30 0 Now work out replicating portfolio at time 0 St = C u – C d = 6.13 – 0 = 0.3065 S u – S d 50 – 30 B = C d – S d t = 0 - 30(0.3065) = - 8.67 1 + r f 1.06

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13 Options Financial Options/Pricing So the Call value at Time 0 is C = St + B = 40(0.3065) +(-) 8.67 = 3.59

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14 Options Financial Options/Pricing For European options if we let each period shrink to zero and have an infinite number of periods then we may use the Black-Scholes formula to calculate the binomial pricing………….. but we wont But remember the important factors in the pricing

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15 Options Financial Options/Pricing The strike price The stock price The exercise date The risk free interest rate The volatility

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16 Options Real Options And there are Real Options The right to take a particular business decision e.g. a capital investment decision. Main distinction is that the asset is normally not traded

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17 Options Real Options Until now we have considered a stream of cash flows during the project, starting from today, to determine the NPV But what about alternatives such as delaying the start or abandoning the project after a while?

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18 Options Real Options To analyse the alternatives we need Decision Trees A graphical representation of future decisions and uncertainty resolution (B & DeM)

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19 Options Real Options Meet (re meet) Megan Goes to markets Sells, average profit 1,100 Costs of Booth 500, in advance Go to meet Stay at home profit 1,100 – 500 = 600 0

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20 Options Real Options Now add some uncertainty If it rains (25% chance) she will make a loss = -100 If it is sunny her profit is higher = 1,500

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21 Options Real Options Go to meet sunshine 75% 1,500 Stay at home Rain 25% - 100 Decision node Information node 0 - 500

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22 Options Real Options Go to meet or not? Dont pay for booth Pay for booth - 500 Sunshine 75% Rain 25%Go to meet Stay at home Go to meet 1,500 0 -100 0 0

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23 Options Real Options So what is the value of this real option to Megan? Expected profit without choice i.e. go to meet regardless = 1,500 x.75 +-100 x.25 = 1,100 Expected profit with choice = 1,500 x.75 = 1,125 So choice/option worth 25

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24 Options Real Options Should Megan pay for the booth? Expected profit will be 1125 -500 = 625 So Yes

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25 Options Real Options When else may they be used? -Option to delay Invest now only where NPV is substantially greater than zero But What are costs of delay? What is volatility? What are costs of investment?

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26 Options Real Options Option to Grow Option to Expand Option to Abandon Option to Prepay

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Properties of Stock Option Prices Chapter 9

Properties of Stock Option Prices Chapter 9

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