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Options

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

herrod-hodges
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Options

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  1. Options

  2. OptionsFinancial Options • There are Options and Options - Financial options - Real options

  3. OptionsFinancial 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

  4. Table 20.1 Option Quotes for Amazon.com Stock

  5. OptionsFinancial 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%

  6. OptionsFinancial Options/Pricing 0 1 Stock Bond Call 60 1.06 max (60-50,0) = 10 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

  7. OptionsFinancial 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

  8. Generalising we get St = Cu – Cd and B = Cd – Sdt Su – Sd 1+rf This gives us the replicable portfolio The Call option price then follows C = St + B or 50x.5 – 18.8679(1) = 6.13 OptionsFinancial Options/Pricing

  9. OptionsFinancial Options/Pricing • But what about multi period models? • Strike price of 50, Rf = 6% 0 1 2 Periods 60 50 40 40 30 20

  10. OptionsFinancial Options/Pricing • We start at the end and work back 1 2 60 Max(60 -50,0) = 10 50 40 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

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

  12. OptionsFinancial Options/Pricing • Now move back a period 0 1 Stock Call 50 6.13 40 30 0 Now work out replicating portfolio at time 0 St = Cu – Cd = 6.13 – 0 = 0.3065 Su – Sd 50 – 30 B = Cd – Sdt = 0 - 30(0.3065) = - 8.67 1 + rf 1.06

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

  14. OptionsFinancial 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 won’t • But remember the important factors in the pricing

  15. OptionsFinancial Options/Pricing • The strike price • The stock price • The exercise date • The risk free interest rate • The volatility

  16. OptionsReal 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

  17. OptionsReal 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?

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

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

  20. OptionsReal 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

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

  22. OptionsReal Options • Go to meet or not? 1,500 Go to meet Sunshine 75% Stay at home Pay for booth - 500 0 Rain 25% Go to meet -100 Don’t pay for booth Stay at home 0 0

  23. OptionsReal 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

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

  25. OptionsReal 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?

  26. OptionsReal Options • Option to Grow • Option to Expand • Option to Abandon • Option to Prepay

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