Ch11HullOFOD6thEd - Binomial Trees Chapter 11 A Simple...

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Binomial Trees Chapter 11
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A Simple Binomial Model l A stock price is currently $20 l In three months it will be either $22 or $18
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A Call Option ( Figure 11.1, page 242) A 3-month call option on the stock has a strike price of 21.
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Setting Up a Riskless Portfolio l Consider the Portfolio: long shares short 1 call option l Portfolio is riskless when 22 – 1 = 18 or = 0.25
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Valuing the Portfolio (Risk-Free Rate is 12%) l The riskless portfolio is: long 0.25 shares short 1 call option l The value of the portfolio in 3 months is 22 × 0.25 – 1 = 4.50 l The value of the portfolio today is 4.5e – 0.12 × 0.25 = 4.3670
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Valuing the Option l The portfolio that is long 0.25 shares short 1 option is worth 4.367 l The value of the shares is 5.000 (= 0.25 × 20 ) l The value of the option is therefore 0.633 (= 5.000 – 4.367 )
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Generalization (Figure 11.2, page 243) A derivative lasts for time T and is dependent on a stock
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Generalization (continued) l Consider the portfolio that is long shares and short 1 derivative l The portfolio is riskless when S 0 u ƒ u = S 0 d ƒ d or
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Ch11HullOFOD6thEd - Binomial Trees Chapter 11 A Simple...

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