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# Ch11 - Binomial Trees Chapter 11 Click to edit Master...

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Click to edit Master subtitle style  7/7/11  Options, Futures, and Other Derivatives, 7th  Binomial Trees Chapter 11 11

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7/7/11  Options, Futures, and Other Derivatives, 7th  A Simple Binomial Model A stock price is currently \$20 In 3 months it will be either \$22 or \$18 22 Stock Price = \$18 Stock Price = \$22 Stock price = \$20
7/7/11  Options, Futures, and Other Derivatives, 7th  A Call Option ( Figure 11.1, page 238) A 3-month call option on the stock has a strike price of 21. 33 Stock Price = \$18 Option Price = \$0 Stock Price = \$22 Option Price = \$1 Stock price = \$20 Option Price=?

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7/7/11  Options, Futures, and Other Derivatives, 7th  Setting Up a Riskless Portfolio Consider the Portfolio: long shares short 1 call option Portfolio is riskless when 22 – 1 = 18 or 44 22 1 18
7/7/11  Options, Futures, and Other Derivatives, 7th  Valuing the Portfolio (Risk-Free Rate is 12%) The riskless portfolio is: long 0.25 shares short 1 call option The value of the portfolio in 3 months is 22 × 0.25 – 1 = 4.50 The value of the portfolio today is 4.5e – 0.12 × 0.25 = 4.3670 55

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7/7/11  Options, Futures, and Other Derivatives, 7th  Valuing the Option The portfolio that is long 0.25 shares short 1 option is worth 4.367 The value of the shares is 5.000 (= 0.25 × 20 ) The value of the option is therefore 0.633 (= 5.000 – 4.367 ) 66
7/7/11

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