# MGTC71-9 - A Simple Binomial Model MGTC71-Lecture 9 A stock...

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1 1 MGTC71-Lecture 9 Binomial Trees Ata Mazaheri 2 2 A Simple Binomial Model A stock price is currently \$20 In three months it will be either \$22 or \$18 Stock Price = \$22 Stock Price = \$18 Stock price = \$20 3 3 Stock Price = \$22 Option Price = \$1 Stock Price = \$18 Option Price = \$0 Stock price = \$20 Option Price=? A Call Option ( Figure 11.1, page 242) A 3-month call option on the stock has a strike price of 21. 4 4 Consider the Portfolio: long Δ shares short 1 call option Portfolio is riskless when 22 Δ – 1 = 18 Δ or Δ = 0.25 22 Δ – 1 18 Δ Setting Up a Riskless Portfolio 5 5 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 6 6 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 )

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7 7 Generalization A derivative lasts for time
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MGTC71-9 - A Simple Binomial Model MGTC71-Lecture 9 A stock...

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