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Derivatives

Derivatives. Lecture 18. Option Valuation Methods. Case 1 Stock price falls to $60 Option value = $0. Case 2 Stock price rises to $106.67 Option value = $26.67. Genentech call options have an exercise price of $80 and expire in one year. Option Valuation Methods.

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Derivatives

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  1. Derivatives Lecture 18

  2. Option Valuation Methods Case 1 Stock price falls to $60 Option value = $0 Case 2 Stock price rises to $106.67 Option value = $26.67 Genentech call options have an exercise price of $80 and expire in one year.

  3. Option Valuation Methods If we are risk neutral, the expected return on Genentech call options is 2.5%. Accordingly, we can determine the price of the option as follows, given equal probabilities of each outcome.

  4. Binomial Pricing The prior example can be generalized as the binomial model and shown as follows.

  5. Binomial Pricing a = 1.0083 u = 1.1215 d = .8917 Pu = .5075 Pd = .4925 Example Price = 36 s = .40 t = 90/365 D t = 30/365 Strike = 40 r = 10%

  6. Binomial Pricing 40.37 32.10 36

  7. Binomial Pricing 40.37 32.10 36

  8. Binomial Pricing 50.78 = price 40.37 32.10 25.52 45.28 36 28.62 40.37 32.10 36

  9. Binomial Pricing 50.78 = price 10.78 = intrinsic value 40.37 .37 32.10 0 25.52 0 45.28 36 28.62 40.37 32.10 36

  10. Binomial Pricing 50.78 = price 10.78 = intrinsic value 40.37 .37 32.10 0 25.52 0 45.28 5.60 36 28.62 The greater of 40.37 32.10 36

  11. Binomial Pricing 50.78 = price 10.78 = intrinsic value 40.37 .37 32.10 0 25.52 0 45.28 5.60 36 .19 28.62 0 40.37 2.91 32.10 .10 36 1.51

  12. Binomial Model The price of an option, using the Binomial method, is significantly impacted by the time intervals selected. The Genentech example illustrates this fact.

  13. Price Comparions • Black Scholes price= 1.70 • Binomial price = 1.51

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