1. Lecture 18

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

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

6. 40.37 32.10 36 Binomial Pricing

7. 40.37 32.10 36 Binomial Pricing

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

9. 50.78 = price 10.78 = intrinsic value 40.37.37 32.10 0 25.52 0 45.28 36 28.62 36 40.37 32.10 Binomial Pricing

10. 50.78 = price 10.78 = intrinsic value 40.37.37 32.10 0 25.52 0 45.28 5.60 36 28.62 40.37 32.10 36 The greater of Binomial Pricing

11. 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 Binomial Pricing

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.  Black Scholes price= 1.70  Binomial price = 1.51