Lecture 18

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 $ Option value = $26.67

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.

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

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

Binomial Pricing

Binomial Pricing

50.78 = price Binomial Pricing

50.78 = price = intrinsic value Binomial Pricing

50.78 = price = intrinsic value The greater of Binomial Pricing

50.78 = price = intrinsic value Binomial Pricing

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.

 Black Scholes price= 1.70  Binomial price = 1.51