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Derivatives

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Derivatives

Lecture 18

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.

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.

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

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 = 40r = 10%

40.37

32.10

36

40.37

32.10

36

50.78 = price

40.37

32.10

25.52

45.28

36

28.62

40.37

32.10

36

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

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

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

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