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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

Derivatives

Lecture 18


Option valuation methods

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 methods1

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

Binomial Pricing

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


Binomial pricing1

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 = 40r = 10%


Binomial pricing2

Binomial Pricing

40.37

32.10

36


Binomial pricing3

Binomial Pricing

40.37

32.10

36


Binomial pricing4

Binomial Pricing

50.78 = price

40.37

32.10

25.52

45.28

36

28.62

40.37

32.10

36


Binomial pricing5

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


Binomial pricing6

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


Binomial pricing7

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


Binomial model

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.


Price comparions

Price Comparions

  • Black Scholes price= 1.70

  • Binomial price = 1.51


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