Chap 11

A Simple Binomial Model ,[object Object],[object Object],Stock Price = $22 Stock Price = $18 Stock price = $20

A Call Option ( Figure 11.1, page 24 2 ) ,[object Object],Stock Price = $22 Option Price = $1 Stock Price = $18 Option Price = $0 Stock price = $20 Option Price=?

[object Object],[object Object],[object Object],Setting Up a Riskless Portfolio 22  – 1 18 

Valuing the Portfolio (Risk-Free Rate is 12%) ,[object Object],[object Object],[object Object],[object Object]

Valuing the Option ,[object Object],[object Object],[object Object],[object Object],[object Object]

Generalization (Figure 11.2, page 24 3 ) ,[object Object],S 0 u ƒ u S 0 d ƒ d S 0 ƒ

Generalization (continued) ,[object Object],[object Object],S 0 u  – ƒ u S 0 d  – ƒ d

Generalization (continued) ,[object Object],[object Object],[object Object],[object Object]

Generalization (continued) ,[object Object],[object Object],[object Object]

p as a Probability ,[object Object],[object Object],p (1  – p ) S 0 u ƒ u S 0 d ƒ d S 0 ƒ

Risk-neutral Valuation ,[object Object],[object Object],[object Object],[object Object]

Original Example Revisited ,[object Object],[object Object],[object Object],[object Object],S 0 u = 22 ƒ u = 1 S 0 d = 18 ƒ d = 0 S 0 ƒ p (1  – p )

Valuing the Option Using Risk-Neutral Valuation ,[object Object],[object Object],[object Object],S 0 u = 22 ƒ u = 1 S 0 d = 18 ƒ d = 0 S 0 ƒ 0.6523 0.3477

Irrelevance of Stock’s Expected Return ,[object Object],[object Object]

A Two-Step Example Figure 11.3, page 246 ,[object Object],[object Object],20 22 18 24.2 19.8 16.2

Valuing a Call Option Figure 11.4, page 247 ,[object Object],[object Object],[object Object],20 1.2823 22 18 24.2 3.2 19.8 0.0 16.2 0.0 2.0257 0.0 A B C D E F

A Put Option Example; K =52 Figure 11.7, page 250 ,[object Object],[object Object],50 4.1923 60 40 72 0 48 4 32 20 1.4147 9.4636 A B C D E F

What Happens When an Option is American (Figure 11.8, page 251) 50 5.0894 60 40 72 0 48 4 32 20 1.4147 12.0 A B C D E F

Delta ,[object Object],[object Object]

Choosing u and d ,[object Object],[object Object]

Chap 11

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Chap 11