Unformatted text preview: ta (∆).
In the above problem, the option delta is x :
Option delta = 1/4. Notice:
The up/down spread is $150  $50 = $100 for the stock
The up/down spread is $25  $0 = $25 for the call Option Delta Option delta measure how sensitive the option value is to
movements in the stock price.
Notice:
When an option is deep in the money, the ∆ will be close to 1
(but slightly less)
When an option is deep out of the money, the ∆ will be close
to 0
Also notice: if we buy the call and ∆ shares of the stock, we’ll
have a risk less portfolio (no sensitivity to stock price movements) Binomial Stock Example I: Alternate Solution
We want to price the call option:
Stock: 100 150
50 Bond: 95 100
100 C0 =??? 25
0 If we buy the call and short ∆ shares of stock, the future value of
the portfolio is:
Vup = 25 − 150∆
Vdown = 0 − 50∆
Now, Vup = Vdown when
25 − 150∆ = 0 − 50∆ ⇒ ∆ = 25 − 0
1
=
150 − 50
4 Binomial Stock Example I: Alternate Solution (continued) We can ﬁgured out ∆ = 1
4 just by noticing: The up/down spread is $150  $50 = $100 for the stock
The up/down spread is $25  $0 = $25 for the call
So the up/down mov...
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This document was uploaded on 10/28/2013.
 Spring '13

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