FBE559.slides.07

In the above problem the option delta is x option

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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.

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