options3 - Option Pricing By Dr. Fernando Diz Two State...

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Option Pricing By Dr. Fernando Diz
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Two State Option Pricing We shall price a European option one period  before expiration. Suppose we have a European CALL option  with one year to Expiration and an EXERCISE  price of 110.0. We also know that in one year there are only  two possible rates of return for the Stock,  namely, -10% =r d s   and +20%=r u s We shall assume that the riskless rate of  return is 10%=r.
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Two State Option Pricing S 0 S 0  (1+r u s ) S 0  (1+r d s ) 100.0 100*(1+0.2) = 120.0 100*(1-0.1) =  90.0
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Two State Option Pricing 100.0 100*(1+0.2) = 120.0 100*(1-0.1) =  90.0 C=?  max(0,120.0-110) = 10.0 max(0,90.0-110) = 0.0
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Two State Option Pricing Although we know the terminal values of the call  option we do not know how much that call will  be selling for at time 0!!! We know however, that if a portfolio is riskless it  has to earn the T-Bill rate of return. Why?
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Two State Option Pricing If a portfolio is riskless and it earns more than  the T-Bill rate, then I can borrow at the T-Bill  rate the full amount of that commodity, buy it  and make money without bearing any risk!!! An  arbitrage opportunity!
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Two State Option Pricing Is there a strategy that uses call options  such that the strategy is riskless? Yes there is. One such strategy is to: Buy Stock Sell call options on the stock. 
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Two State Option Pricing Sounds like a covered call write. However, the important question is: How many call options should we sell per 100  shares of the stock we hold to make this  portfolio riskless? I will tell you how many.
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# of calls per share = high - low spread for stock high - low spread for option What is the  high - low spread   for the stock? What is the 
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This note was uploaded on 02/09/2010 for the course FIN 459 taught by Professor Yildary during the Spring '07 term at Syracuse.

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options3 - Option Pricing By Dr. Fernando Diz Two State...

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