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OptionArbitrage

# OptionArbitrage - Option Arbitrage by Dr Fernando Diz...

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Option Arbitrage by Dr. Fernando Diz Syracuse University

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Option Arbitrage Mimicking positions Suppose that a Trader has the following  position: Long one May 100 Call Short one May 100 Put If the options are European, what does the  trader own at expiration?
Option Arbitrage Two ways of thinking about it: 1. Payoff of the portfolio at expiration. 2. Delta of the position.

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Option Arbitrage 1. Payoff of the Long call at expiration?  S-X when S>=X 2. Payoff of the Short put at expiration? -(X-S) = S-X when S<X So the payoff of this position is always S- X! Graph.
Option Arbitrage Long Call and Short Put -60 -40 -20 0 20 40 60 Asset Price Call Put Call + Put

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Option Arbitrage 2. For simplicity suppose the Stock price is  100. What is the Delta of the call? (Roughly) What is the Delta of the put? (Roughly) What is the Delta of the strategy?
Option Arbitrage The delta of an at-the-money call is  roughly 0.5. The delta of an at-the-money put is  roughly -0.5. But remember that the put is  short!! So what is the delta of a short put?  The delta of the strategy is 0.5+0.5 = 1,  the same delta as the underlying!

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Option Arbitrage In effect, the trader owns the underlying  asset payoff stream as if he held the  underlying long! This is called a mimicking LONG  underlying. How do we get a mimicking short  underlying?
Option Arbitrage Short Call and Long Put -60 -40 -20 0 20 40 60 Asset Price Call Put Call + Put

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Option Arbitrage Observations: 1. A Mimicking underlying behaves like  the true underlying.
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OptionArbitrage - Option Arbitrage by Dr Fernando Diz...

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