673_12_Options__2_

673_12_Options__2_ - SIMPLE ARBITRAGE RELATIONSHIPS FOR...

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1 SIMPLE ARBITRAGE RELATIONSHIPS FOR OPTIONS NBA 673 March 2, 2006
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2 Call Property: Result #1 (Result 1) If the stock price is zero, then the value of an American call must be zero, i.e. if S (0) = 0 then C (0) = 0 . Proof The price of the stock is the sum of its future discounted cash flows. When the stock price is 0, there are no future cash flows. The price will always stay at 0, so the call will always be worthless.
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3 Call Property: Result #2 (Result 2) The minimum value of an American call is greater of 0 or S (0) – K : C (0) Max{0, S (0) - K } . Proof Option are limited liability assets. So C (0) 0. Suppose S (0) > K . If C (0) < S (0) - K , buy the option and immediately exercise to make arbitrage profits.
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4 Call Property: Result #3 (Result 3) An American call option can never be worth more than the underlying asset: S (0) C (0) . Proof If S (0) < C (0) , arbitrage opportunity opens up: Buy stock, sell call => positive cash flow at t=0. Future cash flow is positive: a) if call is exercised, deliver stock and receive strike; b) otherwise, you own stock.
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5 Results 1, 2, and 3 (combined)
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6 Call Property: Result #4 (Result 4) For a stock with no-dividends, the minimum value of a European option is zero or S (0) - KB (0, T ) , whichever is greater: c (0) Max{0, S (0) - KB (0, T )} . Proof European option is a limited liability asset. So, c (0) 0 . (see next slide)
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7 Call Property: Result #4 (cont’d) Proof (cont’d) Consider 2 investment strategies: If Payoff to Strategy 1 Payoff to Strategy 2 (always) Then, Cost of Strategy 1 Cost of Strategy 2 Strategy 1 (Date 0) Buy a European call with strike K at a cost of c (0).
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This note was uploaded on 09/28/2008 for the course NBA 6730 taught by Professor Janosi,tibor during the Spring '06 term at Cornell.

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673_12_Options__2_ - SIMPLE ARBITRAGE RELATIONSHIPS FOR...

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