Options definition and payoffs 2 factors affecting

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Options: definition and payoffs 2. Factors affecting option prices 3. Put-Call parity for European options 4. Trading strategies involving options: 1. Synthetic forward 2. Synthetic Stock 3. Stock/Options Combinations 4. Spreads Fin330 36
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Creating a Synthetic Stock Fin330 37 t=0 t=T (A) Buy Call + Sell Put + Invest e rT K (B) Buy a share Since the two portfolios have the same payoffs at T , they must cost the same at time 0 ! Cost at time 0 : Portfolio A: Portfolio B: Therefore, we must have c – p + Ke -rT = S 0 . Again, the put-call parity holds.
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Creating Synthetic Stock Fin330 38 t=0 t=T (A) Buy Call + Sell Put + Invest e -rT K - c + p -e -rT K S T - K + K (B) Buy a share -S 0 S T Since the two portfolios have the same payoffs at T , they must cost the same at time 0 ! Cost at time 0 : Portfolio A: c – p + Ke -rT ; Portfolio B: S 0 . Therefore, we must have c – p + Ke -rT = S 0 . Again, the put-call parity holds.
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Outline 1. Options: definition and payoffs 2. Factors affecting option prices 3. Put-Call parity for European options 4. Trading strategies involving options: 1. Synthetic forward 2. Synthetic Stock 3. Stock/Options Combinations 4. Spreads Fin330 39
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Positions in an Option & the Underlying 40 Profit S T K Profit S T K Profit S T K Profit S T K (a) Covered call (b) (c) Protective put (d) l Covered Call and Protective Put Long stock Short call Long stock Short stock Short stock Long call Short put Long put
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Outline 1. Options: definition and payoffs 2. Factors affecting option prices 3. Put-Call parity for European options 4. Trading strategies involving options: 1. Synthetic forward 2. Synthetic Stock 3. Stock/Options Combinations 4. Spreads Fin330 41
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Butterfly Spread A butterfly spread can be created, for example , by buying one call with strike price K 1 , selling two calls with strike price K 2 , and buying one call with strike price K 3 , where K 1 < K 2 < K 3 and K 2 = (K 1 + K 3 )/2 . Long K 1 call Short K 2 call Short K 2 call (1) (1) Long K 3 call Long butterfly Payoffs as a function of S T K 2 K 1 K 3 K 2 K 1 K 3 K 2 K 1 K 3 K 2 K 1 K 3 K 2 K 1 K 3 K 2 K 1 K 3 K 2 K 1 K 3 + + + = =
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Butterfly Spread A butterfly spread can be created, for example, by buying one call with strike price K 1 , writing two calls with strike price K 2 , and buying one call with strike price K 3 , where K 1 < K 2 < K 3 and K 2 = (K 1 + K 3 )/2 . Long K 1 call Short K 2 call Short K 2 call (1) (1) Long K 3 call Long butterfly K 2 K 1 K 3 K 2 K 1 K 3 K 2 K 1 K 3 K 2 K 1 K 3 K 2 K 1 K 3 K 2 K 1 K 3 K 2 K 1 K 3 + + + = = Why would you use this strategy? Payoffs as a function of S T
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