4_Options_sol.pdf

# Payoffs and profits at expiration long a put k s if k

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Payoffs and Profits at Expiration: Long a Put < = K S if 0 K S if S K Payoff T T T Payoff , Profit S T K Fin330 13

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Profit = max(K-S T ,0) – FV(p) Payoffs and Profits at Expiration: Long a Put < = K S if 0 K S if S K Payoff T T T Payoff , Profit S T K -pe rT K – pe rT Fin330 14
Profit = -max(K-S T ,0) + FV(p) Payoffs and Profits at Expiration: Short a Put < = K S if 0 K S if ) S K ( Payoff T T T Payoff , Profit S T Fin330 15

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Profit = -max(K-S T ,0) + FV(p) Payoffs and Profits at Expiration: Short a Put < = K S if 0 K S if ) S K ( Payoff T T T Payoff , Profit S T K Fin330 16
Profit = -max(K-S T ,0) + FV(P 0 ) Payoffs and Profits at Expiration: Short a Put < = K S if 0 K S if ) S K ( Payoff T T T Payoff , Profit S T K pe rT – K pe rT Fin330 17

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Terminology: “Moneyness” l In the money Call: S > K Put: S < K – Exercise of the option would be profitable (Positive payoff if exercised now) l Out of the money Call: S < K Put: S > K – Exercise of the option would not be profitable (Negative payoff if exercised now) l At the money S = K – Zero payoff if exercised now Fin330 18
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 19

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Payoffs at maturity, maximum losses and gains Position Payoff at Maturity Maximum Loss Maximum Gain Long Forward S T – F 0 – F 0 Unlimited Short Forward F 0 – S T Unlimited F 0 Long Call Max{ S T – K , 0} – FV(c) – FV(c) Unlimited Short Call – Max{ S T – K , 0} + FV(c) Unlimited FV(c) Long Put Short Put l Assumption: S T = [0, Unlimited] Fin330 20
Factors affecting option prices l K : Strike price l S 0 : The current stock price l σ : Volatility of the asset l T : Time to Expiration l r : Risk-free interest rate l D : dividends l Style: American vs. European 21 Fin330

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Factors affecting option prices 22 Fin330 Variable European Call European Put American Call American Put Stock price, S 0 + + Strike price, K + + Maturity, T ? ? + + Volatility, σ + + + + Risk-free rate, r + + Dividends, D + + + indicates that an increase in the variable causes the option price to increase . – indicates that an increase in the variable causes the option price to decrease . ? indicates that the relationship is uncertain.
Options in the Interactive Brokers Fin330 23 Options on S&P 500 stock index

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Options in the Interactive Brokers Fin330 24
Options in the Interactive Brokers Fin330 25

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Options in the Interactive Brokers Fin330 26
Outline 1. Options: definition and payoffs 2. Factors affecting option prices 3.

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• Spring '16
• Chang
• Options, Strike price, put-call parity

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