For all parts of the problem, suppose the stock price today is So = $100 and...

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For all parts of the problem, suppose the stock price today is So = $100 and suppose that at all horizons the zero rate is r = 0, Part (c) can be done independently of (a) and (b). Consider the following portfolio of three European options: • Long one put option with strike price $100. • Long one call option with strike price $100. • Short one call option with strike price $150, Each option has a time to expiration of 1 year. (a) (5 points) Draw the payoff graph for this option portfolio. Make sure yourz-axis spans $0 to $200 (plot the payoff for ST € 10, 200]). (b) (10 points) Find the price or best price bounds you can for this portfolio. That is, either find the price, or find the best lower and upper bounds for the value of this portfolio that you can using no-arbitrage arguments. Now, suppose you instead considered the following portfolio: • Long one share of the stock. • Long one call option with strike price $110. Short one put option with strike price $110. Short one call option with strike price $120. • Long one put option with strike price $120. All options have a time to expiration of 1 year, and all options are European. (c) (10 points) Find the price or best price bounds you can for this portfolio based on no- arbitrage. Use any method or shortcuts you like, but make sure you show your reasoning. Hint: the calls and puts come in pairs at the same strike prices. For all parts of the problem, suppose the stock price today is So = $100 and suppose that at all horizons the zero rate is r = 0, Part (c) can be done independently of (a) and (b). Consider the following portfolio of three European options: • Long one put option with strike price $100. • Long one call option with strike price $100. • Short one call option with strike price $150, Each option has a time to expiration of 1 year. (a) (5 points) Draw the payoff graph for this option portfolio. Make sure yourz-axis spans $0 to $200 (plot the payoff for ST € 10, 200]). (b) (10 points) Find the price or best price bounds you can for this portfolio. That is, either find the price, or find the best lower and upper bounds for the value of this portfolio that you can using no-arbitrage arguments. Now, suppose you instead considered the following portfolio: • Long one share of the stock. • Long one call option with strike price $110. Short one put option with strike price $110. Short one call option with strike price $120. • Long one put option with strike price $120. All options have a time to expiration of 1 year, and all options are European. (c) (10 points) Find the price or best price bounds you can for this portfolio based on no- arbitrage. Use any method or shortcuts you like, but make sure you show your reasoning. Hint: the calls and puts come in pairs at the same strike prices.

Answer rating: 100% (QA)

a The payoff graph for the given option portfolio will be For ST 100 the payoff is 100 ST since we a... View the full answer