Applying the concept: Rational people think at the margin.

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5. Some people find options expensive and use more complex structures to reduce the cost. For example, consider buying a call with a strike of $55 and selling a call with a strike of $60. a. What is the cost of establishing this combined position? b. What is the payoff of the combined position if the market price goes to $60? c. What is the payoff of the combined position if the market price goes to $100?

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Chapter 1, Problem 5PA

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Applying the concept: Rational people think at the margin.

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5. Some people find options expensive and use more complex structures to reduce the cost. For example, consider buying a call with a strike of $55 and selling a call with a strike of $60. a. What is the cost of establishing this combined position? b. What is the payoff of the combined position if the market price goes to $60? c. What is the payoff of the combined position if the market price goes to $100?

3. An investor has $1,000 to invest. They believe the price of the underlier will increase to $60 within one year. a. How many shares of stock could they buy with the $1,000 at the current price of $50, and how much would they make if the share price increased to $60? b. How many calls with a strike of $55 could they buy for the same $1,000, and how much would they make if the share price increased to $60? c. How much would they make (or lose) from the stock and from the calls if the share price declined to $40? 4. What is the premium on a call with a strike of $0.01? Why is the premium so close to the $50 share price?

1. We want to examine the comparative statics of the Black Scholes model. Complete the following table using the Excel model from class or another of your choice. Provide the call premium and the put premium for each scenario. Underlier Risk-free Scenario price rate Volatility Time to expiration Strike Call premium Put premium Baseline $50 5% 25% 1 year $55 Higher strike $50 5% 25% 1 year $60 Higher volatility $50 5% 40% 1 year $55 Higher risk free $50 8% 25% 1 year $55 More time $50 5% 25% 2 years $55 2. Look at the baseline scenario. a. What is the probability that the call is exercised in the baseline scenario? b. What is the probability that the put is exercised? c. Explain why the probabilities sum to 1.