### Question details

1. An investor sells a European call option with strike price of E and maturity T and
\$ 30.00

1. An investor sells a European call option with strike price of E and maturity T  and buys a put with the same strike price and maturity on the same underlying asset.

• A. Create a payoff table of this position at expiration
• B. Show this payoff on a graph

2. The price of a non-dividend paying stock is \$19 and the price of a three-month European call option on the stock with a strike price of \$20 is \$1. The risk-free rate is 4% per annum. What is the price of a three-month European put option with a strike price of \$20?

3. The price of a European call which expires in 6 months and has a strike price of \$30 is \$2.00. The underlying stock's price is \$29 and a dividend of \$.50 is expected in 2 months and in 5 months. The term structure is flat with all risk free interest rates being 10%. What is the price of a European put option that expires in 6 months and has a strike price of \$30? (Hint adjust the put call parity for dividends).

4. Three put options on a stock have the same expiration date and an exercise price of \$55, \$60, and \$65. The market prices are \$3, \$5, and \$8, respectively. Explain how a butterfly spread could be created. Construct a table showing the profit from the strategy. For what range of stock prices would the butterfly spread lead to a loss?

5. The price of a stock is \$40. The price of a one-year European put option on the stock with a strike price of \$30 is quoted as \$7 and the price of a one-year European call option on the stock with a strike price of \$50 is quoted as \$5. Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put options.

• A. Construct a payoff and profit/loss table
• B. Draw a diagram illustrating how the investor’s payoff and profit or loss at expiation.

### Solutions

Available solutions
• 1. An investor sells a European call option with strike price of E and maturity T and
\$30.00

1.

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