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# Derivative problems: Option Pricing

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1) Option pricing principles are now often used in corporate finance applications. It is common to look at equity in a corporation as an option. What type of option is equity similar to? Discuss what factors would affect the price of equity and in what direction based on this option pricing view.

2) Given recent events Yahoo options have become very popular. Answer remaining questions based on the following information regarding July 2008 (162 day) options.
Stock Price = \$29
Interest rate = 4%
X Call Put
25 1.20
30 2.04 2.85
35 6.10
a. Compute the value of the \$35 call based on put/call parity.
b. Verify that the \$30 call and put are selling at prices above their lower bounds.

3. The price of the \$25 call is \$4.30. Describe an arbitrage opportunity. Detail all your transactions and compute the minimum and maximum

Compute the breakeven points, maximum gain and maximum loss to the following positions:
a. A covered call with exercise price = \$30.
b. A bull spread: Long the put with X=\$35 and short the put with X=\$25
In a two-period pricing model (each period consists of 81 days) u = 1.16 and d = 83. Compute the value of an American put with exercise price = \$30.

4. Use the Black/Scholes model to price a put with X=\$30. (You can either use the equation for a put or calculate the value of a call and find the value of a put using put/call

5. You own 100 shares of Yahoo in your retirement account and would like to hedge against any loss in value (locking in the recent price increase). You want to use options to do so.
a. Based on the delta you calculated in number 6 what position should you take in the option market to hedge your position?
b. Subsequently, stock price decreases \$5. Compute your percentage gain or loss over the 162 day period on your total portfolio (stock and options

6. You own 100 shares of Yahoo in your retirement account and would like to hedge against any loss in value (locking in the recent price increase). You want to use options to do so.
a. Based on the delta you calculated in number 6 what position should you take in the option market to hedge your position?
b. Subsequently, stock price decreases \$5. Compute your percentage gain or loss over the 162 day period on your total portfolio (stock and options).