## Solving Various Problems

**Problem 1**

A bank has sold a product that offers investors the total return (excluding dividends) on the OBX index over a one year period. The return is capped at 20%. If the index goes down the original investment of the investor is returned. What option position is equivalent to the product?

**Problem 2**

Suppose that a European put option to sell a share for $60 costs $4 and is held until maturity.

a) Under what circumstances will the seller of the option (i. e. the party with the short position) make a profit?

b) Under what circumstances will the option be exercised?

Problem 3

Option traders often refer to “straddles” and “butterflies.” Here is an example of each:

Straddle Buy call with exercise price of $100 and simultaneously buy put with exercise price of $100. Butterfly Simultaneously buy one call with exercise price of $100, sell two calls with exercise price of

$110, and buy one call with exercise price of $120. 1. Draw position diagrams for the straddle and butterfly, showing the payoffs from the investor’s net position.

**Problem 4**

A call option is at expiration with an exercise price of 105 on a stock trading for 100. What is the value of the option?

**Problem 5**

A stock is selling for $31. There is a call option on the stock with an exercise price of $27. What is an appropriate minimum value of the call option today?

**Problem 6**

The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.2. The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 1.4. The correlation between the futures price changes and the spot price changes is 0.7. It is now October 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15. The producer wants to use the December live-cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle. What strategy should the beef producer follow?

**Question 7**

It is now June. A company knows that it will sell 5,000 barrels of crude oil in September. It uses the October CME Group futures contract to hedge the price it will receive. Each contract is on 1,000 barrels of ‘‘light sweet crude.’’ What position should it take? What price risks is it still exposed to after taking the position?

**Question 8**

A company wishes to hedge its exposure to a new fuel whose price changes have a 0.6 correlation with gasoline futures price changes. The company will lose $1 million for each 1 cent increase in the price per gallon of the new fuel over the next three months. The new fuel’s price change has a standard deviation that is 50% greater than price changes in gasoline futures prices. If gasoline futures are used to hedge the exposure what should the hedge ratio be? What is the company’s exposure measured in gallons of the new fuel? What position measured in gallons should the company take in gasoline futures? How many gasoline futures contracts should be traded? Each futures contract is on 42,000 gallons.

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