Derivative Securities

Question 1

This strategy contains buying one call with a relatively low strike price (A), selling two calls with medium price (B), and buying one call with high strike price (C). Assume strike price is S.

Payoff table of long butterfly spread

[pic 1]

When the spot price is lower than the strike price A, there is no profit from this strategy, no matter investors take long call option or short call option. Investors who take long call option would have profit, when spot price is greater than strike price A , by the amount of . When investors take short call option, they would get loss as long as spot price is bigger than strike price B (), and the loss would be S-B. When investors take long call option with strike price C, they would make a profit so long as spot price is greater than strike price C (), the profit equals to the value of (). [pic 2][pic 3][pic 4][pic 5][pic 6]

Thus, we get the total payoff table. When spot price falls into the range between A and B, the total payoff is . When spot price falls into the range between B and C, the total payoff is . When spot price is higher than strike price C, the total payoff is.[pic 7][pic 8][pic 9]

Let’s assume intervals among 0 to A, A to B, B to C are equal.

Payoff Diagram:[pic 10]

Investors adopt the butterfly spread strategy when they are certain that prices will fluctuate significantly and want to limit their downside risk. This strategy limits both the upside potential and downside risk.

Question 2

Characteristics of the future contract:

1. Future contract is traded on a regulated and highly controlled market. And its size and expiration time is standardized.

2. Liquidity and flexibility. Hedge position may be entered and exited when needed.

3. Delivery is realized several days after maturity and can be settled daily.

4. Futures require a margin to be posted at the initiation.

5. Clearinghouse is the buyer for every seller and the seller for every buyer, in order to eliminate the risk of default, and allows traders to reverse their position at a future date.

Margin account for a long position:

Note: The future contract on gold of the CME Group specifies that the trading units is 100 troy ounces and the price is quoted per troy ounce.

• Monday (time 0)

The long position entered and the future settlement price is equal to . However, there is no cash changes and no interest earned at the end of Monday. So the margin account is the same as the initial margin i.e. 4500.[pic 12]