For example, if an out-of-the-money options contract is chosen for hedging programs, protection will be low in cost but not as extensive as the protection provided by programs using in- or at-the-money options. In order to be exercised, out-of-the-money options require the greatest difference in the price of the underlying future, resulting in less risk to the options seller. The distance between the strike price of the options contract and the value of the underlying futures contract can be viewed as the equivalent of an insurance deductible. In return for the higher premium paid for in- and at-the-money options, the deductible is reduced and protection is immediate beyond the cost of the options contracts. In fact, an in-the-money options contract will behave similarly to the underlying futures contract.

Each of the strategies presented here contains a brief description and a profit/loss profile. The profit/loss profile of individual options strategies is examined with respect to changes in futures prices. Maximum profit and maximum loss at expiration are indicated on each chart. Profit/loss measures the change in value of the entire position implicit in each strategy, including those cases in which multiple options and futures positions are examined. Net debits, credits and deltas reflect the entire position.

The delta of an options contract can also be considered as a hedge ratio. Deltas of deep in-the-money options are approximately equal to one; deltas of at-the-money options are 0.5, and deltas of deep out-of-the-money options approach zero. The delta can also be thought of as a measure of the probability of an options contract finishing in the money on the expiration date.

Options premiums were estimated using the Black-Scholes options pricing model. All strategies are based on NYMEX Division light, sweet, crude oil options and the COMEX Division gold options.

The crude oil options contract is priced in dollars per barrel, 1,000 barrels per contract; the gold options contract is priced in dollars per troy ounce, 100 ounces per contract. For these examples, the following assumptions were made:

The crude oil futures price is $20 per barrel when the position is established; the gold futures price is $260 per ounce.

Crude oil volatility is 30%. Gold volatility is 13%.

The interest rate is 5%.

The options contract expires in 90 days from the time the position is established. The time to expiration affects options premiums.

In each example, debits are funds paid out by the buyer of the position and credits are funds received by the writer of the position.

Potential strategies include:

Long At-the-Money Call
Short Out-of-the-Money Call
Covered Call
Ratio Write
Long Out-of-the-Money Call
Long At-the-Money Put
Short Out-of-the-Money Put
Short Covered Put
Bull Call Spread
Bear Call Spread
Bear Put Spread
Bull Put Spread
Long At-the-Money Straddle
Long Strangle
Short At-the-Money Straddle
Short Strangle
Call Ratio Backspread
Put Ratio Backspread
Synthetic Long Put
Synthetic Long Call
Synthetic Short Futures
Synthetic Long Futures
Fence

*Information Courtesy of