Understanding Option Price Behavior

by Keith Schap   ISSUE 209 | NOV 2003

Option pricing differs from futures pricing. Option prices move in a ratio to the movement of futures prices. The markets themselves provide the information you need to know what that ratio will be.

Consider the corn market. Futures traders must ultimately take into account how much of last year's crop remains, how big this year's crop might be, and what kind of demand is in the market. As the growing season unfolds, every weather event has the potential to affect futures prices. Ultimately, even technical indicators must respond to these drivers.

A Glance at the Pricing Models

All of this matters in the pricing of options, but option prices start with the pricing models, the best known of which is the Black-Scholes model. Fortunately, you can start trading options without going too deeply into the complexities of the models, but it is useful to understand that option prices depend on five factors:

• the underlying futures price
• the strike price
• time to expiration
• the interest rate
• the volatility

The first four of these factors are essentially givens. You can find the relevant futures price on a quote screen. While a variety of strike prices are available, the one you trade is your choice. Your quote service might give days to option expiration, but you can also get this from your broker, or figure it out from the option expiration dates you can find on the exchange Web site (for Chicago Board of Trade contracts, visit www.cbot.com). The relevant interest rate is usually a short-term financing rate close to the Fed Funds rate. Volatility is more complex, but that is a topic for another time.

The Nature of Option Price Changes

Back to the fact that options move in a ratio to futures price moves. When you pull up a page of option quotes, you will see a format that more or less resembles that of Exhibit 1. You will see other data as well, but for now, consider only four details: the underlying futures price, the strike prices listed, the option prices, and a value called delta.

Exhibit 1: December call options on corn futures
December Corn: 226 1/4
Days to Expiration: 57
Strike Price	Option Price	Delta
220	10 1/2	0.65
230	6 1/8	0.44
240	3 3/8	0.27

For the moment, consider Exhibit 2, which shows what will happen to the prices of these three calls if the futures price rises 3 3/4 cents a bushel to 230 after one day has passed and if nothing else changes.

Exhibit 2: Comparing option and futures price changes
	Starting Prices	Ending Prices	Price Change	Options Change/ Futures Change
Corn futures	226 1/4	230	3 3/4
Call strikes
220	10 1/2	13	2 1/2	0.6667
230	6 1/8	7 5/8	1 5/8	0.4333
240	3 3/8	4 3/8	1	0.2667

Notice that the price of the 220 December call gained 2 1/2 cents a bushel and that this is very close to 67 percent of the futures price change. The price change of the 230 call is close to 43 percent of the futures change, and that of the 240 call is right at 27 percent of the futures price change. These percentages very nearly match the values in the delta column of Exhibit 1.

Delta Defined

Based on this, you should be able to see that the delta of an option defines the ratio that relates the option price change to the futures price change. Indeed, the Greek letter delta is a fairly universal symbol of change. By definition, the delta of an option whose strike price is the same as the futures price (an at-the-money option) will be 0.50. Also by definition, the delta of the underlying futures is 1.00.

In the case of calls, deltas range from 0 to 1. Put deltas range from 0 to -1. If the call strike price is higher than the futures price, as are the 250 and 260 strikes in Exhibit 1, they are out of the money. The farther out of the money, the smaller the delta. A call strike price that is lower than the futures price is in the money. The farther in the money, the larger the delta, and the more this option will trade like the futures.

In the case of puts, strike prices higher than the futures price are in the money, and the deltas grow progressively larger the farther above the futures price the strike price ranges. Put strike prices that are lower than the futures price are out of the money, and the farther they range away from the money, the smaller the delta.

Delta Can Help You Decide Which Option to Buy

Suppose you are thinking about buying a call on December corn futures and have narrowed your choice to either the 230 December call or the 240 December call. Keep in mind that this gives you the right to buy a futures contract at the strike price. In practice, you will be more likely to offset your call. If you initially bought the 230 call, you offset by selling the 230 call.

A natural reaction might be to say you’d rather pay 3 3/8 cents per bushel than 6 1/8 cents per bushel. We all like a discount. But it’s important to ask what you might get for what you pay—whether the extra 2 3/4 cents per bushel might be worth paying.

Consider what would happen to these option prices if the only pricing factors that change are the passage of seven days and a futures price increase to 235 cents per bushel. Exhibit 3 shows the results.

Exibit 3: Comparing option and futures price changes after 7 days
	Starting Prices	Ending Prices	Price Change	Options Change/ Futures Change
Corn futures	226 1/4	235	8 3/4
Call strikes
230	6 1/8	10 1/4	4 1/8	0.4714
240	3 3/8	5 7/8	2 1/2	0.2857

Notice that the 230 December call netted 4 1/8 cents per bushel while the 240 call netted 2 1/2 cents per bushel. Veteran options traders are fond of saying that, with options, you get what you pay for. Also, note that these price changes are approximately what the deltas said they would be.

For more information about options trading, visit www.cbot.com or contact your broker.

Keith Schap is a Senior Writer in Business Development at the Chicago Board of Trade.

Laura Oatney is editor of LindForum. She can be reached at editor@Lind-Waldock.com.

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