Imagine trading stocks, futures or options without the assistance of market makers. The result would be many orders unfilled along with large jumps in prices as buyers and sellers try to agree on acceptable market values. Thus, market makers are a vital part of trading, dependably taking risks and committing capital for the benefit of all.
The tools that market makers use to provide liquidity are powerful pricing mechanisms. The rest of us can use them to improve our own options trades or establish profitable spreads between strike prices at the same expiration date. Here, we’ll offer up some analysis that suggests ways to accomplish these objectives.
Market prices for futures and equity options typically are based on variants of the Black/Scholes theoretical pricing model that originated in 1973. These models permitted the growth in computerized option trading that began on the Chicago Board Options Exchange and continues today with massive quantities of electronic trading.
Individual benefit
Because of the smooth price surface presented by the current options market, individual traders have relatively little power to influence prices and generally must accept what is given by the theoretical price models in use by financial institutions and the market makers who bridge over gaps related to low trading volume.
However, there is an advantage built into the system that benefits the average options trader. The closely organized pricing of options allows anyone in the market to compute formulas that describe and predict options prices in two ways: First by showing what the option price should be at each strike price given the current underlying asset price, and second by predicting option prices over short time periods given changes in the underlying.
"September crude oil" (below) shows how tightly priced the options for September crude oil are on June 20, 2011. The analytical model is the non-theoretical LLP counterpart of the options market’s theoretical pricing and is available as a free Excel worksheet download here.
Over the span of 16 strike prices for September crude oil, the largest variation from the predicted price is approximately 0.02% of one option point, or $20 at $1,000 per option point. Only two variations are larger than 1% of the option premium. The chart in "September crude oil" presents the market price and predicted price at each strike price. The close fit between the two series of prices is shown by the regression-predicted price falling on top of the market price at each strike price.
The main advantage of the LLP analysis is that it doesn’t matter what form the institutional theoretical options pricing models take as long as the regression formula can analyze and predict market prices accurately based on current data. Arbitrage in the options market keeps prices at every strike close to a theoretically correct value. However — as shown in the table — there remains a small amount of slack in the system. In the case of September crude oil on June 20, the differences between market and predicted prices extend from plus $14.68 to minus $24.61.
Variation trading
Because the option valuation models used by financial institutions generate prices that are slightly different from those computed by the LLP formula, it is possible to observe short-term movements of differences between the predicted and actual market prices. The results show that the variations between predicted and actual market prices fall into patterns that have individual characteristics related to specific options and stocks. Examples for corn and crude oil are shown in "Pricing variations" (below).
Prices observed at approximately 5 p.m. on several days indicate variations from the predicted option price curves for September 2011 corn and crude oil futures contracts. On the sample days, corn variations from predicted prices are maintained between plus and minus $3 for 16 strike prices between $6.50 and $7.60. The small differences do not leave much space for a trader to spread price changes between strike prices. Consistency of differences between predicted and actual prices for corn calls suggests an automated trading rule by the market makers: "Keep the price variations between plus and minus $3 of the theoretical price."
More leeway for spread trades is shown in the crude oil variation chart, with price differences from predicted values extending from plus $30 to minus $12. Crude oil futures variations illustrate three possible areas of pricing:
- When strike prices are high relative to the underlying, there is lower trading volume and greater potential for market makers to determine prices within a narrow range around predicted values
- As strike prices are lower compared to the underlying, trading volume increases and there is increased variability around predicted prices, and
- When the underlying price increases toward equality with the strike price, the option pricing model tends to over-price the options and larger negative variations are observed.
"Calling on Apple" (below) lists September 2011 Apple Inc. call options. It analyzes strike prices from $340 to $420 on June 29, 2011 when the stock’s price is $334.04. Dollar variations from predicted values extend from plus $21 to minus $18, a range that would appear to leave room for spreads between several strike prices.
For options spreads, the slope or delta value at each strike price is required information because the slope indicates the expected price change in an option’s price given a change in the underlying. For example, the slopes shown for Apple strike prices of $360 and $370 are 0.304 and 0.212, respectively. A spread trade involving the sale of the $360 strike at a $640 premium theoretically would be matched with a purchase of 0.304/ 0.212, or 1.43 calls at the $370 strike.
Differences from the predicted price curve for September Apple calls on June 28 and 29 suggested that the long 370/360 call spread (long 370, short 360 call) could be a profitable trade. The price variation chart in "Calling on Apple" illustrates the area of lower-volume trades from the $420 strike to $370, at which the underlying stock price at $334.04 is 90% of the strike price. For higher strikes, the general market may be hesitant to trade out-of-the-money calls, permitting market makers to complete the needed pricing by staying close to theoretical models that are close to the LLP price curve.
Results from the Apple spread trade are known the following day, when on June 30 the option premiums change from $640 to $630 for the $360 strike, and from $380 to $415 for the $370 strike price. The $45 net gain does not include the extra income that would result from equalizing the two slopes.
When out-of-the-money options are priced in a narrow range around the predicted price curve — as they are on "November orange juice" (below) — benchmark in-the-money prices may be found by holding the predictive formula constant and computing an option price for each additional strike price, given the current underlying futures market price. For the days shown on "November orange juice," strike prices above $2.00 are out-of-the-money and in this upper range prices are controlled by market-makers and vary within plus and minus $5 of the predicted price. Conversely, variations of in-the-money calls are as large as plus $20 and minus $15.
Success of trading based on variations from predicted option prices depends on several factors, including the dollar amount of variation, dependability of prices to return to expected values, and cost of trading compared to the variations in price movements. Experience with options on specific futures or stocks should indicate which strike prices present more favorable trading opportunities. Increased knowledge of market maker tendencies related to price variations from option price curves also should aid in trading — whether using the variations to enhance straight buy and sell orders, or estimating possible profits from spreads between strike prices.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.
