From the May 01, 2009 issue of Futures Magazine • Subscribe!

The put and call comfort zone

Market prices for options are rigidly structured by computer models. An option trader may have opinions on the proper buying or selling price, but ultimately the price will be placed close to an option price curve that is the result of time-tested mathematical formulas based on the probabilities of future price variations. For this reason, it is difficult in the option market to get away from the crowd; however, having lots of company may also lend a sense of comfort to trading that is usually considered to have substantial risk.

In “Building a better strangle” (March 2009), it was shown that the market consensus for underlying prices at expiration dates is expressed by breakeven prices for delta-neutral hedge trades. These are the prices that will result in zero profit or loss for a trader who sells the underlying futures short, while buying the number of calls determined by the delta value (the slope of the option price curve at a given strike price).

“Calls on July crude oil futures” shows closing option prices on March 20, 2009, when the underlying price is $55.20. The predicted option prices show that the LLP spreadsheet (available for free download at generates results that are close to current market prices. Crude oil futures are based on 1,000 barrels of oil, so that a call price of 4.64, for example, equals a premium of $4,640.

A delta-neutral trade using the $60 strike would suggest buying 1/0.449 or approximately 2.227 calls to cover the short sale of one July future at 55.20. At expiration, if the underlying is between $72.345 and $44.875, the trade will be profitable before transaction costs. An ending futures price at either breakeven will result in zero profit or loss for the delta-neutral trade.

The pricing of all options is related to the probability of underlying prices at expiration falling between the estimated upper and lower breakeven points.

A strangle trade is the sale of a naked call and a naked put where both are sufficiently far out-of-the-money that the trader does not expect the expiration price of the futures contract to go beyond either strike price. Continuing with the $60 strike for July 2009 crude oil futures puts and calls, the delta-neutral breakeven prices can be used to determine the strike prices for selling options.

The trader finds that the call at a strike price of $80 may be sold at 1.04, or $1,040, while a put at the $38 strike may be sold at 1.06, or $1,060. These price combinations are located on, “Option price snapshot”.


Because both put and call strike prices for the strangle trade are further out of the money than those recommended by the breakeven price spread, the trader believes this should make the short option sales have an even lower risk. If July crude oil futures expire between $80 and $38, the trader will keep both premiums for a total of $2,100, less transaction costs. In the event that futures prices exceeded the breakeven range in either direction, risk management trades would be needed, leading to potential losses.

Sale of the put and call options at approximately equal premiums would make it possible, in the strangle example, to compute futures prices that permit the trader to exit the strangle position with approximately zero profit or loss if the July futures price rises or falls at an uncomfortable rate. At any time during the trade, a 200% range can be computed by using an updated underlying price and revised option price curve.

At the initial futures price of $55.20 for July crude oil, the $38 put has a price of 1.06, or $1,060. At the same time the $80 call has a price of $1,040. By entering different futures prices in the LLP model, a 200% price range may be found by trial and error. By this method, it is determined that at a futures price of $61.33 the call should be $2,080, and at a futures price of $46.80 the put should be $2,120. The initial 200% range of $14.53 between put and call prices is considerably less than the strangle range of $42, but the trader knows that the short option trade may be exited with only a small loss with a purchase at 200% approximately equal to the total premiums received on the original option sales.


New put and call prices based on revised futures prices are continuously affected by changes in the option price curves. The 200% price range calculated above implies that the price curve has not changed while the futures price increases or decreases. While it is true that option price curves are stable over short periods, through hours or days, it is always safer to recalculate the pricing equation using new data. Initial estimates of option price changes related to movements in underlying futures prices are also at risk due to the increased variability in delta as the time premiums decay with shorter periods to expiration dates. Variations in delta are shown on “Percent change in delta”.

For shorter times to expiration, the percent changes in delta from one strike price to the next are much larger for the shorter-term calls. For example, between strikes of $65 to $70, delta for the May expiry changes more than 30% compared to approximately 15% for July and August. This means that although the higher strike price and shorter time to expiration seem to have reduced risk for the seller of a $65 or $70 call on May futures, the initial low delta will increase with a rising futures price and possibly decrease the seller’s advantage of decaying time premium. In Greek terms, this is related to gamma risk.

The shift in delta values for different times to expiration may be viewed on “Crude oil futures calls and puts” (page 38). These charts show increasing time premiums from May through August. The gap between the curves accelerates as the expiration date grows nearer, and the shorter-term curves have noticeably sharper changes in delta slopes for equal changes in underlying price movements.

On March 20, there were only 27 days to expiration for the May crude oil calls and the time premium percentage of 7.37% on that date (a Friday before the loss of two more days over the weekend) reflected the market’s perceived high volatility for crude oil futures. Expressing the accelerating decay in time value, premium percentages for August, July, June and May calls on March 20 were 12.93%, 11.90%, 9.93% and 7.37%, respectively.


Although puts and calls are derivatives based on futures and equities, upper and lower breakeven prices computed for options should be useful to traders in the underlying assets as well as those in the options market. By assessing future probabilities of price changes for futures contracts and stocks, the options market is performing a service for the futures and equities markets by showing what a risk-sensitive set of hedgers and speculators believe to be the spread in underlying prices at given future dates.

On any option trade in which the strike price is at some distance from the current underlying asset price, trading volume is likely to be small and price changes sporadic. Bid/ask spreads may exist for some time until buyers and sellers agree on a price. In this case, a reasonable bid or ask price can be generated by the LLP option pricing model.

An idea of how well the market consensus performs in its forecasts of expiration prices can be judged over the late spring and summer months of 2009 by reviewing “Option price snapshot” (page 37) as the May, June, July and August expiration dates occur. As pointed out in “Building a better strangle,” the forecasts are not predictions of future prices but are probability-based estimates of price variations. Breakeven spreads show how far from the current underlying price the future prices are likely to stray, based on the market’s view of past and present price variations. Applying the breakeven price analysis to the June 2009 S&P 500 stock index futures permits a comparison with the results for June crude oil futures shown above.

On March 24, 2009, the June S&P 500 futures price was 805.40. At the strike price of 800 the upper and lower breakeven prices at expiration were 949.60 and 701.30. A trader who decides to sell a call and put beyond the breakeven range and also to make the premiums on the sales approximately equal might sell the 1,000 call at a price of 5.10, or $1,275, and a 535 put at 5.00, or $1,250.

The unequal distances from the current futures price of 805.4 are related to the larger time premium for June S&P futures puts, which is 7.80% as opposed to 7.47% for June calls. If the S&P 500 at expiration in June is between 1,000 and 535, the trader would keep the total premiums of $2,525, less transaction costs. The rate of return over 87 days to expiration would depend on the amount of margin required to maintain the short option position, assuming that the index stayed within the breakeven range so that no further cash outflows were required.

Paul Cretien is an investment analyst and financial case writer. E-mail him at

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