Option values depend primarily on time and volatility —enough time for prices to vary and sufficient price volatility to make time worthwhile. Options on metal futures reflect these valuation principles. On a relative basis, the most valuable options are not necessarily those connected to the highest priced underlying assets, but given equal time to expiration, are those having the greatest volatility perceived by the market.
The price chart for a single option with one expiration date, such as “Silver, December 2008” includes both time and volatility, although their effects are invisible until the option is compared with others on a relative basis. The silver December 2008 option prices on June 27, 2009, show how the price curve is shaped, with the slope increasing as the underlying futures contract moves higher in relation to the strike price.
On June 27, 2008, silver December 2008 futures prices are trading at $17.856 per oz. At the strike price of 18, the December 2008 option price is $1.467. The slope of the price curve at that point is 0.487. That means that a long position of 1/0.487 or 2.053 December 2008 silver calls held against a short sale of the underlying futures contract should result in a net gain of zero at expiration, if the ending silver price is either $14.846 (the lower breakeven price) or $20.998 (the upper breakeven price). The option price, 1.487, is the point above $17.856 on a straight line between $20.998 on the horizontal axis and the point on the intrinsic value line that is directly above $14.846. The line connecting the two breakeven points has a slope (the delta value) of 0.487.
To compare relative option valuations, futures and option prices are divided by strike prices. By this method, charts for silver, gold, copper and aluminum options are shown for several expiration dates. Silver and gold are shown for December 2008, 2009 and 2010, while copper and aluminum are shown for December 2008 and 2009.
The charts in “Relative values” illustrate increasing values of options with longer times to expiry and, conversely, decreasing values for those with shorter times remaining. The gold and silver charts show that the distance between December 2009 and December 2010 price curves is smaller than the distance between December 2008 and December 2009. The reason for this difference is the accelerated decline in time value as option expiration dates grow nearer. December 2008 call prices have fallen away from the longer expiration values.
TIME SPREAD STRATEGIES
The strategy of selling options on futures that have near-term expirations is shown in “Price changes.”
A call sold on December 2008 aluminum futures on June 27, strike price 1.25, would have received a premium of 0.2185¢ per lb., or $96.14 for the 44,000 lb. contract. By July 18, the December 2008 call had fallen to 0.1655¢, or $72.82. On “Price changes” it is noted that on July 18, the call price is equal to intrinsic value of 0.1655 (the futures price of 1.4155 less the strike price). Over this short period, the time value for the 1.25 call evaporated as the price curve moved down.
Another example of the strategy that takes advantage of comparative time values involves calls on silver December 2008 futures. On June 27, a silver December 2008 call, strike price 17, at $1.957 ($9,785) is sold and a December 2009 call at the same strike price at $3.315 ($16,575) is bought. On July 21, with silver futures having increased in price, the silver December 2008 call is $2.292 ($11,460), and December 2009 is $3.879 ($19,395).
The price changes in the silver time spread, plus $2,820 for December 2009 less $1,675 for December 2008, yield a net gain of $1,145, mainly attributable to the December 2008 call price curve falling more rapidly than the December 2009 curve as time values fell for both expiration dates. From June 27 to July 21, the time premium for December 2008 silver (defined as the height of the option price curve at the strike price as a percentage of the strike price) decreased from 8.58% to 7.86%, while the time premium for the December 2009 fell from15.45% to 15.07%. The time spread may be improved by using a moderate ratio such as 1.25 of shorter-to-longer term options.
Other information provided on “Price changes” includes the futures and calls gains and losses — aluminum and copper with falling prices, and gold and silver with increasing prices. Delta ratios for gold and silver calls are larger on July 18, as their call prices follow increased futures prices up the option price curve. On the other hand, the new delta for the 3.800 strike copper call is lower than the June 27 delta slope as the futures and call price dropped by 5.53% and 36.73%. Aluminum is shown with a slope equal to 1.00 because each of the strike prices sampled on June 27 produced an option price equal to its intrinsic value (zero time value) on July 18.
VOLATILITY ISSUES
Although the four metal option charts measure the effects of time on option prices, they do not show the impact of volatilities of the underlying futures. “Volatilities 2008” compares the four metals’ option price curves on a relative basis with underlying and option prices divided by strike prices.
The volatility comparison shows that silver and copper options share the highest relative valuations, while gold is a distant third and aluminum is the lowest in terms of the market’s perceived volatility (and expected time value) of the underlying futures prices.
With volatilities computed for metal futures having the same expiration date, it is possible to create pure volatility spreads. For example, suppose that the option price curve for December 2008 copper calls fell while the price curve for silver stayed at a higher level. Assuming no change in the underlying fundamentals for the two metals, the deviation from normal volatilities could result in a profitable spread trade when the price curves return to their normal relationship.
FOUR METALS
“Metals compared” lists price and valuation features for silver, gold, copper and aluminum call options on June 27, 2008. Volatility measures include the time premium percentage at each strike, the breakeven price spread as a percent of the underlying price, and the standard deviation and variance of underlying prices implied by the Black-Scholes pricing model.
On the “Metals compared” table, volatility measures reflect the conclusion from the “Volatilities 2008” chart in that valuations according to perceived volatilities run in this order: silver, copper, gold and aluminum.
It should be noted that these measures are valid on a given day, and shifts in market prices and trends are likely to change the computed results and the ranking order over time.
Hedging metal futures presents choices involving the use of futures vs. options on futures and selling options to gain premium when volatility appears to be higher than expected. Given a computed delta measure lower than 1.00 for a call, holding the inverse ratio of calls should result in a loss somewhat lower than the change in the underlying when the futures price falls, and a gain that is less than the increase in the underlying price when the futures price rises.
Aluminum options on June 27 had option price curves with slopes close to 1.00 for lower strikes. Such a pattern would have an advantage with call options at the upper end of the curve participating in rising futures prices while having downside protection with lower slopes as the futures price declines. However, this strategy depends on option price curves staying high enough so there is still time value when the futures price declines. Aluminum put options share this benefit on the opposite side, with deltas close to 1.00 at the lower futures prices and downside protection when futures prices rise as long as time values stay positive.
Time values do not necessarily move down continuously. Given a change in supply and demand variables in the metals market, a shift in perceptions regarding aluminum, for example, might cause option price curves to re-inflate until the passage of time once again brings premiums lower. With option pricing models, revised price curves may be simulated to see the potential profits or losses from hedging or speculation.
OTHER MARKETS
It is possible to compare any of the metals, copper for example, with futures options in other markets. “Markets compared” shows price curves for December 2008 futures calls on July 21, 2008, for copper, corn, the euro currency and crude oil.
On “Markets compared,” it is obvious that crude oil call options are at the top in terms of the market’s perceived time value. This is not surprising in view of the current price variations for oil. Copper and corn call price curves are comparable in terms of time value and volatility, while euro options show the lowest time value of the four call price curves.
Watching the metals group for temporary shifts in time and volatility spreads may be easier than observing options on futures having seasonality such as grains or other fundamental variables affecting price changes. Supply and demand factors may cause variations in metal pricing as well, and these should be considered in any proposed spreads.
Paul Cretien, CFA, is an investment analyst and financial case writer. E-mail him at PaulDCretien@aol.com.
