# On the market.

In our last installment, we explored the potential benefits a
roaster might obtain by writing combinations to hedge anticipated
summertime inventory turnover.

Readers might recall that we suggested stringing together a series of combinations (March, May, July) rather than selling a July combination from the outset.

We asked James J. Bowe, senior vice president for market development and planning at the Coffee, Sugar & Cocoa Exchange, Inc. (CSCE) to explain the reasons behind selling three shorter-term combinations instead of one long-term combination.

Essentially, an option writer is likely to earn more premium by writing a series of short-term combinations versus one longer-term combination. Why? Because the mathematics that define option pricing cause time value to erode more quickly as an option nears its expiration date - a phenomenon known as time value decay.

An option's premium is largely comprised of two components: intrinsic value and time value. Intrinsic value measures the dollars and cents difference between the option strike price and the current futures price. An option with intrinsic value has a strike price making it profitable to exercise and is said to be "in-the-money". An option not profitable to exercise is "out-of-the-money". "At-the-money" options have strike prices at or very near futures prices. In general, an option's premium is at least equal to its intrinsic value (the amount by which it is "in-the-money").

Time value is the sum of money buyers are willing to pay for an option over and above any intrinsic value the option may presently have. Time value reflects a buyer's anticipation that, at some point prior to expiration, a change in the futures price will result in an increase in the option's value. Premiums for at- and out-of-the money options almost entirely reflect their time value.

An option's time value is affected by the time remaining before expiration, market volatility and short-term interest rates. As an option moves closer to expiration, its time value decreases - time decay. Time decay does not follow a straight line, however. It accelerates as expiration nears.

The underlying theory for time value decay can be easily understood in terms of insurance policies. The longer the term of any insurance policy, the more it costs - a function of the probability that adverse events will occur. However, the cost of adding one day of insurance one year away is much less than adding one day to a policy with only five days remaining. The same holds true for option premiums. The longer the life of an option, the greater the probability that it will become profitable to exercise- and the larger the premium. Option writers command more premium for taking that risk, but the proportional price increase in premium is far larger the nearer the option is to expiration.

Indeed, an option's decay over time does not adhere to what common sense might dictate. To wit: while a 60-day at-the-money option might cost 4.00 [cents]/lb., a 30-day option with the same strike price does not cost 2.00 [cents]/lb.. Instead, picture the decay along the lines of "one day of time value". Removing 1 day from 240-day life of an option does not dramatically reduce the probability that the option will at some point in time be profitable to exercise. On the other hand, removing 1 day from a 30-day option has a proportionally more significant impact on that probability. Accordingly, as expiration nears, premiums fall precipitously.

Consider the following: assume on March 6, December 1992 coffee futures trade at 80 [cents]/lb. and an at-the-money December 80 call for 5.02 [cents]/lb. By using an option pricing model and assuming that July futures remain constant at 80 [cents]/lb. and volatility remains the same, we can approximate the option's time value:

As the table indicates, the option loses 51% of its time value in the 60 days prior to expiration, while it takes 180 days to lose the first 49%.

What does this mean for the option seller? Some have said that time decay is the best friend of all short option strategies. Theoretically, the option seller benefits by selling a shorter-term option because he is able to receive relatively more premium at a point where time decay begins to accelerate. Using our hypothetical example as a basis, an option writer can earn 10.32 [cents]/lb. for writing four 60-day options (2.58 x 4 = 10.32) as compared to 5.02 [cents]/lb. for one 240 day option. The option writer is, in effect, receiving 51% of the premium for 25% of the time remaining before expiration.

Readers might recall that we suggested stringing together a series of combinations (March, May, July) rather than selling a July combination from the outset.

We asked James J. Bowe, senior vice president for market development and planning at the Coffee, Sugar & Cocoa Exchange, Inc. (CSCE) to explain the reasons behind selling three shorter-term combinations instead of one long-term combination.

Essentially, an option writer is likely to earn more premium by writing a series of short-term combinations versus one longer-term combination. Why? Because the mathematics that define option pricing cause time value to erode more quickly as an option nears its expiration date - a phenomenon known as time value decay.

An option's premium is largely comprised of two components: intrinsic value and time value. Intrinsic value measures the dollars and cents difference between the option strike price and the current futures price. An option with intrinsic value has a strike price making it profitable to exercise and is said to be "in-the-money". An option not profitable to exercise is "out-of-the-money". "At-the-money" options have strike prices at or very near futures prices. In general, an option's premium is at least equal to its intrinsic value (the amount by which it is "in-the-money").

Time value is the sum of money buyers are willing to pay for an option over and above any intrinsic value the option may presently have. Time value reflects a buyer's anticipation that, at some point prior to expiration, a change in the futures price will result in an increase in the option's value. Premiums for at- and out-of-the money options almost entirely reflect their time value.

An option's time value is affected by the time remaining before expiration, market volatility and short-term interest rates. As an option moves closer to expiration, its time value decreases - time decay. Time decay does not follow a straight line, however. It accelerates as expiration nears.

The underlying theory for time value decay can be easily understood in terms of insurance policies. The longer the term of any insurance policy, the more it costs - a function of the probability that adverse events will occur. However, the cost of adding one day of insurance one year away is much less than adding one day to a policy with only five days remaining. The same holds true for option premiums. The longer the life of an option, the greater the probability that it will become profitable to exercise- and the larger the premium. Option writers command more premium for taking that risk, but the proportional price increase in premium is far larger the nearer the option is to expiration.

Indeed, an option's decay over time does not adhere to what common sense might dictate. To wit: while a 60-day at-the-money option might cost 4.00 [cents]/lb., a 30-day option with the same strike price does not cost 2.00 [cents]/lb.. Instead, picture the decay along the lines of "one day of time value". Removing 1 day from 240-day life of an option does not dramatically reduce the probability that the option will at some point in time be profitable to exercise. On the other hand, removing 1 day from a 30-day option has a proportionally more significant impact on that probability. Accordingly, as expiration nears, premiums fall precipitously.

Consider the following: assume on March 6, December 1992 coffee futures trade at 80 [cents]/lb. and an at-the-money December 80 call for 5.02 [cents]/lb. By using an option pricing model and assuming that July futures remain constant at 80 [cents]/lb. and volatility remains the same, we can approximate the option's time value:

As the table indicates, the option loses 51% of its time value in the 60 days prior to expiration, while it takes 180 days to lose the first 49%.

What does this mean for the option seller? Some have said that time decay is the best friend of all short option strategies. Theoretically, the option seller benefits by selling a shorter-term option because he is able to receive relatively more premium at a point where time decay begins to accelerate. Using our hypothetical example as a basis, an option writer can earn 10.32 [cents]/lb. for writing four 60-day options (2.58 x 4 = 10.32) as compared to 5.02 [cents]/lb. for one 240 day option. The option writer is, in effect, receiving 51% of the premium for 25% of the time remaining before expiration.

Days Before Time Value as % of Expiration Value 240-day Premium 240 5.02 100% 210 4.72 94% 180 4.39 87% 150 4.03 80% 120 3.63 72% 90 3.16 63% 60 2.58 51% 30 1.85 37% 0 0.00 0%

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Title Annotation: | examining economic aspects involved in exercising options on coffee |
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Publication: | Tea & Coffee Trade Journal |

Date: | Jul 1, 1992 |

Words: | 806 |

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