So, How Often Do We Win?

Before we make any decision about whether to help ourselves to a chunk of the optimists’ capital, we’ve a little bit more work to do. We naturally want to learn what our pricing model has to say about the probability of success if we write WOOM August unleaded calls at this time. Table 6.2 is our usual incremental analysis of the expectation for writing the HUQ 92.00-strike call options, expiring on July 26.The SV of HUQ is a measurable number, but it reflects the recent past.

The deltas and the IVs of its call options, as ever, represent the current sentiment of all the market participants regarding the future price of HUQ. Evidently,sentiment is relatively modest at this moment, because the IV of the HUQ options has ranged from 33.2% to 55.1% over the past six months and tonight’s IVs are down toward the low end of this range, at 38.0%.

Oddly, even given the lowish call IVs (we prefer to write options with relatively higher ones, per their recent 6-month range of volatility) and considering the theoretical possibility of severe supply disruption due to wars or related occurrences, we should have a high degree of confidence in this trade. The non-seasonal tendency of this market at this time is solidly on our side, as indicated by Table 6.1, and we’ve also enlisted in our cause our favorite ally, time.

When a trader buys a short-dated WOOM option, he not only must be correct in his view about the direction of the market, he must be correct P.D.Q., and he has taken much the short end of the odds, in this case roughly 93-to-7 against. Do you want to trade along with the option buyer in such a situation? Very likely not, I’d wager. Each day that passes without some amount of market movement in his favor is another nail in his coffin, and we who have sold him this option find our trading capital increasing merely by courtesy of the passage of time.

A very painless process,I assure you.When we write short-dated options, we have a useful measure for approximating our potential rate of dollar gain. This measure is theta, the rate of decay per day of the time premium remaining in an option. Other considerations being equal or roughly so, theta increases steadily for near-themoney options toward the end of an option’s life.

Theta’s rate of daily increase actually accelerates going into these last few weeks, if the market remains fairly close to the option’s striking price. When the option moves or stays WOOM as it nears expiration, theta becomes more or less irrelevant—there’s little time premium left to decay. For those of us who write options,especially short-dated WOOM options, theta is easily the best friend we have other than the price of the underlying asset moving smartly away from the striking price of the option we’re writing.

All the numbers generated by our pricing model are approximations, as we’ve seen, and we must keep in mind three other things. First, the probability of the success of our trade will change daily, as the market moves up and down. Second, and this point cannot be overemphasized, any computations using the lognormal model to measure expectation and/or success/ failure apply only to the whole term of the trade, only if we sit until the expiration of the options.

Third, the numbers in Table 6.1 do not consider the amount of loss we can incur if HUQ moves outrageously higher. This is, again, why we must perform the incremental analysis of expectation as shown in Table 6.2. To skip this step would be at minimum careless and self-deceiving, and we would be plainly stupid for putting our capital at risk by simply ignoring potentially useful information . . . creating in effect a sort of voluntary knowledge risk.The first and second points are related.

The typical lognormal model treats a trade as something to be examined in one big chunk; it says nothing at all about what may happen during the term of the trade. If we wanted to analyze a trade thoroughly, we would perform an analysis similar to our preceding incremental analysis for each day remaining in the trade and compute what amounts to a cumulative sum of each day’s expectation.

Doing such an analysis is quite possible (such an analysis is the heart of the Cox-Ross-Rubenstein and Whaley quadratic models, for instance), but the analysis is somewhat involved and is, in my view, better suited and more useful to institutional traders. We can—and we will—put and keep profitability on our side without such an extensive analysis.