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On surface level, Norwegian Cruise Line Holdings Ltd. (NYSE:NCLH) appears to be a complete mess. Despite delivering what on paper would seem to be solid financial results, the cruise ship operator struggled to stave off travel-sector-related anxieties. As such, NCLH stock suffered a sharp drop of more than 15% during Tuesday's afternoon session. Still, the quantitative picture presents a hidden informational arbitrage that data-driven options traders can potentially exploit. Looking at the headline print, nothing would really suggest that NCLH stock deserves such a steep correction. Yes, third-quarter revenue of $2.9 billion missed analysts' consensus target of $3.02 billion. However, this tally represented a 5% year-over-year lift and was a record performance. Further, adjusted earnings per share of $1.20 beat the consensus target of $1.16, along with company guidance of $1.14. So, what caused the turmoil in NCLH stock? Likely, the culprit was EPS guidance for the fourth quarter, which was adjusted to 27 cents and thus below the 30-cent estimate. Unfortunately, management had to guide down profit expectations due to cost uncertainties and weakening consumer demand. Interestingly, in late August, I wrote about Norwegian, specifically drawing attention to its heavily accumulative quantitative structure. At the time of publication, NCLH stock had printed eight up weeks and two down weeks, with an overall upward slope, a sequence I abbreviated as 8-2-U. Primarily, the argument was that, based on past analogs, NCLH stock historically has failed to sustain such robust momentum. Subsequently, I worried that the security could correct — and it did just that. Sadly, the corrective pressure arrived much later than the data suggested it would, meaning that the underlying trading ideas failed. However, what I find encouraging is that, at the time of publication, I noted that NCLH stock could drop to $18.08 to $18.66 at the conclusion of the next 10 weeks. That would put it right around today. If you've ever wondered about the viability of the quantitative approach, this is it. I'm bringing the receipts as the kids like to say. No, I didn't get the specific trading idea accurately. But the overall trend was called with remarkable precision. Going The Other Way With NCLH Stock At the core, quantitative analysis is the empirical study of price behaviors and their statistical responses to various market stimuli. Foundationally, the quant approach gets its fuel from observations made by GARCH (Generalized Autoregressive Conditional Heteroskedasticity) studies, which describe the diffusional property of volatility as a clustered, non-linear phenomenon. Essentially, volatility does not occur in an orderly, independent manner but rather diffuses in relationship to prior volatile events. By logical inference, we can state that different market stimuli yield different market behaviors. If you think about it, this is Newtonian mechanics but adapted for the equities sector. Now, under normal or homeostatic conditions, the forward 10-week median returns of NCLH stock would be expected to form a distributional curve, with outcomes ranging from $18.50 to $19.60 (assuming an anchor price of $18.79). Further, price clustering would be expected to occur at around $18.90. However, we know through Norwegian's post-earnings meltdown that NCLH stock is not anywhere near a homeostatic state. Instead, it's in a heavily distributive state. Quantitatively, NCLH is structured in a 3-7-D sequence: three up weeks, seven down weeks, with an overall downward slope. Under this condition, we can expect an expansion of the forward 10-week risk tail to $18. However, the speculative opportunity is that the reward tail jumps to over $23. More importantly, price clustering would be expected to occur around $20. This is the heart of the informational arbitrage opportunity. At this juncture, bullish traders have the potential to profitability exploit a 5.82% positive delta between expected and conditionally realistic price densities. No one in the financial publication realm is talking about these density variances yet this is the crux of Bayesian inference models and decision-making protocols. My friends, this isn't merely an options-focused philosophy but rather a life lesson. In any circumstance involving the expenditure of limited resources, you must determine whether the benefits of expenditure outweigh the benefits of not committing said resources. The problem that I have with traditional methodologies — fundamental analysis, technical analysis, unusual options screeners, etc. — is that none of them highlight the discrepancy between expected and conditionally realistic outcomes. So, call me mean, call me angry — I'm the only one signaling you to these price density gaps that exist for every stock. A Tempting Trade Shines In The Spotlight With all that said, there's one trade that stands out like a bright flare in the night sky: the 19/21 bull call spread expiring Dec. 19. This transaction involves buying the $19 call and simultaneously selling the $21 call, for a net debit paid of $80 (the most that can be lost). Should NCLH stock rise through the second-leg strike ($21) at expiration, the maximum profit is $120, or a payout of 150%. Further, breakeven lands at $19.80. This should be a realistic target since the terminal median price on Dec. 19 is projected to reach higher than $20. What's really fascinating is that, according to calculations derived from the Black-Scholes-Merton (BSM) model, the probability of profit of NCLH reaching breakeven is only about 37%. Not to sound arrogant but I dispute this figure, which is where the informational arbitrage argument also centers. Because the terminal median is forecasted to be above $20, the conditional probability — based on the framework mentioned earlier — should be north of 50%. Of course, the criticism is that no one knows for sure which model will win out: the BSM model, my quant model or something else entirely. However, because I'm running my data on NCLH's actual price history — rather than a presumed reality based on implied volatility metrics — I trust my model more. Yes, it's a self-serving statement. But unlike so many others in the finpub industry, I'm showing you the receipts. The opinions and views expressed in this content are those of the individual author and do not necessarily reflect the views of Benzinga. Benzinga is not responsible for the accuracy or reliability of any information provided herein. This content is for informational purposes only and should not be misconstrued as investment advice or a recommendation to buy or sell any security. Readers are asked not to rely on the opinions or information herein, and encouraged to do their own due diligence before making investing decisions. Read More: Options Corner: Kimberly-Clark’s Implosion Offers An Unusual Informational Arbitrage Opportunity Image: Shutterstock