It is inevitable that on any given day, Wall Street will be mispricing the option premium on a publicly traded security. Specifically, the standard Black-Scholes model effectively states the following for debit-based transactions: Assuming the stock moves randomly with constant volatility and no memory, the fair price of a call option is the expected discounted benefit of holding the stock above the strike price at expiration.
As such, the model provides a clean template as a reference point but without much contextual support. Before I am inundated with emails from angry pedants willing to defend the honor of Black-Scholes, let’s really consider the trifecta of why I made the above statement. We know that:
Stock market movements are not random (as we observe autocorrelation and clustered behavior).
Volatility is not constant (as it typically expands and contracts depending on the underlying catalysts).
Actions have memory (since what happened before affects what may happen later).
In fact, the last point about market memory is one of the philosophical foundations of the Markov property. Under this framework, the future state of a system is determined solely by its current state. In other words, according to Markovian reasoning, the fulcrum of transitional logic centers on the immediate behavioral state. According to Black-Scholes, behavioral states are not considered, neither in the immediate framework nor in the deep past.
To be clear, this lack of calculation does not make Wall Street’s standard pricing mechanism incorrect, but it does make the projections generated potentially suboptimal. This is because according to Black-Scholes, since the state context is not considered, risk is largely defined in proportion to the distance of the location. That’s like saying a 3-pointer is harder to make than a layup, which is usually a reasonable statement.
However, in real game conditions, the path to the layup could be heavily defended. In that case, the open player outside the arc may have the easier shot, even though the distance is greater. That’s basically the Markov property. It is a second-order analysis that derives probabilities from context rather than model assumption.
Let’s get to work. Palo Alto Networks (PANW) has a spot price of $187.68 at the time of writing. According to the Black-Scholes-based expected movement calculator, for the options chain expiring on February 20, PANW stock would be expected to gain between $171.31 and $204.01. Since this range represents a perfectly symmetrical high-low spread of 8.71%, one can see the potentially suboptimal nature of the price dispersion.
Basically, if we assume no contextual bias, then PANW stocks should be dispersed across the projected spectrum. However, what we are saying is that PANW is definitely biased. Heading into the weekend, the stock posted just three weeks of gains out of the last 10 weeks, leading to an overall downward slope. Therefore, Palo Alto enters the weekend on a downbeat note.
However, history shows that under 3-7-D conditions, PANW stock tends to rise reflexively. Over the next five weeks, we can expect the probability density to peak between $196 and $200. Using data provided by Premier Bar Chartthe 195/200 bullish spread expiring on February 20 is attractive. If PANW stock exceeds the $200 strike at expiration, the maximum payout exceeds 156%.
NetEase (NTES), a China-based internet technology company, has a spot price of $137.98 at the time of writing. Using the expected move calculator, the market expects a spread between $127.52 and $148.43 for the February 20 options chain. This is a first-order dispersion based on implied volatility and days to expiration, but does not take into account the market context.
And what is that context? In the past 10 weeks, NTES stock has only recorded three weeks of gains, leading to a downward slope. Normally, this 3-7-D sequence would have negative implications for investors as it implies that the bears are in complete control. However, when this quantitative signal flashes, the above data shows that NTES tends to resolve to the upside.
Using the Markov property under a hierarchical lens, we can calculate that over the next five weeks, the probability density will likely peak around $155. Therefore, I really like the 145/155 bullish spread expiring on February 20. If NTES shares rose during the strike back to expiration, the maximum payout would be 212.5%.
Sporting goods retailers don’t often offer great business ideas these days, but that could change for Dick’s Sporting Goods (DKS). At the moment, DKS shares have a spot price of $215.32. According to the expected movement calculator, the market anticipates a spread from $198.07 to $232.57 for the February 20 options chain. As we said earlier, this evaluation provides a clean model without second-order context.
To get a better idea of ​​where DKS stock may land on the dispersion over the next five weeks, we would apply the Markov property. Currently, DKS is displaying a 3-7-D sequence, which naturally has negative implications. However, in this context, security tends to be resolved higher, and that is what we are going to rely on.
Using earlier analogues of the 3-7-D sequence, we can calculate that the probability density would likely peak at $230. From an optimal speculation standpoint, the 220/230 bullish spread expiring on February 20 would seem to make the most sense. If DKS shares rise during the strike back to expiration, the maximum payout would be 150%.
On the date of publication, Josh Enomoto had no (directly or indirectly) positions in any of the securities mentioned in this article. All information and data in this article are for informational purposes only. This article was originally published on Barchart.com
