The Saturday Spread: Leveraging the Markov Principle to Identify Undervalued Prospects (PANW, NTES, DKS)

Understanding Option Pricing and Market Inefficiencies

On any given trading day, it's common for Wall Street to incorrectly value the premiums of publicly traded options. The widely used Black-Scholes model, especially for debit transactions, assumes that stock prices move randomly with unchanging volatility and no influence from past movements. According to this model, the fair value of a call option is calculated as the expected discounted payoff if the stock finishes above the strike price at expiration.

While Black-Scholes offers a straightforward benchmark for pricing, it often lacks real-world context. Before anyone rushes to defend the model, let’s break down the main reasons behind this critique:

• Stock prices do not move in a purely random fashion; patterns and clusters in price action are observable.
• Volatility is dynamic, expanding and contracting in response to various market events.
• Stocks exhibit memory, meaning previous movements can influence future behavior.

The concept of market memory, in particular, challenges the Markov property, which states that only the current state matters for predicting the future. Black-Scholes, however, ignores both recent and historical behavioral states, focusing solely on the present price and volatility.

This omission doesn’t necessarily make Black-Scholes inaccurate, but it can lead to less-than-optimal forecasts. Since the model doesn’t account for context, it defines risk mainly by how far the price is from the current spot. This is similar to assuming a three-point shot is always harder than a layup, which isn’t always true—sometimes, a layup is more difficult if heavily defended, while an open three-pointer may be easier. The Markov property, in contrast, incorporates context to refine probability estimates.

Case Study: Palo Alto Networks (PANW)

Let’s examine Palo Alto Networks (PANW), which was trading at $187.68 at the time of analysis. The Black-Scholes-based Expected Move calculator projects that, by the February 20 options expiration, PANW could fall anywhere between $171.31 and $204.01—a symmetrical range representing an 8.71% spread. This highlights the model’s tendency to overlook market context.

If we ignore any underlying trends, PANW’s price should theoretically fall within this range. However, recent performance tells a different story: PANW has only posted gains in three of the past ten weeks, indicating a downward trend and a bearish sentiment heading into the weekend.

Despite this, historical data suggests that under similar 3-7-D conditions, PANW often rebounds. Over the next five weeks, the probability distribution peaks between $196 and $200. According to Barchart Premier, a 195/200 bull call spread expiring February 20 could be attractive. If PANW closes above $200 at expiration, the maximum return exceeds 156%.

Case Study: NetEase (NTES)

NetEase (NTES), a leading Chinese internet technology company, was priced at $137.98 at the time of review. The Expected Move calculator estimates a price range of $127.52 to $148.43 for the February 20 options expiration. This projection is based solely on implied volatility and time, without considering broader market dynamics.

Looking at recent trends, NTES has also only seen three positive weeks out of the last ten, suggesting a bearish phase. Ordinarily, this 3-7-D pattern would be a warning sign for investors. However, historical patterns reveal that NTES often rallies after such signals.

Applying a hierarchical Markov analysis, the probability density for NTES over the next five weeks is likely to peak near $155. This makes the 145/155 bull call spread expiring February 20 an appealing choice. If NTES surpasses the $155 strike at expiration, the maximum potential return is 212.5%.

Case Study: Dick’s Sporting Goods (DKS)

Although sporting goods retailers aren’t typically top picks for traders, Dick’s Sporting Goods (DKS) may be an exception. DKS was trading at $215.32 at the time of analysis. The Expected Move calculator predicts a price range of $198.07 to $232.57 by February 20, again providing a basic estimate without deeper context.

To refine this outlook, we apply the Markov property. DKS is currently exhibiting a 3-7-D sequence, which usually signals a bearish trend. However, historical data indicates that DKS often moves higher in similar scenarios, providing a bullish opportunity.

Based on previous occurrences of the 3-7-D pattern, the probability density is expected to peak around $230. For those seeking optimal speculative trades, the 220/230 bull call spread expiring February 20 appears promising. If DKS closes above $230 at expiration, the maximum return would be 150%.