Why Are OTM Verticals So Cheap?

Key Concepts

• Options Pricing Models (Black-Scholes, Binomial): Mathematical models used to determine the theoretical price of an option, based on factors like stock price, strike price, time to expiration, volatility, and interest rates.
• Strike Space vs. Price Space: Options are fundamentally based on strike prices and probabilities, not directly on stock prices. Price is an output of a model, not an input.
• Delta, Gamma: Greek letters representing the rate of change of an option's price with respect to changes in the underlying asset's price (Delta) and the rate of change of Delta (Gamma). Gamma reflects the accelerating change in Delta as the underlying price moves.
• Put-Call Parity: A relationship defining the equivalence between a call option, a put option, the underlying asset, and a risk-free bond.
• Information Value of Options: Options derive their value from the information they provide about the potential future price of the underlying asset, not just from the potential profit.
• Synthetic Positions: Creating equivalent positions using combinations of options (e.g., a synthetic long stock position).
• Probability & Statistical Compression: Understanding how the probability of an option being in-the-money changes over time, and how this impacts its value.
• Binomial Tree: A visual representation of possible price movements of an underlying asset over time, used to model option pricing.

Understanding Options: Beyond Price – A Deep Dive into Information and Probability

This session of Market Rebellion’s “Coach’s Corner” with Bill Johnson and Stu focuses on a common misperception among options traders: the belief that out-of-the-money (OTM) vertical spreads are cheap simply because of their low price. The core argument presented is that focusing solely on price is a fundamental error; options trading is about understanding information and probability, not just finding a low cost.

I. The Illusion of Price

Many traders are drawn to OTM vertical spreads because they appear to offer a favorable risk-reward ratio – a small initial cost for a potentially larger profit. The typical reasoning is, “I can spend $1 to make $4.” However, Johnson and Stu emphasize that this is a superficial view. They highlight that options don’t “live in price space” but rather in “strike space.”

This means that the price of an option is an output of a pricing model (like Black-Scholes), not an input. The model takes factors like stock price, exercise price, time to expiration, volatility, and interest rates to calculate the theoretical option price. Traders mistakenly work backward, searching for the cheapest price without understanding the underlying dynamics.

II. The Role of Pricing Models & Inputs

The discussion acknowledges the existence of numerous options pricing models, all with minor variations. However, the fundamental principle remains the same: these models are based on inputs, and the price is the output. The models are interchangeable; leaving out one input will result in that input being calculated by the model.

This reinforces the idea that price is a consequence of the underlying factors, not a primary driver of value. The mystique surrounding options and market makers is largely unfounded, as the process is fundamentally logical and understandable.

III. Information as Value: The Cup Game Analogy

To illustrate this concept, Johnson and Stu use a compelling analogy: 50 cups, one containing a $50 bill. The fair value of a bet to turn over a cup is $1, reflecting a 1/50 chance of winning $50.

Crucially, as cups are turned over and revealed to be empty, the value of the remaining bets increases. This isn’t because the stock price changed, but because information has been gained. The probability of winning has increased, even though the potential payout remains the same.

This illustrates the concepts of Delta (the change in option value with a change in the underlying asset’s price) and Gamma (the rate of change of Delta). The initial cup flips represent minimal changes in Delta, but as more cups are eliminated, Delta increases significantly, especially as the end approaches. This accelerating change is Gamma.

IV. Time Decay & Information Revelation

The speakers emphasize that time doesn’t inherently make an option safer. Instead, time allows for more information to be revealed. The analogy of a roulette wheel is used to demonstrate this: casinos don’t extend the spin time because it would reduce the anticipation and the information gained with each rotation.

They contrast this with the common misconception that more time equates to safety. They argue that rolling an option out in time simply resets the information clock, returning the trader to a state of lower knowledge.

V. The Binomial Tree & Probability Compression

A binomial tree model is introduced to visually represent how probabilities change over time. Each branch represents a possible price movement. As time passes and branches are eliminated (revealing where the stock isn’t), the probability of the remaining outcomes increases.

This leads to the concept of statistical compression: the probability distribution becomes narrower as time passes, and the option’s value changes accordingly. The key takeaway is that options value is derived from the reduction of uncertainty, not just the potential for profit.

VI. Synthetics & Put-Call Parity

The discussion delves into the concept of synthetic positions, specifically how a call spread and a put spread can be combined to create a risk-free position (a “box spread”). This demonstrates that the price of the call spread is not arbitrary but is linked to the price of the corresponding put spread through put-call parity.

The cheapness of the OTM call spread is explained by the fact that the corresponding put spread is being sold, reflecting a belief that the stock is more likely to move upwards than downwards.

VII. The Miami Workshop Preview

Johnson and Stu promote their upcoming workshop in Miami (January 29th & 30th), promising a deep dive into these concepts from academic, retail, and professional market maker perspectives. They claim the workshop will reveal information rarely encountered elsewhere, covering topics like shelling points, Nash equilibriums, and limit order book dynamics.

VIII. The Core Message: Beyond Risk-Reward Ratios

The central message is that traders should move beyond simplistic risk-reward calculations and focus on understanding the underlying information dynamics of options. Buying an OTM vertical spread for $1 to potentially make $4 isn’t a good deal simply because of the ratio; it’s a good deal if the trader understands why it’s priced that way and has a well-informed view of the probability distribution of the underlying asset.

In conclusion, this session emphasizes that successful options trading requires a shift in perspective – from focusing on price to understanding information, probability, and the underlying mechanics of options pricing models. The speakers advocate for a more nuanced approach, urging traders to recognize that options are not simply bets on price movement but rather tools for managing risk and capitalizing on informed views of future market probabilities.