Pricing Options and the Greeks - Intro to Options #2

Pricing Options and the Greeks - Intro to Options #2

Unfamiliar with options? Read part 1 of our options education series for a foundation in the basics and historical examples.

The oracles of Greek legend were known for their powers of prophecy, offering glimpses into the future. Option Greeks can't grant you the ability to see the future of the market, but they can equip you to make informed decisions and navigate the options market with greater confidence.

Option Greeks have little to do with myth and everything to do with math. Gaining their name from the Greek letters used to represent them, the Greeks are a powerful set of metrics that can help you make more informed decisions in your trading strategy.

The Option Greeks act like financial gauges, measuring how sensitive an option's price is to various factors that can influence the underlying asset. The Greeks reveal insights into the market that are only accessible to those that can read them. Mastering the Greeks can give a trader a pulse on the market, making it easier to position themselves to benefit from shifting market conditions.

Understanding Pricing is Key to Options Trading

In any trade, the perceived value of an asset can differ from its current market value. This difference, along with the time frame for the market to recognize that perceived value, is what traders look to exploit. They seek opportunities where the market has mispriced an asset, believing the market will eventually adjust and reflect the asset's true worth within their desired time frame. 

Unlike buying an asset, an option you purchase is a contract that has an expiration date indicating the exact moment it can no longer be exercised and has no value. This makes having an exit strategy for your trade even more important. (Don't worry. Scholes Protocol will settle all options at expiry based on their intrinsic value at expiry meaning you won't accidentally miss out on that In-The-Money (ITM) option trade.)

So, how exactly do options traders profit within this time frame? 

To achieve this, traders essentially forecast both the direction and the timing of the underlying asset's price movement. There are two ways an option trader can profit, but it's important to remember that any profit must exceed the premium paid for the option contract:

  • Exercising the option contract: This captures the intrinsic value, which is the difference between the underlying asset's price and the strike price (for call options) or vice versa (for put options). However, the profit needs to be larger than the premium paid for the option to be worthwhile. Only In-The-Money (ITM) options have an intrinsic value.
  • Selling the option contract itself at a profit: This relies on the time value, also known as extrinsic value. Here, the trader hopes to sell the option contract for a higher price than they paid for it, again factoring in the initial premium.

This additional layer of complexity introduces factors beyond just the underlying asset's price that influence the option's value, including implied volatility (IV).

Implied Volatility (IV) reflects the market's expectation of future price fluctuations in the underlying asset. However, unlike the underlying asset's price itself, which is a known quantity, IV is an estimate. It's a dynamic factor that can change rapidly based on market sentiment and upcoming events.

“Pricing In” Volatility

Market makers, also known as underwriters, write or sell option contracts. They set the price (premium) by considering factors like the underlying asset's price, time to expiration, and most importantly, implied volatility (IV). In other words, underwriters must set their premiums to account for (or "price in") the expected volatility.

Underwriters only profit from selling options at the right price. However, finding that “right price” requires accurately predicting IV. Higher IV translates to a higher premium because the underwriter is charging more for the increased chance of significant price movements. Conversely, lower IV results in a cheaper option as the underwriter anticipates less volatility.

Options Traders Capitalize on the Guesswork

Since market makers rely on accurate IV predictions for profitability, options traders can capitalize on potential mispricings. By analyzing both the underlying asset and implied volatility, traders can identify situations where the current market price of an option doesn't seem to reflect their own assessment.

Imagine a token's price has been steadily rising, but the options market shows low implied volatility (IV). A trader who expects a breakout leading to increased volatility might see this as a mispricing due to underestimating IV. By strategically buying call options, they could potentially profit if IV spikes and the price surges beyond the strike price before expiration.

Having unpacked implied volatility (IV), we can discuss another facet of options trading: the Greeks. Implied volatility acts as the foundation for the Greeks, shaping how options react to potential price swings in the underlying asset.

What are Option Greeks?

There are numerous metrics that are considered "Greeks" in options trading, but the four most important and widely used are Theta, Delta, Gamma, and Vega. While other Greeks exist, these four are the most critical tools for understanding and managing the risks and potential rewards associated with options trading.

Theta (Θ)

Theta measures the rate of decay in an option's price due to time passing (time decay). The value of an option is the combination of its intrinsic value and time value. The time value can be described as the amount an investor is willing to pay for an option above its intrinsic value. 

Even options that are Out-Of-The-Money (OTM) and have no current intrinsic value still have a time value because the option hasn’t expired yet and there is still a chance the market shifts in its favor. As options approach their expiration date, the potential for future price movements to increase the intrinsic value of the option (becoming In-The-Money) dwindles. This decline in potential translates to a decrease in the option's time value.

Key takeaway: Theta is important because it reminds you that options are decaying assets in terms of their time value. The closer they get to expiration, the less time value they hold, and the faster their price decays. This is especially true for options that are out-of-the-money (OTM) since they have no intrinsic value to begin with.

How Traders use Theta:

By understanding its impact on time value, traders can strategically choose expiration dates that align with their confidence level in the underlying asset's price movement.

  • Extended Time Horizons: When a trader is more certain of the direction of the price movement, but the timing remains unclear, options with longer expirations are preferred. This strategy minimizes the erosive effect of theta on time value, particularly for out-of-the-money (OTM) options that rely heavily on this component for their price.
  • Capitalizing on Short-Term Moves: Conversely, for traders with high conviction in a short-term price movement, options with shorter expiration dates can be advantageous. While theta decay will be more pronounced, the lower upfront cost of these options can be offset by a significant increase in intrinsic value if the price moves favorably within the shortened time frame.

Delta (Δ)

Delta (Δ) measures the rate of change in an option's price for every $1 change in the underlying asset's price. Think of it as a gauge for how much the option price will move in the same direction as the asset price. Delta ranges from -1 to +1. In other words, the +/- sign reflects whether you expect the option price to move in the same direction (positive delta) or opposite direction (negative delta) as the underlying asset price.

  • Delta closer to +1: This suggests the option price will move nearly dollar-for-dollar with the asset price, offering high initial correlation to price increases of the underlying asset but with limited upside potential compared to options with a lower delta. In other words, you're paying a higher premium for a favorable option position.
  • Delta closer to 0: This signifies the option price is less sensitive to the underlying asset's price movements and provides lower initial correlation to underlying asset price movements that increases rapidly as the option moves ITM.
  • Delta closer to -1: This indicates the option price will move in the opposite direction of the asset price, but with a nearly 1:1 ratio.

Key takeaway: Delta provides a valuable starting point for understanding how your option will react to price movements in the underlying asset. It helps you gauge the direction and magnitude of the option's price change based on the asset's movement. In some cases, buying a lower delta option can be more cost-effective for acquiring leverage later.

How traders use Delta:

  • Directional bets: Delta helps you choose options with a higher chance of profiting from your directional view. If you're bullish, buying calls with a delta closer to +1 offers high initial correlation to benefit from price increases of the underlying asset. Alternatively, you might purchase calls with a delta closer to 0 hoping to gain leverage at a cheaper upfront cost.
  • Hedging strategies: Delta is essential for constructing option spreads where you combine options with different Deltas to create a defined risk profile. Understanding Delta allows you to balance the price movements of different options within a spread.

Gamma (Γ)

Gamma (Γ) measures the rate of change of Delta, essentially telling you how quickly the Delta itself changes as the underlying asset price moves. Think of it as the acceleration or deceleration of the option's price movement relative to the underlying asset price. While Delta tells you how much the option price will move for a $1 change in the asset price, Gamma tells you how quickly that relationship between the two changes.

  • High Gamma: This suggests that Delta will change rapidly as the underlying price moves. This is often seen with at-the-money (ATM) options, where small price movements can significantly impact the option's sensitivity to further changes. High Gamma indicates the potential for quicker gains if the asset moves in your favor, but also faster losses if it moves against you.
  • Low Gamma: This indicates that Delta will change slowly as the underlying price moves. This is more common with deeply in-the-money (ITM) or deeply out-of-the-money (OTM) options, where price movements have a less pronounced effect on the option's sensitivity. Low Gamma suggests a more stable and predictable change in the option price relative to the asset price.

Key takeaway: Gamma helps you understand how the option's responsiveness to price movements (Delta) will change as the underlying asset price fluctuates. High Gamma indicates the potential for amplified gains or losses depending on the direction the asset price moves. Low Gamma suggests a more measured change in the option price.

How Traders use Gamma:

Risk management: Gamma adds another layer to understanding how your option will react to price movements. It goes beyond Delta's static measure of sensitivity and tells you how quickly that sensitivity changes. Options with high Gamma can be riskier due to the amplified price movements, so it's essential to have a solid risk management plan in place, especially when combined with higher delta for calls or puts.

Trading strategies: Gamma can be used strategically for some options trades, such as delta-neutral strategies where you aim to offset the Gamma of one option with the opposite Gamma of another option in a spread.

Vega (ν)

Vega (ν) measures the sensitivity of an option's price to changes in implied volatility (IV). Remember, implied volatility reflects the market's expectation of how much the underlying asset's price might fluctuate in the future. Vega helps you understand how much an option's price will change if this expectation of volatility itself increases or decreases.

  • Higher Vega: This indicates that the option's price is more sensitive to changes in implied volatility. Options with high Vega will experience larger price swings when the market's volatility expectations fluctuate. This can be beneficial if volatility increases significantly in your favor, but also risky if it moves against you.
  • Lower Vega: This suggests the option's price is less sensitive to changes in implied volatility. Options with low Vega will have smaller price movements even if implied volatility experiences shifts.

Key takeaway: Vega helps you gauge how much your option's price can be impacted by the market's changing expectations of future price movements (reflected by implied volatility). High Vega options offer the potential for amplified gains but also magnified losses due to volatility swings. Low Vega options provide a more stable price response to changes in implied volatility.

How Traders use Vega:

  • Volatility expectations: Consider Vega when choosing options if you have a strong opinion on whether implied volatility will increase or decrease. High Vega options can be beneficial if you expect volatility to rise significantly, but can hurt you if it falls.
  • Volatility hedging: Vega can be used in conjunction with other options or futures contracts to hedge your portfolio against unexpected changes in volatility.


The world of options trading may seem complex at first glance, but the Option Greeks serve as powerful tools to illuminate the path towards informed decisions. By understanding Delta, Theta, Gamma, and Vega, you gain valuable insights into how options react to various market movements. This knowledge empowers you to:

  • Gauge potential profits and losses: Analyze how your option's price will likely change based on underlying asset price movements (Delta), time decay (Theta), and changes in implied volatility (Vega).
  • Develop effective strategies: Utilize the Greeks to construct option spreads with balanced risk profiles (Delta) and potentially hedge your portfolio against unexpected changes in volatility (Vega).

Remember, the Greeks are not crystal balls. They provide a framework for analysis, but market conditions can be unpredictable. It's critical that you combine your understanding of the Greeks with sound risk management practices and ongoing market research.

Now that you speak Greek… Coming up next, we’ll dig deeper into options trading strategies and the relationship between options and perps.

Scholes Protocol aims to be the go-to platform for navigating the exciting world of on-chain options trading. Join the Scholes Community to be the first to hear updates when our public testnet is going live!

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