THE GREEKS EXPLAINED: A GUIDE TO OPTION SENSITIVITIES

Introduction to the Greeks

The "Greeks" are essential tools used in options trading to measure various risk dimensions and sensitivities of an options position. Named after Greek letters, they help traders and investors assess how different factors — such as changes in the price of the underlying asset, time decay, volatility, and interest rate shifts — can affect the price and profitability of options.

Each Greek quantifies the impact of a specific variable on the value of an options contract. Skilled options traders use them to make strategic decisions, manage risk, and construct complex positions that align with their market outlook. The primary Greeks — Delta, Gamma, Theta, Vega, and Rho — are foundational concepts in options theory and pricing models like Black-Scholes and Binomial models.

Understanding these risk sensitivities isn't just for professional traders; even retail investors benefit significantly by knowing how each component influences their portfolio's behaviour.

Why the Greeks Matter

• Risk Management: The Greeks help identify and neutralise various forms of risk in an options position.
• Strategy Design: Traders use the Greeks to tailor positions based on their expectations around price movements, time, and volatility.
• Hedging: Managing the Greeks allows for constructing hedged portfolios that neutralise directional or volatility exposure.
• Scenario Analysis: They help assess how an options position responds to hypothetical market conditions.

In this guide, we break down what each Greek measures in practical terms.

Understanding Delta in Options Trading

Delta (Δ) represents the sensitivity of an option’s price to a change in the price of its underlying asset. Specifically, Delta measures how much the price of an option is expected to move for every one-point change in the price of the underlying security, holding other factors constant.

Delta typically ranges between 0 and 1 for call options and 0 and -1 for put options.

Calculating and Interpreting Delta

• A call option with a Delta of 0.70 will gain approximately £0.70 if the underlying asset increases by £1.
• A put option with a Delta of -0.30 will decrease by about £0.30 for every £1 increase in the asset’s price, and vice versa.

Practical Uses of Delta

Traders often use Delta to understand directional exposure. For example, buying a call option with a high Delta mimics the behaviour of owning the underlying asset but with less capital at risk. Additionally, the Delta value also approximates the probability of the option finishing in-the-money at expiration.

• Hedging: Delta is pivotal in constructing Delta-neutral portfolios, where the position’s overall market risk is offset by balancing positive and negative Deltas.
• Portfolio Exposure: Delta informs options-based strategies like covered calls or protective puts.

Delta and Expiry

As expiration nears, Delta for in-the-money options tends to approach 1 (or -1 for puts), while out-of-the-money options approach 0. At-the-money options generally have a Delta near 0.50 for calls and -0.50 for puts.

Real Example

Suppose you hold a call option for a stock priced at £50 with a Delta of 0.6. If the stock price increases to £51, the option price (all else equal) should rise by about £0.60. If you own 10 contracts (each representing 100 shares), your profit from Delta sensitivity would be 10 × 100 × 0.60 = £600, prior to fees and spreads.

Gamma, Vega, and Time Decay Insights

While Delta measures immediate price sensitivity, other Greeks describe how that sensitivity changes, capture insights about volatility, and quantify the effect of time passage. Let’s explore three main Greeks that complement Delta: Gamma, Vega, and Theta.

Gamma (Γ): Rate of Change of Delta

Gamma measures the rate of change in Delta per one-point change in the underlying asset’s price. It represents the "second derivative" of the option’s price and evaluates how stable Delta is likely to be.

• High Gamma indicates Delta is more volatile and can change rapidly with small moves in the stock.
• Options with short expirations and at-the-money strikes typically have the highest Gamma.

Traders monitor Gamma closely as large values may require quick adjustments in hedging activities.

Vega (ν): Sensitivity to Volatility

Vega measures an option’s price change in response to a 1% change in implied volatility. Unlike Delta and Gamma, Vega affects both calls and puts similarly.

• If Vega is 0.10, a 1% rise in implied volatility increases the option's price by £0.10.
• Longer-dated and at-the-money options exhibit higher Vega sensitivity.

Volatility trading strategies, such as long straddles or strangles, depend heavily on Vega behaviour. An increase in Vega benefits those holding long positions in options, while a decrease hurts their profits.

Theta (Θ): Time Decay

Theta quantifies the rate at which an option loses value as time progresses, assuming all other variables remain constant. It is expressed as a negative number for long option positions, indicating that the option will depreciate over time.

• A Theta of -0.05 means the option loses £0.05 in value each day.
• Time decay accelerates as the option approaches expiration, especially for at-the-money options.

Use Cases

These Greeks enable traders to manage risks beyond price changes:

• Gamma scalping: Active hedgers use Gamma signals to rebalance Delta frequently.
• Volatility forecasting: Vega is vital in earnings plays or volatile markets.
• Income strategies: Theta is leveraged in short premium trades like iron condors or credit spreads.

Real-World Example

An options trader believes volatility will increase around a corporate earnings release. She buys a straddle with a high Vega value. Post-announcement, implied volatility surges, increasing the option's value accordingly — fulfilling the strategy's Vega-driven thesis.