Options strategies and greeks - Delta gamma theta and vega

Learning Outcomes

After reading this article, you will be able to explain and compare major options strategies and interpret the meaning and practical use of key option “greeks”: delta, gamma, theta, and vega. You will be able to calculate and analyze the risk/return impact of these greeks for different strategies and understand how they inform hedging, pricing, and portfolio risk considerations for CFA Level 1.

CFA Level 1 Syllabus

For CFA Level 1, understanding options is required, both in constructing risk/reward strategies and in applying greek sensitivity measures. For revision, focus your study on:

• Describing and evaluating common options strategies (spreads, straddles, combinations).
• Explaining option delta, gamma, theta, and vega, and their economic implications.
• Calculating the greeks for basic positions and using them to explain risk exposures.
• Demonstrating how the greeks inform dynamic hedging and risk management.

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. What does a delta of 0.55 for a call option indicate, and how might an option trader use this information?
2. Which greek best describes an option position's sensitivity to underlier volatility, and why is this important?
3. If the gamma of an option position is high, what does this mean for delta hedging?
4. Explain why theta is typically negative for a long call option.

Introduction

Options strategies are used to construct risk/return profiles for a wide range of financial goals. While understanding payoff diagrams is a basis, effective management of portfolios requires knowledge of the “greeks,” which measure how different variables affect option prices. Delta, gamma, theta, and vega are the most important for CFA Level 1. They allow candidates and practitioners to assess risk exposures, adjust hedges, and understand position sensitivities.

Key Term: options strategy
A position or combination of options and/or the reference asset designed to achieve a specific risk/return or hedge profile.

Key Term: greeks
Quantitative measures that represent the sensitivity of an option’s price to changes in various factors, including the price of the underlier, volatility, time, and interest rates.

Major Options Strategies

Options can be used to create directional, neutral, or volatility-based bets. Common strategies include:

• Long or short calls and puts: Simple bullish or bearish bets.
• Spreads: Combining two or more options (e.g., bull spreads, bear spreads) to limit both risk and reward by buying and selling options at different strikes.
• Straddles and strangles: Buying or selling both a call and a put (same or different strikes), usually to profit from large or small moves in the underlier.
• Covered call or protective put: Using options alongside an existing position in the underlier.

For each strategy, identifying its profit/loss diagram and scenario analysis is fundamental, but understanding the strategy’s “greeks” is essential to managing risk over time.

Option Greeks Overview

The greeks quantify how an option’s price responds to small changes in factors affecting its value. The main greeks to understand for CFA Level 1 are delta, gamma, theta, and vega.

Delta

Key Term: delta
The expected change in an option’s price for a small change in the price of the reference asset.

Delta represents the directional exposure of an option. For standard European calls, delta ranges from 0 to 1; for puts, it ranges from –1 (deep in the money) to 0 (deep out of the money). Delta is also used in dynamic hedging, showing how many units of the underlier are required to hedge the option’s price risk.

Gamma

Key Term: gamma
The rate of change of delta with respect to changes in the reference asset’s price.

Gamma shows how much delta will change if the reference asset moves by a small amount. High gamma means delta is sensitive, typically highest for at-the-money options close to expiry. Gamma is critical for hedgers, as high gamma positions need frequent rebalancing.

Theta

Key Term: theta
The expected change in an option’s value for a small decrease in the time to expiry, holding all else equal.

Theta measures time decay—how much value an option loses as time passes, with all other factors unchanged. Long options (calls or puts) generally have negative theta, while short positions have positive theta.

Vega

Key Term: vega
The expected change in an option's value for a small increase in the volatility of the reference asset.

Vega reflects sensitivity to implied volatility. All else equal, as volatility rises, both calls and puts become more valuable. Vega is highest for at-the-money options with longer time to expiry.

Applying the Greeks to Options Strategies

Options strategies combine positions, so total exposure to the greeks is the sum of each position’s greek exposure. The main risk for each strategy arises from the combination of greeks, informing the investor’s risk and reward trade-offs.

Worked Example 1.1

You buy an at-the-money European call on XYZ stock (spot at $50, strike $50, 3 months to expiry). The call delta is 0.52, gamma is 0.11, theta is –0.08, vega is 0.21. What do these greeks imply for your position?

Answer:

• Delta 0.52: If XYZ stock rises by $1, the call gains approximately $0.52. You have moderate bullish exposure.
• Gamma 0.11: If the stock rises by another dollar, delta increases by 0.11 to 0.63, meaning your position becomes even more sensitive to the underlier.
• Theta –0.08: Each day, your option loses about $0.08 in value, all else constant.
• Vega 0.21: If implied volatility rises by 1 percentage point, the call gains $0.21 in value.

Worked Example 1.2

Suppose you construct a long straddle by buying an at-the-money call and an at-the-money put on the same stock. How are your greek exposures affected?

Answer:

• Delta: Calls and puts offset; total delta is near zero (unless the underlier moves).
• Gamma: Both options have positive gamma, so the combined position has high gamma (delta changes rapidly with price moves).
• Theta: Both options have negative theta. The straddle suffers high time decay if the underlier remains near the strike.
• Vega: Positive and potentially large. The straddle gains if volatility rises.

Worked Example 1.3

A trader is short an at-the-money put, with delta –0.50, gamma 0.13, theta 0.09, vega –0.19. What are the risk implications?

Answer:

• Delta –0.50: The short put gains value as the underlier rises.
• Gamma 0.13: If the underlier falls, the position's delta becomes more negative, requiring risk-management attention.
• Theta 0.09: Positive theta means the position gains value from time decay.
• Vega –0.19: If volatility falls, the put's price decreases, benefiting the seller.

Exam Warning

On CFA exam questions, always pay careful attention to the sign (positive or negative) of each greek. For example, a long call has positive delta and vega but negative theta. Short positions invert the signs.

How Greeks Help Manage Options Risk

• Delta hedging: Use the option’s delta to neutralize price risk by holding a position in the reference asset. For more accurate hedging, high gamma means you must rebalance frequently.
• Gamma awareness: High gamma strategies (straddles) need active management. Small price moves cause large changes in delta.
• Theta management: Watch for positions with large negative theta. Time decay can erode profits rapidly, especially for long multi-leg positions.
• Vega sensitivity: Understand that volatility changes disproportionately affect strategies with high vega, like long straddles or calendar spreads.

Summary

Option strategies allow precise risk/return exposures, but effective management requires interpreting and combining the major greeks. Delta shows directional sensitivity, gamma shows curvature or convexity, theta measures time decay, and vega measures volatility risk. Exam candidates must calculate, interpret, and apply these greeks for common strategies.

Key Point Checklist

This article has covered the following key knowledge points:

• Describe and compare major options trading strategies and their risk/return goals.
• Define and interpret delta, gamma, theta, and vega for CFA Level 1.
• Calculate greek exposures for individual options and combined strategies.
• Use greeks to analyze, hedge, and manage options strategies in dynamic markets.
• Recognize the impact of sign and magnitude of each greek for risk control.
• Apply time decay and volatility measures to forecast position changes.

Key Terms and Concepts

• options strategy
• greeks
• delta
• gamma
• theta
• vega