Delta of a Stock Option 🔺 Finance Lessons for Quants

Summary

This video explains the concept of delta in stock options, detailing its role in measuring an option's sensitivity to the underlying stock price. The script breaks down delta's behavior for call and put options, with real-world examples, showing how it ranges from 0 to 1 for calls and from 0 to -1 for puts. It also highlights delta's correlation with probability, acting as a quick proxy for the chance an option will end in the money. The video previews a stock options course, focusing on the Greeks and their practical use in trading strategies.

Takeaways

• 😀 Buying stock directly ties up significant capital, but call options provide leverage, allowing for the same potential upside with less upfront money.
• 😀 Delta is a measure of how much an option's price is expected to change for every $1 move in the underlying stock price, providing insight into the option's directional exposure.
• 😀 A call option with a delta of 0.65 means that for every $1 the stock rises, the option’s price will increase by approximately 65 cents.
• 😀 Delta ranges from 0 to 1 for call options, where 0 means the option is far out of the money and 1 means it is deep in the money.
• 😀 The delta of a deep in the money call is 1, meaning its price moves one-for-one with the stock’s price.
• 😀 An at-the-money call option has a delta of about 0.5, meaning a $1 move in the stock causes about a 50 cent move in the option’s price.
• 😀 Put options have a negative delta, meaning their price moves in the opposite direction of the stock’s price.
• 😀 A deep in the money put option has a delta close to -1, meaning for every $1 the stock price decreases, the option’s value increases by almost $1.
• 😀 The delta of an at-the-money put option is about -0.5, meaning a $1 increase in stock price results in a 50 cent drop in the put's value.
• 😀 Delta is not just a measure of sensitivity; it also approximates the probability of an option finishing in the money, ranging from 0 (0% chance) to 1 (100% chance).
• 😀 As the stock price moves, the delta of an option changes too. For example, a delta of 0.5 can rise to 0.6 or 0.7 as the stock price increases, signaling a need for further analysis using Gamma.

Q & A

What is the main advantage of using a call option instead of buying 100 shares of stock?

The main advantage of using a call option is leverage. It allows you to gain the same potential upside with less capital upfront compared to buying 100 shares, which ties up more capital.

What does the delta of an option represent?

Delta represents how much an option's price is expected to change for every $1 move in the underlying stock's price. It essentially measures the sensitivity of the option's price to stock price movements.

How does the delta of a call option behave as the stock moves?

For a call option, the delta starts at 0 when the option is far out of the money, increases as the option moves closer to the money, and approaches 1 when the option is deep in the money. This reflects the increasing sensitivity of the option price to stock price movements.

What happens to the delta of an option as the stock price moves?

As the stock price moves, the delta of an option can change. For example, if the stock price rises, the delta of a call option might increase from 0.5 to 0.6, indicating that the option becomes more sensitive to further stock price movements.

How is delta related to the probability that an option will finish in the money?

Delta is closely tied to the probability of an option finishing in the money. A delta of 0.5 suggests a 50% chance of finishing in the money, while a delta of 1 indicates nearly a 100% chance, and a delta of 0 suggests virtually no chance.

What is the delta of a call option that's far out of the money?

The delta of a call option that's far out of the money is close to 0, meaning there's virtually no chance the option will gain value if the stock price rises by $1.

What is the delta of a call option that is deep in the money?

The delta of a call option that is deep in the money is close to 1, meaning for every $1 increase in the stock price, the option's price will increase nearly $1.

What is the delta of a put option compared to a call option?

The delta of a put option works in reverse to a call option. While a call option has a delta ranging from 0 to 1, a put option's delta ranges from -1 to 0. A negative delta means the put option's price moves in the opposite direction of the stock.

How do the deltas of at-the-money call and put options compare?

For at-the-money call and put options, their deltas are approximately 0.5 and -0.5, respectively. This means the price of an at-the-money call increases by about 50 cents for every $1 rise in the stock price, while the price of an at-the-money put decreases by about 50 cents for every $1 rise in the stock price.

How can you use delta to estimate the change in an option's price?

To estimate the change in an option's price, you multiply the delta by the amount the stock price moves. For example, if you hold a call option with a delta of 0.7 and the stock rises by $1, the option's price is expected to increase by $0.70.