Options Foundations

# The Greeks

In options trading, the Greeks are mathematical parameters that can help you better understand and manage the behavior and risk of options contracts.

### Delta

Delta is the sensitivity meter. It predicts how much the price of an option might change for every \$1 of movement in the price of the underlying stock. Delta ranges from -1 to +1. The closer it is to these extremes, the more sensitive the option.

### Gamma

If Delta is about option price sensitivity and is a point-in-time reference, Gamma is about the acceleration of that sensitivity; how quickly is the Delta changing over time. It predicts how Delta itself will change with a \$1 price movement in the stock. Since Delta’s cannot exceed 1 or -1, Gamma is usually smaller the closer Delta gets to its extremes.

### Theta

Theta can be thought of as the ‘timekeeper’. With every day that passes, an option loses some of its value, even if everything else remains the same. Theta tells us how much time value the option will lose daily. For example, if the Theta is -0.10, the option might lose ten cents in value every day, even if the stock price remains unchanged.

### Implied volatility

While not a Greek, it is important to understand implied volatility as it drives Vega. Implied volatility is a measure that shows how much traders think a stock’s price might swing in the future. It is reflected in option prices, and higher values mean traders are expecting bigger price moves, up or down.

### Vega

Vega tells us about an option's sensitivity to changes in implied volatility. If the stock is expected to become more volatile and this expectation rises, Vega shows us how the option's price might change. For example, a Vega of 0.20 indicates that the option's price could go up or down by 20 cents with a 1% increase in implied volatility.

### Rho

Rho is also a sensitivity indicator, representing how sensitive an option’s price change is to changes in interest rates. It measures how much the price of an option is expected to change with a 1% change in the risk-free interest rate. Options almost in-the-money with a long time to expiration are often the most sensitive to changes in interest rates.

For call options, a positive rho indicates that the option's price is expected to increase when interest rates rise, as the value of potential gains becomes more valuable. Conversely, for put options, a positive rho suggests that the option's price is expected to decrease when interest rates rise, as the value of potential losses becomes less significant.

## Basic example

Assume you're considering a call option that costs \$10 per contract. In this example, the option’s current Delta is 0.6, Gamma 0.1, Theta -0.05, and Vega 0.20. Now, let's say there’s a rumor that FlyFit is about to launch a new product, causing its stock price to jump by \$2 and increasing its implied volatility by 2%.
1. Delta: The option’s Delta would suggest a \$1.20 increase in the option’s price. We get that by multiplying the Delta by the \$2 rise in stock price, or 0.6 times 2 equals \$1.20.
2. Gamma: Remember that Gamma predicts how Delta will change with a \$1 price movement in the stock. In this instance, we multiply the Gamma of 0.1 by the \$2 price increase to discover that our Delta would now become 0.8 for any subsequent stock price changes.
3. Vega: Moving on to the 2% increase in volatility, Vega tells us there would be a 40-cent change in the option’s price. Again, it’s because we take the Vega value and multiply it by the 2% increase.
4. Theta: Regardless of these changes, our option will still lose \$0.05 in value every day, thanks to time decay. So if a day passes, that's a five-cent decrease.
Putting it all together, we’d expect that the new price of the option would be about \$11.55—the original value of \$10, an extra \$1.20 due to the stock price rise, an extra \$0.40 due to a rise in implied volatility, and \$0.05 less due to 1-day of time decay.
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The examples used above are fictional, and do not constitute a recommendation or endorsement of any investment.

Options are not suitable for all investors and carry significant risk. Certain complex options strategies carry additional risk. There are additional costs associated with option strategies that call for multiple purchases and sales of options, such as spreads, straddles, among others, as compared with a single option trade.

Prior to buying or selling an option, investors must read the Characteristics and Risks of Standardized Options, also known as the options disclosure document (ODD).

Option strategies that call for multiple purchases and/or sales of options contracts, such as spreads, collars, and straddles, may incur significant transaction costs.

### Options resource center

Options Foundations
Chapter 1Options 101
Chapter 2P/L charts
Chapter 3Time value
Chapter 4The greeks
Chapter 6Assignment
Fundamentals
Multi-leg Strategies
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