## Definition and Examples of Delta

Delta measures how the value of an option changes with respect to a price move in the underlying security from which it is derived.

To see how it is used in a simple illustration, consider that you have a stock worth $45 and a call option on that stock is worth $3. Further assume that the delta is 0.4. This indicates that the value of the option is expected to rise by 40 cents for every $1 increase in the price of the stock.

Using that formula, if the price of the stock rises to $46, then the price of the call option is expected to rise to $3.40. If the stock’s price increases to $47, then the option price is expected to be $3.80.

## Alternatives to Delta

Delta is just one of the Greek symbols used to describe or analyze changes in option values. Greek letters vega, theta, gamma, and rho are also used.

### Note

Each of these Greek letters’ formulas measures price sensitivity of a derivative relative to some characteristic of the underlying security on which it is based.

Here’s how the other letters are used by investment analysts and portfolio managers:

**Vega**: Quantifies expected changes in an options price based on the volatility of the underlying security.**Theta**: Options values are influenced in part by the amount of time remaining before they expire. The portion of an options value above its current intrinsic value that exists because of this time is called the time value or time premium. Theta measures the rate at which the value of an option falls over time, which is known as time decay.**Gamma**: This is a derivative of delta, and it measures the rate of change in delta against the change in the price of a security. If the value of a security increases or decreases by $1, gamma will illustrate how much this affects the option price.**Rho**: Measures the effect of changes in the risk-free interest rate on the price of an option and is expressed as the amount of money an option will lose or gain with a 1% change in interest rates.

## What It Means for Individual Investors

An investor can use an understanding of delta to implement an option strategy to protect themselves by offsetting changes in the price of a stock they hold. This type of strategy is called a hedging strategy, and an options delta is used in calculating a hedge ratio.

Assume an investor holds 100 shares of a given stock and a corresponding call option has a delta of 0.25. Again, this means that the price of the option will rise by 25 cents for every $1 rise in the price of the stock. The investor can use this relationship to their advantage in a hedge by doing what’s known as writing calls.

To find the number of calls that must be written to offset a shift in the stock’s price, simply take the reciprocal of the hedge ratio, which is 1/hedge ratio. In this case 1/0.25 = 4. To hedge this position in the stock, the investor must write four calls.

To see how this hedges the investor’s position, remember that a standard options contract represents a right to buy or sell 100 shares.

If the investor owns 100 shares that each fall by $1, then their long position in the stock has fallen by a total of $100. Because each option contract represents 100 shares, each contract price falls by $25 (at 25 cents per share). Four contracts, each falling in value by $25, is $100. The investor could buy these contracts back on the open market. If the investor buys back the contracts, they have written them for $100 less than what they received for them—perfectly offsetting their loss on the stock.

### Note

An investor can also use delta as a probability estimate of whether an option will be in the money, meaning—using call options as an example—that the current price of the underlying asset is higher than the agreed-upon purchase price at expiration.

In this application, the delta value is simply expressed as a probability. Here, it would be used to interpret that the contract has a 25% chance of expiring in the money.

## How To Get Delta

Delta is a component of the Black-Scholes option pricing model. While you can calculate it yourself using the Black-Scholes model, it is also available to you through options quotes and may be provided by the brokerage firm you use to trade options.

### Key Takeaways

- Delta is a measure of how the price of an options contract changes in relation to price changes in the underlying asset.
- Delta is one type of Greek calculation value used to describe changes in the value of an option.
- An understanding of delta can help an investor implement a hedging strategy using options.