**Options Delta**

Options Greeks are a number of risk measures denoted by the Greek letters. They indicate the sensitivity of an option to volatility, time value decay, and movements in the price of the option’s underlying asset. The four primary Greek risk measures are known as theta, vega, delta, and gamma.

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__What are Options Delta:__

An options “delta” is a measure of the change in an options premium or price due to a change in the underlying security. Delta is one of the measures used by options traders for analyzing risk. A calculated value that estimates the rate of change in the price of an option given a 1-point change is known as Options Delta. It tells us the expected price change of that option comparative to a one-dollar movement in the stock price. Delta can be positive or negative. For a call option, the delta ranges from 0 to 1. This is because the price of the call options increases due to an increase in the price of the underlying asset. On the other hand, the put option delta ranges from -1 and 0 because the price of the put option decreases as the price of the underlying asset increases. Basically, it tells us how much the price of an option would change when the stock price increases by 1.

__Characteristics of Delta:__

- It expresses the amount of price change a derivative will see based on a stock or underlying asset.
- Delta can be positive or negative which depends on the type of option.
- Call option delta ranges from 0 to 1.
- Put option delta ranges from 1 to 10.

__Formula:__

The formula for calculating delta is:

**Δ****=****∂ S/∂V**

****

__Examples:__

Let’s look at few examples here to understand the impact of Delta on the stock prices:

- Suppose we have a call option priced at $5 and the delta is 0.75. This means that if the stock price increases by $1, the option will increase by $0.75 to $5.75. On the other hand, if the stock price decreases by $1 that $5 call option is expected to lose $0.75 based on the Delta of 0.75 and hence be worth $4.25.
- Suppose we have a put option priced at $3 and the delta is -0.25. This means that if the stock price increases by $1 the option will decrease by $0.25 to $2.75. On the other hand, if the stock price falls by $1, that $3 put option is expected to gain $0.25 and hence be worth $3.25.
- A stock is trading at $120, the call option on $135 strike price with 90 days to expiry is worth $8. If the delta is 0.35, what would be the price of an option when the stock trades at $125? The stock price has increased by $125-$120 = $5. The delta of an option is 0.35, the best guess of the option value is that it will increase by $5 * 0.35 = 1.75. Thus, the option will be worth $8 + $1.75 = $9.75.

__Effects of the delta on Call and Put options:__

__How is Delta used in Options Trading?__

Different traders use different scales for measuring option delta. Some typically use a 0-1 scale, while some others use a 0-100. Delta hedging reduces the risk of price movements in an asset by offsetting long and short positions. If the trader holds one call option with a delta of 0.30 and one put option with a delta of -0.30 then the net delta of the position is 0. Generally, straddles have a zero delta. Delta hedging is done with stocks and options. For e.g.: Let us say Mr. N is holding a call option with a delta of 0.50. Assuming that the lot size of the stock is 100 shares then Mr. N can perfectly hedge 1 lot of the call option by selling 50 shares of the stock.

__Importance:__

- Option delta is important for options traders that like to make directional trades. Positive delta shows bullish directional strategy while negative delta shows bearish directional strategy.
- Delta is also indicative of the degree of risk at stake. High deltas indicate more risk and lower delta indicating less risk.
- It also indicates the hedge ratio which is the number of shares that need to be traded to hedge the option position with stock.
- An option’s delta estimates the probability of the stock expiring beyond the strike price at expiration.

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__Key Takeaways:__

- Delta is one of the four option Greeks. The option Greeks help us to understand how our option positions are expected to perform relative to changes in specific things in the environment.
- An options delta helps the trader understand how an options price will change for a given change in the price of the underlying assets.
- Option Greeks break down the intrinsic value of call and put options and analyze different aspects of price movements.
- Delta measures the extent to which the price of the option will change given there is a difference of 1 point in the stock price. It basically plays with the stock and strike price of an asset.

**Author – Abha Shetty and Urvi Surti**

**About the Author:**

Abha is a second-year BMS student and FRM level 1 candidate. She is very intrigued by the world of financial markets and hopes to master the art of investing and trading.

Urvi is a commerce graduate and has a keen interest in Finance. She has completed her Chartered Wealth Management (CWM) from the American Academy of Financial Management and is currently pursuing a career in Financial Risk Management (FRM).

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