Delta Formula

What is Delta Formula?

Delta formula is a type of ratio that compares the changes in the price of an asset to the corresponding price changes in its underlying. The numerator is the change in the price of the asset, which reflects how the asset changed since its last price. The asset could be any derivative like a call option or put option. These options have stock as their underlying, and that is the key aspect that affects the prices of these assets.  In capital markets, this Delta is also referred to as the Hedge Ratio.

The formula for Delta is:

Delta = Change in Price of Asset / Change in Price of Underlying.

Delta Formula

However, even the Black and Scholes model is used to determining the value of Delta, where there is a variable in it, which is N(d1), which can be calculated using computer software.

Examples of Delta Formula (with Excel Template)

Let’s see some simple to advanced examples of the delta equation to understand it better.

You can download this Delta Formula Excel Template here – Delta Formula Excel Template

Delta Formula Example #1

Suppose that change in the price of the asset is 0.6733, and the change in the price of the underlying is 0.7788. You are required to calculate Delta.

Solution:

We are given both the figures that change in the price of the asset, which is 0.6733, and change in the price of the underlying, which is 0.7788. Therefore, we can use the above equation to calculate the Delta.

Use below given data for calculation of Delta.

  • Change in Price of Underlying: 0.7788
  • Change in Price of Asset: 0.6733

Calculation of Delta is as follows,

Excel 1.1

Delta =0.6733 / 0.7788

Delta will be –

Delta Formula Example 1.2

Delta = 0.8645

Hence, the Delta will be 0.8645

Delta Formula Example #2

ABC stock has been listed for a number of years but has remained quite volatile in nature. The traders and investors have been suffering losses in the stock due to its unnatural price movement. The stock has now been listed for five years now and is now eligible to enter into the derivatives market. John already holds the position of this stock in his portfolio.

The current price of the stock is $88.92, and the call option of strike price $87.95 is trading at $1.35, which has an expiration of 1 month left. John wants to hedge his position, and hence he wants to calculate the Delta for this stock. Next trading day, he notices that the stock price is moved down to $87.98, and so as the call option price has moved down slightly to $1.31.

On the basis of the given data, you are required to calculate the Delta, which shall be a basis for the hedge ratio for the trader.

Solution:

Use below given data for calculation of Delta.

  • Call Option Price at Begining: 1.35
  • Call Option Price at End: 1.31
  • Stock Price at Begining: 88.92
  • Stock Price at End: 87.98

Calculation of Delta is as follows,

Delta Formula Example 2.1

Here, the asset is the call option, and it is underlying it’s the stock. So, first, we will find out the changes in the price of the asset, which is the change in the price of call option which shall be $1.35 less $1.31 that is equal to $0.04, and now the change in underlying price would be $88.92 less $87.98 which shall equal to $0.94.

We can use the above equation to calculate Delta (rough figure, a true figure can be obtained through other complex models like Black and Scholes)

Delta =$0.04 00/ $0.9400

Delta will be –

Calculation 2.2

Delta = $0.0426

Hence, the Delta will be $0.0426.

Delta Formula Example #3

JP Morgan is one of the biggest investment banks in the United States of America. They have multiple stock, bond, derivatives positions sitting in their balance sheet. One such position is in WMD stock, which is trading at $52.67. The company has long exposure to this stock. On the next trading day, the stock trades at $51.78. The trader who is acting on behalf of the company has put option which shall hedge the losses.

The strike price of the put option is $54.23 and when it is currently trading at $3.92. The price of the put option closed $3.75 yesterday. The trader wants to know the rough Delta and asks you to calculate the Delta of the WMD put option.

Solution:

Use below given data for calculation of Delta.

  • Put option Price at Begining: 3.75
  • Put Option Price at End: 3.92
  • Stock Price at Begining: 52.67
  • Stock Price at End: 51.87

Calculation of Delta is as follows,

Example 3.1

Here, the asset is the put option, and it is underlying it’s the stock. So, first, we will find out the changes in the price of the asset, which is the change in the price of the put option which shall be $3.75 less $3.92 that is equal to $-0.17 and now the change in underlying price would be $52.67 less $51.78 which shall equal to $0.99.

We can use the above equation to calculate Delta (rough figure, the true figure can be obtained through other complex models like Black and Scholes)

Delta = $-0.1700 / $0.8000

Delta will be –

Delta Formula Example 3.2

Delta =$-0.2125

Hence, the Delta will be $-0.2125.

Delta Formula Calculator

You can use the following delta formula calculator.

Change in Price of Asset
Change in Price of Underlying
Delta
 

Delta =
Change in Price of Asset
=
Change in Price of Underlying
0
= 0
0

Relevance and Uses

Delta is a vital calculation (mostly done by software), as this is one of the key reasons that the prices of the option move in a particular direction, and this is an indicator as to how to invest. The behavior of put option and call option delta can be greatly predictable and can be very useful to traders, portfolio managers, individual investors, and hedge fund managers.

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