What is Delta Formula?
Delta formula is a type of a ratio which 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 call option or put option. These options have stock as their underlying and that is the key aspect which affects the prices of these assets. In capital markets, this delta is also referred to as the Hedge Ratio.
The formula for Delta is:
However, even the Black and Scholes model is used to determining the value of delta where there is 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 delta equation to understand it better.
Delta Formula Example #1
Suppose that change in the price of the asset is 0.6733 and the change in the price of 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 above equation to calculate the delta.
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Use below given data for calculation of delta
Calculation of delta is as follows,
Delta =0.6733 / 0.7788
Delta will be –
Delta = 0.8645
Hence, the Delta will be 0.8645
Delta Formula Example #2
ABC stock has been listed for the 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 5 years now and is now eligible to enter into 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 at $1.31.
On the basis of given data, you are required to calculate the delta which shall be a basis for hedge ratio for the trader.
Solution:
Use below given data for calculation of delta
Calculation of delta is as follows,
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 –
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 position 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. 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 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
Calculation of delta is as follows,
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 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 =$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 = 


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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