Understanding Options delta

A naïve option trader may think that if the underlying price of the stock moves up Rs 1, the option value will also move up Rs 1. This is not true. The price of an option may move in varying degrees according to changes in the underlying stock. This relation between underlying asset’s price and related option contract is explained by computing the Delta of an option . For example, if a stock option has a Delta of .50 it means that, for every Rs 10 movement in the stock’s price, the option price would move Rs 5. This is a very important information for every option trader because, it helps to reasonably estimate the profit / loss if the stock price increases / decreases to a certain level.

Delta may be positive or negative. When delta is expressed for call options, it is expressed as a positive number (between 0 and 1) since a call will increase / decrease in value as the underlying price of the asset increases / decreases. The positive sign is used to denote the nature of relation between call options and underlying asset price. Positive delta gains in value as the underlying price of the stock increases. Conversely, the delta of Put options is expressed as a negative number between -1 and 0. The negative sign denotes the relationship between the put value and the underlying stock’s price. As the price of the underlying stock increases, the put option decreases in value. The underlying stock price has to fall for a negative delta to gain in value.

The second feature of delta measure is that in-the-money options will have higher delta and out-of-the money options will have lower delta measures. As the option keeps moving deep in- –the –money, the Delta will tend to move towards 1 quickly. The reverse will happen when the option keeps falling out-of-the money -the Delta measure would quickly drop near to ‘0’.

It is also interesting to note that when the time to expiry is less, the delta of in-the-money options will tend to move towards 1 and delta of out-of-the-money option will tend to move towards 0. The reason is that, as the time to expiry decreases day by day, the chances of the stock price to move against the trend is less.

In short, one of the main factors that influence the delta measure is the ‘time factor’ or the ‘time till expiry’ of the option contract. As you would have logically observed, the delta measure is not a constant figure. It will keep on changing as the time to expiry shortens with every passing day.

The third feature is that Delta values would increase as the underlying asset’s price volatility decreases. This is because, as the price volatility decreases, the asset price is more likely to stay where it is and hence, if the option is in-the- money, the chance of that option to end in-the-money on expiry is greater. This increases the Delta of that option. In short, volatility is the second important factor that influences the delta measure of an option.


  • Time to expiry, volatility and underlying asset price are the three factors that influence the delta measure of an option.
  • Delta values may be positive or negative.
  • Delta values will be positive (between 0 and 1) for call options and it would be negative (between -1 and 0) for put options.
  • In-the-money options will have higher delta and out-of-the money options will have lower delta measures.
  • At the money option (whether call or put) will always have a delta of .5
  • Delta measure will keep on changing.

First, to estimate the sensitivity of option prices to changes in the price of the underlying asset.

Second, delta measure tells you the probability of an option staying in-the-money at expiry. For example, if an option has a delta of 1, we can assume that the option has almost 100% chances to be in the money at expiry. An option with a delta of .5 means that the option is AT-the-money or in other words, the option has 50% chance to be in-the-money at expiry. An option with .25 delta means that the option has only a 25% chance to end up in-the-money on expiry. The relevance of this information is that it allows you to take calculated risks. For example if you think that the stock markets are about to rally , choosing to go long on an option that has a delta of more than .5 would be a better idea.

Third, to decide the optimal hedge ratio. ‘To hedge’ means to invest in an asset with the intention to offset the loss that may be suffered in another investment so that the effect of loss is minimized. So hedging is more like insurance. For example – you hold 10 call options of HDFC which has a delta of .80 or 80%.That means a 10 rupee rise (or fall) in HDFC’s price will have the effect of options gaining (or losing) Rs 8. If you want to mitigate the probable loss, you will also buy puts in such a way that when you lose in one position, you gain in another. So in the above example you’ll buy 20 put option which has a delta of (-.40) so that the net effect is as follows:

This mitigates the probability of loss should the price of the underlying shares fall. When the price of shares fall, you gain in puts and you lose in calls and hence, nullifies the effect of price fluctuations.

That’s a brief idea about delta, it’s importance and uses. Knowing delta measure of an option enables you to take more intelligent actions in the option market. Delta is only one among many Option Greeks we explained earlier. We will check out Option Gamma measure in our next post.

You may like these posts:

  1. Options: Understanding strike price.
  2. Options: Option styles
  3. Option Greeks

6 Responses to “Understanding Options delta”


March 29, 2013 at 10:59 pm

superbbbbbbbb…….very good explanation……. Thankyou


March 30, 2013 at 9:48 pm

Simple and very informative.
Thanks & wishes for your efforts.


April 12, 2013 at 6:47 pm

excellent.and very impresive explanation


April 12, 2013 at 6:50 pm

i was searching for classes for future and option but i think i dont need of it now. thanks


July 19, 2013 at 11:15 am

its really interesting and easy to understand…………..thank you so much.if there is any book related to this site written by you………….please inform.so it will be useful .


August 15, 2013 at 11:48 am

Respected sir,
If there is any book return by you , please let me know, i will buy it.


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