What happens to the option price when the underlying price moves?

From time-to-time, we either receive great questions or see interesting ones asked online in various forums. We realise that these are probably very common questions for both new and experienced traders alike.

Question: Is there a way to forecast the price change of an option based on the price change of the underlying stock or index?

To answer this question, you can use the Option’s Greeks to make this estimate – specifically the Delta and Gamma values. The ‘Delta’ is a measure of the sensitivity of an option's price to changes in the underlying asset's price. It is sometimes expressed as a percentage and is a measure of how much the option moves in value for a one-point move in the underlying asset's price. For example, if an option has a delta of 0.50, then the option's value will move by half a point for every one-point move in the underlying asset's price.

Delta is expressed as a number between 0 and 1 or -1 and 0. If the delta is 0, this means the option price will not move in response to a price change in the underlying asset. If the delta is 1, it means the option price will move in perfect proportion to the underlying asset’s price. Alternatively, if the delta is -1, then the option price will move in the opposite direction of the underlying asset’s price. Long call options and short put options have a delta range from 0 to +1; they cannot have a value outside of this range. Long put options and short call options have a delta range from -1 to 0 and cannot have a value outside of this range.

Let’s walkthrough an example ITC is currently trading at 468.49. Call options with a strike price 465 expire within the next week have a delta of 0.69. By comparison, call options that are out-of-the-money with a strike price of 475 have a delta of 0.30.

Let's just use the 465-strike as an example. The LTP is ₹5.95 for the contract. The Delta gives an estimate of the change in the option price based on a one-unit change in the underlying. So, if ITC goes from ₹468.49 to ₹469.49 (+1.00), then this option will go by ₹0.69 which is the current delta value.

What happens if the stock or underlying continues to move up (or down) in price? The delta doesn’t stay still and will continually change as the underlying changes. The ‘Gamma’ provides an estimate of the change in Delta based on a one-unit change in the underlying. The Gamma for the 465-strike is 0.041. Once ITC moves up to ₹469.49 (+1.00), the delta will no longer be 0.69. Instead, the delta will move up by +0.041 to a value of approximately ₹0.73. Continuing on, an additional increase in price of ITC from ₹469.49 to ₹470.49 would raise the option price by ₹0.73. If you wanted to know how a larger price change in ITC would impact its option price, you could keep extrapolating by using the Delta and Gamma values.

In summary Delta is important because it helps to identify how much an option’s price is likely to move when the underlying stock price changes. Knowing the delta can help you determine how much risk you are taking on when you buy or sell an option. It also helps you to better manage the risk of the option position by understanding how much your option position will be affected by a given price change in the underlying stock.