 Delta Delta

# Delta

Option Delta, by definition, is a first order option Greek, measuring the sensitivity of option premium to the change in underlying price. If the option under consideration is an equity option, implies that the underlying is stocks, or NSE F&O segment stocks. On NSE, the F&O segment has equity indices, also, like Nifty/BankNifty/FinNifty. Nifty traders, can trade the index using options or futures, of which options are the preferred contracts. The basic knowledge of option trading isn’t sufficient for efficient option trades. The need to understand option greeks is extremely necessary.

As discussed, Option Delta, first-order option Greek, is change in option premium, due to directional price change in the underlying, keeping other factors same. So, for example, if option Greek, delta, is 0.68, implies that if the underlying directional change is +1, then the option premium shall increase by 0.68 in case of a call option, and drop by 0.68 in case of a put option.

An option delta of 1 means that the option price will move in lock-step with the underlying asset's price, while a delta of 0 means that the option price will not change with the underlying asset's price. As the put option (discussed in above example) reduces in price on increase in underlying price, the direction of the two price movements is opposite and option Greek, delta of the put option is therefore, negative. Delta can also be expressed as a percentage, with values ranging from 0 to 100 for call options and from 0 to -100 for put options.

Consider the example on option calculator of NIFTY option,

Nifty

Expiry: 25 Jan 2023

CMP: 18158

18200 CE: Rs 45

Observing the option chain, 18200 CE of Nifty, Delta is 0.4 implying if Nifty moves from 18158 to 18168, option should gain by Rs 4.00.

Also, a glance at the Nifty option chain suggests the Implied Volatility is 11.4%. If the Quantsapp’s Nifty Option Calculator is used, it says the ideal price of the option at 11.4% volatility is Rs 42.48, which increases to 46.54, i.e. a jump of about Rs 4.06, which matches with our earlier calculation, as the Nifty underlying is changed from 18158 to 18168, keeping all other variables constant, including volatility.  Alternative definition of Option Delta can be thought of as an estimate of the probability that an option will expire in the money, but it is important to note that delta is not an exact probability.  However, delta can vary depending on the current price of the underlying asset, Nifty or Bank Nifty or F&O stock, the time until expiration, and the volatility of the underlying asset, among other factors. This means that delta values can change over time, even if the underlying asset price remains constant. As a result, Option Greek, delta should be used as a rough estimate of an option's likelihood of expiring in the money, but not as an exact probability.

Hence close to expiry, “ITM options delta surges and more deep in the money option, more it converges towards 1 or 100%”

While “ATM options are close to 0.50 or 50%”

And, “OTM options transition towards 0 (zero), as their probability to jump to be ITM options diminishes, as time elapses.” ### What Does Option Delta Show in Option Trading?

Option delta is a measure of the rate of change of the price of an option (i.e. rate of change of option premium) with respect to the underlying asset's price. The underlying asset may be an index like Nifty or BankNifty or stocks from the F&O segment. Option delta is expressed as a number between -1 and 1 and represents the amount by which the option's price is expected to change for a 1 point move in the underlying asset's price.

### Can Option Delta be Zero?

Yes, it is possible for the delta of an option to be 0. The delta of an option measures its sensitivity of option premium to changes in the price of the underlying asset and is expressed as a decimal between -1 and 1. An option with a delta of 0 means that its price will not change if the price of the underlying asset changes.

Typically, delta option Greek of 0 is most likely to occur for options with a strike price that is far away from the current price of the underlying asset. For example, if Nifty is quoting at about 18000, deep OTM call option with strike price of 19000, has delta of about 0.02, which is nearly close to zero, similarly delta of a deep OTM put option would have delta close to 0 from the negative side.

### Can Option Delta be Negative?

Yes, let’s understand what negative delta option options trading means. Delta which measures the sensitivity of option premium to the change in underlying asset, tends to be negative when underlying asset’s price increases and option premium decreases in proportion to that delta. This means for every increase in underlying asset price, there is a drop in option premium and vice versa, i.e. like that of a put option, suggestive of a negative delta, due to opposite directional behaviour of the two variables under study.

### Why put Option Delta is Negative?

The magnitude of delta option Greek reflects the degree of the option's sensitivity to changes in the price of the underlying asset. A put option favours the bear (rather than the bull), so it generally rises in value, when the underlying like Nifty falls. A put option with a delta of -0.5, for example, will increase in value by Rs 0.50 if the price of the underlying asset decreases by Rs 1. The closer the delta is to -1, the more sensitive the option is to changes in the price of the underlying asset. The negative sign indicates that for an increase in value of the underlying asset like Nifty, value of put option falls (i.e. opposite direction).

### How to Calculate Delta of an Option?

Theoretical option delta can be calculated from the theoretical evaluation of delta of the Black Scholes option pricing model. In a practical perspective, it is measured by taking the ratio of option premium change to the change in underlying asset’s price.