InvestorQ : What is option Delta and how to interpret it in practice?
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Lavanya Subramanian made post

What is option Delta and how to interpret it in practice?

Answer
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ishika Banerjee answered.
2 years ago


One of the most popular options Greeks is the Delta. What exactly do we understand by the Delta? The option's delta is the rate of change of the price of the option with respect to its underlying security's price. In other words, the Option Delta measures the sensitivity of the option price to the changes in the price of the underlying stock. The delta of an option ranges between the range of 0 to 1 for calls (0 to -1 for puts) and reflects the increase or decrease in the price of the option in response to a 1 point movement of the underlying asset price. Typically, very far out-of-the-money options have delta values close to 0 while deep in-the-money options have deltas that are close to 1. That is because the deep OTM options are anywhere worthless and the deep in the money options are almost like futures. Let us understand the concept of Delta from the table below.

Simulating Option Greeks on Reliance Industries 1100 Strike

Underlying Price

1110

Underlying Price

1130

Exercise Price

1100

Exercise Price

1100

Today's Date

27-11-2018

Today's Date

27-11-2018

Expiry Date

06-01-2019

Expiry Date

06-01-2019

Historical Volatility

20%

Historical Volatility

20%

Risk Free Rate

6.00%

Risk Free Rate

6.00%

Dividend Yield

1.35%

Dividend Yield

1.35%

DTE (Years)

0.11

DTE (Years)

0.11

Call Option

Put Option

Call Option

Put Option

Theoretical Price

37.5093

21.9411

Theoretical Price

50.4571

14.9185

Delta

0.5975

-0.4025

Delta

0.6972

-0.3028

Gamma

0.0053

0.0053

Gamma

0.0047

0.0047

Theta

-0.4582

-0.2785

Theta

-0.4475

-0.2679

Vega

1.4220

1.4220

Vega

1.3060

1.3060

Rho

0.6846

-0.5130

Rho

0.8069

-0.3907

Delta is the sensitivity of the option value to changes in Stock Price

Theta is the sensitivity of the option value to Time Decay

Vega is the sensitivity of the option value to changes in Volatility

In the above instance we have plotted the change in the value of the call option and the put option when there is a change in price. Let us assume that the price of RIL goes up by Rs.20 from Rs.1110 to Rs.1130. We can see the call value going up from Rs.37.5093 to Rs.50.4571. How do we determine to what extent this option will change? That is measured by Delta. In the above case, the Call Delta is 0.5975 but the Delta changes to 0.6972 after the price change. Since delta itself is dynamic, we use the average delta which is 0.6474 {(0.5975 + 0.6972)/2}. The Call option price change will, therefore, be as under:

Old Option Value x Average Delta (Price rise)

= 37.5093 x 0.6474 (20) = Rs.50.457

You can see in the above table that that is exactly the new value of the call option as a result of the increase in the stock price. This can be easily calculated by the use of Delta. Normally short term traders prefer to trade stocks with a higher delta. What about the value of the put option? Let us also see how the Delta can be used to predict fair value of put options.

In the above instance we have also plotted the change in the value of the call option and the put option when there is a change in price. Let us assume that the price of RIL goes up by Rs.20 from Rs.1110 to Rs.1130. We can see the put value going down from Rs.24.9411 to Rs.14.9185. How do we determine to what extent this put option value will change? That is again measured by Delta. In the above case, the Put Delta is (-0.4025) but the Delta changes to (-0.3028) post the price change. Put deltas are always shown in negative symbol to indicate the negative relationship between price movement and the fair value of the put option. Since delta itself is dynamic, we use the average delta which is (-0.3527) {(0.4025 + 0.3028)/2}. The Call option price change will, therefore, be as under:

Old Option Value x Average Delta (Price rise)

= 21.9411 x (-0.3527)* (20) = Rs.14.888

You can see in the above table that that is exactly the new value of the put option as a result of the increase in the stock price. This can be easily calculated by the use of Delta. Normally short term traders prefer to trade stocks with a higher delta.