θ Theta | Understanding – Time is Money

The rate of change of the value of the option with respect to the price with all else remaining the same.

Definition from Investopedia

Theta is a measure of the rate of decline in the value of an option due to the passage of time. It can also be referred to as the time decay on the value of an option. If everything is held constant, the option loses value as time moves closer to the maturity of the option.

Option with only Intrinsic value does not have much theta effect on them. Option with extrinsic value only has theta effect on them. Below is the example why theta does not exist for deep ITM (In the Money) option or rather option with only intrinsic value do not have theta effect on them.

In the below example Underlying Value of Nifty is 9198

Call Option Value: Rs. 2145

= 9198-7050

= 2148 (Intrinsic Value)

Difference between Option Premium & Intrinsic Value

=2148-2145

=3

There is not much difference between the intrinsic value and option premium and hence there is not much premium for theta play. The option premium will move in tandem with the difference with the underlying and hence the opportunities to earn money is very meager.

Now call value option is Rs. 1373 for the Strike Price 10600.

Underlying price of the Nifty is 9198

=10600-9198

=1402 (Intrinsic Value)

Difference between Option Premium & Intrinsic Value

=1402-1373

=29

What is Option Theta?

Now from the above, it is clear that Deep ITM do not have option premium and hence the theta is also negligible. So now let us see the options strike price which has the highest theta.

It is to be noted that highest theta is present At the Money options. There is a very simple reason behind this is that buyers as per the option definition have limited risk and unlimited profit. So sellers to cover up for that calculate the risk and premium is charged.

You could better understand the Premium calculation is the different post.

Now for Strike price, 9200 Call Option Premium is Rs. 97

Underlying Index Nifty = 9198

Difference between underlying and Strike Price = 9200 – 9198 = 2

Extrinsic Value = Rs. 97

Call Option value as per the above calculation process is Rs. 990 when all the other factors are the same till the expiry of the contract.

Now for Strike price, 9200 Put Option Premium is Rs. 83

Underlying Index Nifty = 9198

Difference between underlying and Strike Price = 9200 – 9198 = 2

Extrinsic Value = Rs. 83

Put Option value as per the above calculation process is Rs. 618 when all the other factors are the same till the expiry of the contract.

The formula used to Calculate the Option Value.

Black-Scholes formula for call option delta

Black-Scholes formula for put option delta

Source – Option Greek Calculation

Hence with this, we can conclude that the theta value derive only when the option has Extrinsic Value.

Theta for Option Buyers & Option Sellers?

Keeping all other factors constant time decay causes an option to lose value as it reaches the expiration date. The greek which has to be monitored if you are a net portfolio of option on buying side. Because of this nature of the option they are known as decaying asset. As the time passes option loses its value. Initially, the option value decreases gradually and as the expiration nears it decreases sharply. At the same time, decay is an advantage to the person who writes an option. The price near expiration is less than at the time it was written this benefits the options writers.

Positive Theta & Negative Theta

For any net position if the Theta is Negative it concludes that the net position of the options in the portfolio is on buy side. Every option bought the theta is negative as it daily loses value. Conversely for net options portfolio is of sell position then it is Positive theta. Option writers earn money as the time passes. With the below example one will clearly able to understand when the theta is positive and negative.

Long Call – Negative

Short Call – Positive

Long Put – Negative

Short Put – Positive

Strategy wise net theta would be written in another article since there would be too many things to cover into that.

Time and Its effects on Theta

This is the most important part of the greeks. One has to carefully understand how the time impacts the value of the option. Option premium with an extrinsic value over the period of time with the strike price ATM. Strike price which is Deep ITM do not have any theta value as said earlier and likewise, Deep OTM options have very less premium to understand theta better. Below is the chart of Call and Put options short and long position and how theta effects them everything else keeping constant.

The price of the underlying is 9198 and the strike price of the Long Put option is 9200 for the long position the value of the options keeps falling.

In the same manner for the underlying Index Nifty at 9198 and strike price 9200 ATM short put the value keeps falling but it is profit to the option writer. Since this is positive theta for the option writer.

Underlying Nifty Index is at 9198 with a Strike price at 9200 Short call option hence the option writer gains as he has sold at a higher price and will buy back at a lower price.

Underlying Nifty Index is at 9198 with a Strike price at 9200 long option buyer will lose the money as he has bought at a higher price and will sell at the lower price.

How to see Theta Differently?

Statistics say that 55% – 65% of the options are closed prior to expiry and 25% to 35% of the options expire worthlessly. Since this is a decaying derivative to take benefit out of it to generate a regular income so-called theta play comes into effect.

  • Opportunity to generate monthly cash flow with low-risk strategies.
  • Can be used in all market conditions.
  • Covered call writing is another form of income generating strategy.
  • Does not require you to sit in front of the system all the time.
  • Basic computer or home desktop could do the work.
  • Downside protection and adjustment strategies also possible.
  • Limited but regular profit is generated.
  • Opportunity to generate additional income over the stock held in a demat account.

Why is Theta so Important?

You can ignore theta but you can’t avoid it.

A majority of strategies especially income strategies are based out of a fundamental understanding of theta. The right understanding of theta would give you edge on how to deploy a particular strategy.

Strategy wise & Options Portfolio wise theta would be explained in a later article.

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