Professional Trading through Option Theory

Lesson -> Concept of 'Theta"

14.1 -As we know 'Time is Money'

Keep in mind the old adage, "Time is money". It seems that this adage is very relevant to options trading. We will now focus on one fundamental concept about time. Let's say you have signed up for a competitive exam. You are naturally bright and capable of clearing the exam. However, if the exam is not given enough time and you don't brush up on the concepts, what chance do you have of passing? It all depends on how much you prepare for the exam. Let's put this in perspective. We can compare the chances of passing the exam to the preparation time.

The likelihood of passing the exam is higher if you have prepared for the exam for more days. Keep the same logic in your mind. Let's say Nifty Spot is 8500 and you purchase a Nifty 8700 call option. What is the chance that this call option will expire In The Money (ITM). Let's rephrase the question as mentioned below-

  • Nifty currently stands at 8500. What is the probability of Nifty moving 200pts over the next 30 Days and 8700 CE expiring ITM, given that Nifty is at 8500?
    • Nifty could move 200 points in the next 30 trading days. The likelihood that an option will expire upon expiry is high
  • What if the expiry date is only 15 days?
    • It is reasonable to expect that Nifty will move 200pts over the next 15-days. Therefore, the probability of an option expiring upon expiry is (notice that it isn't very high but just high).
  • What if the expiry date is only five days?
    • Well, it's been 5 days and 200 points. We aren't really sure why 8700 CE will expire in the money. Low
  • What if there were only one day left before expiry?
    • It is unlikely that Nifty will move 200 points in a single day.

What can we infer from this? The likelihood that the option will expire In the Money is greater the longer it takes. Keep this in mind as you shift your focus to the 'Option Seller. An option seller is someone who sells or writes an option and gets the premium. He is well aware that selling an option can be risky and have limited reward potential. He only gets the premium he pays. Only if the option is worthless, he gets to keep his premium. Think about this: If he sells an option in the first month, he clearly knows the following.

  1. He is aware that he is subject to unlimited risk and has limited reward potential
  2. He also knows that there is a possibility for the option he sells to transition into ITM option. This means that he won't get his reward (premium earned).

In fact, the option can expire in the cash at any time, due to "time" (although the chance of this happening decreases as the date approaches). An option seller wouldn't want to sell options because of this. Why would an option seller want to sell options if they know that the option could expire in the future? Time is clearly a risk in the context of option sellers. What if an option buyer offers to pay for the time risk that he (or the seller) takes? It would be sensible to weigh the compensation against the time risk and make a call. This is exactly what happens in real-world options trade. You are actually paying for - when you pay a premium to trade options.

  1. Time Risk
  2. Optional intrinsic value

Premium is Time value + Intrinsic Val . We have already mentioned that 'Intrinsic' refers to the money you would receive if your option were exercised today. Let's refresh our memory by calculating the intrinsic value of the following options, assuming that Nifty is at 84223 -

  1. 8350 CE
  2. 8450 CE
  3. 8400 PE
  4. 8450 PE

The intrinsic value is always either a positive or zero value and cannot be lower. If the value turns negative, the intrinsic value will be considered zero. For Call options, the intrinsic value is " Spike Price – Strike Price" while for Put options it is " Stike Price – Spot Price". The intrinsic values of the options above are therefore as follows:

  1. 8350 CE = 8243 - 8350 = +73
  2. 8450 CE = 8243 - 8450 = 0.
  3. 8400 PE = 8400 + 8423 = -ve Value hence 0
  4. 8450 PE =
    8450 + 8423 = +27

Now that we have an idea of how to calculate the intrinsic worth of an option, let's try to extract the time value as well as the intrinsic value from the premium. Take a look at this snapshot.

These are some details to be aware of:

  • Spot Value = 8531
  • Strike = 8600 CE
  • Status = OTM
  • Premium = 99.4
  • Today's date = 6 7th July 2015.
  • Expiry: 30 th Jul 2015

The intrinsic value of a call option is Spot Price & Strike Price, i.e 8531-8600 = 0. (since it's negative) We know that Premium = Time value + Intrinsic Value 99.4 =Time Value + 0. This means that Time value = 99.4. Can you see it? For an option with no intrinsic value, but high time value, the market will pay Rs.99.4/-. Time is money I took a picture of the same contract the next day, 7 July.
The underlying value of the option premium has increased slightly (8538), but it has fallen quite a lot! Let's break down the premium into its intrinsic and time values - Spot price - Strike price i.e 8538-85600 = 0. (since it is a negative value). We also know that Premium = Time value + Intrinsic 87.9 = 0 This means that Time value = 87.9. You can see the overnight decline in premium value. Soon, we will understand why. Notice - The premium value drop is 99.4 minus.9. = 11.5. This is due to a decrease in volatility, and time.Volatility will be discussed in the next chapter. To make it clear, we will talk about volatility in the next chapter. If spot and volatility were constant, then the decline in premiums would be entirely due to the passage time. This drop in premium would probably be about Rs.5 to Rs.11.5/-, as I suspect. Let's take another example:
(IMAGE 3).

  • Spot Value = 8514.5
  • Strike = 8450 CE
  • Status = ITM
  • Premium = 160
  • Today's date = 7 July 2015
  • Expiry: 30 th Jul 2015

The intrinsic value of a call option - Spot price - Strike price i.e. 8514.5 – 8450 = 64.5. We know that premium = Time value + intranic value 160 = Time value + 64.5. This means that the Time value = 160 + 64.5 = Time value + 95.5. Traders are therefore paying 64.5 towards intrinsic and 95.5 towards time value out of the total premium amount of Rs.160. For all options (both calls or puts), you can do the same calculation and subtract the premium from the Time value.

14.2 - Understanding 'Time movement'

Time, as we all know, moves in one direction. Think of the expiry date being the target time, and consider the time's movement. As time passes, the days left for expiry decreases. Let me ask you the following question: With 18 trading days before expiry traders will pay Rs.100/- towards the time value. Would they be willing to do the same if it was only 5 days? They would not, of course. They will be less willing to pay for time when there is less time before it expires. Here is a snapshot I took in the earlier months -
(IMAGE 4).

  • Date = 29 thApril
  • Expiry Date: 30 April
  • Time until expiry = 1 Day
  • Strike = 190
  • Spot = 179.6
  • Premium = 30 Paisa
  • Intrinsic Value = 179.5 - 190 = 0. It's a negative value and is 0
  • Time value should equal the premium by 30 paisa.

A time value of 30 paise is acceptable for traders who have one day before expiry. If the expiry date was longer than 20 days, the time value would be Rs.5/Rs.8/-. My point is that as the expiry date draws nearer, the time remaining to redeem the option becomes shorter and shorter. This means that option buyers will pay less for time value. If an option buyer today pays Rs.10 for the time value, tomorrow he will likely pay Rs.9.5/= as the time price. We can draw a crucial conclusion: "All things being equal, an options is a depreciating asset." The passage of time causes the option's premium to decrease each day. The next question is: How much would the premium drop on a daily basis due to the passage time? This question can be answered by Theta, the 3 Option Greek.

14.3 - Concept of Theta

As the expiration date approaches, all options - both calls and puts - lose value. The time decay coefficient, also known as Theta, is the rate at what an option loses its value with time. Theta is the number of points that are lost each day, even if all other conditions remain constant. Theta is always positive because time moves in one direction. However, traders may sometimes refer to it as a negative number. Thetas of -0.5 mean that the option premium will lose 0.5% for each day that passes. If an option trades at Rs.2.75/$ with a Theta of 0.05, it will trade at Rs.2.70/$ the next day (assuming that other things remain constant). An option buyer who has a long option will always have a negative ita. This means that the buyer of the option will lose money every day. An option seller will have a shorter option with a positive theta. Theta is a friendlier Greek for the option seller. The option seller's objective is to keep the premium. The option seller can profit from the loss of premium over time, as options are losing value every day. If an option seller has sold options at Rs.54 with a 0.75 theta, then the same option will trade at -=0.75 * 3. = 2.25 = 54 – 2.25 = 51.75. The seller can close the option position at T+ 3 days by buying it back at Rs.51.75/. and making Rs.2.25. This is due to theta. Take a look at this graph.

This graph shows how the premium falls as the expiry date approaches. This graph can be termed as "Time Decay" graph. The graph shows the following:

  1. The option is not worth much at the beginning of the series, when there are many days before expiry. The option traded at 350 when it had 120 days before expiry. However, it was at 300 when it expired after 100 days. low is the result of theta.
  2. The effect of theta on the series is high as we get closer to the expiry date. Notice that when the option was expiring in 20 days, it traded at around 150. However, as we get closer to expiry, the premium drops to below 50.

If you sell options at the beginning of the series, you will have the advantage of a high premium value. However, the premium rate drops. Options can be sold closer to expiry. You will receive a lower premium, but the premium drop is large. This is beneficial to options sellers. Theta is an easy to comprehend and simple Greek word. When we discuss cross dependencies between Greeks, we will return to theta. For now, you can assume you have fully understood what's being said here. Now, let's move on to the most fascinating Greek - Vega.


  1.    For time risk option sellers always gets compensatation  
  2. Premium = Intrinsic Value +Time Value
  3. Options lose money every day, all else being equal, due to Theta
  4. Theta, which is positive, represents the fact that time moves in one direction.
  5. Theta is a friendly Greek option seller
  6. You can make a lot of money if you sell naked options early in the series. However, the premium due to time falls is very low.
  7. The premium drops rapidly when a short option is close to expiry. This is due to time value.