Selling/Writing a Call Option

4.1 – Two sides of the same coin

Do you remember the 1975 Bollywood super hit flick ‘Deewaar’, which attained a cult status for the incredibly famous ‘Mere paas maa hai’ dialogue ☺? The movie is about two brothers from the same mother. While one brother, righteous in life grows up to become a cop, the other brother turns out to be a notorious criminal whose views about life is diametrically opposite to his cop brother.

Well, the reason why I’m talking about this legendary movie now is that the option writer and the option buyer are somewhat comparable to these brothers. They are the two sides of the same coin. Of course, unlike the Deewaar brothers there is no view on morality when it comes to Options trading; rather the view is more on markets and what one expects out of the markets. However, there is one thing that you should remember here – whatever happens to the option seller in terms of the P&L, the exact opposite happens to option buyer and vice versa. For example if the option writer is making Rs.70/- in profits, this automatically means the option buyer is losing Rs.70/-. Here is a quick list of such generalisations –

• If the option buyer has limited risk (to the extent of premium paid), then the option seller has limited profit (again to the extent of the premium he receives)
• If the option buyer has unlimited profit potential then the option seller potentially has unlimited risk
• The breakeven point is the point at which the option buyer starts to make money, this is the exact same point at which the option writer starts to lose money
• If option buyer is making Rs.X in profit, then it implies the option seller is making a loss of Rs.X
• If the option buyer is losing Rs.X, then it implies the option seller is making Rs.X in profits
• Lastly if the option buyer is of the opinion that the market price will increase (above the strike price to be particular) then the option seller would be of the opinion that the market will stay at or below the strike price…and vice versa.

To appreciate these points further it would make sense to take a look at the Call Option from the seller’s perspective, which is the objective of this chapter.

Before we proceed, I have to warn you something about this chapter – since there is P&L symmetry between the option seller and the buyer, the discussion going forward in this chapter will look very similar to the discussion we just had in the previous chapter, hence there is a possibility that you could just skim through the chapter. Please don’t do that, I would suggest you stay alert to notice the subtle difference and the huge impact it has on the P&L of the call option writer.

4.2 – Call option seller and his thought process

Recall the ‘Ajay-Venu’ real estate example from chapter 1 – we discussed 3 possible scenarios that would take the agreement to a logical conclusion –

1. The price of the land moves above Rs.500,000 (good for Ajay – option buyer)
2. The price stays flat at Rs.500,000 (good for Venu – option seller)
3. The price moves lower than Rs.500,000 (good for Venu – option seller)

If you notice, the option buyer has a statistical disadvantage when he buys options – only 1 possible scenario out of the three benefits the option buyer. In other words 2 out of the 3 scenarios benefit the option seller. This is just one of the incentives for the option writer to sell options. Besides this natural statistical edge, if the option seller also has a good market insight then the chances of the option seller being profitable are quite high.

Please do note, I’m only talking about a natural statistical edge here and by no way am I suggesting that an option seller will always make money.

• The stock has been heavily beaten down, clearly the sentiment is extremely weak
• Since the stock has been so heavily beaten down – it implies many investors/traders in the stock would be stuck in desperate long positions
• Any increase in price in the stock will be treated as an opportunity to exit from the stuck long positions
• Given this, there is little chance that the stock price will increase in a hurry – especially in the near term
• Since the expectation is that the stock price won’t increase, selling the Bajaj Auto’s call option and collecting the premium can be perceived as a good trading opportunity

With these thoughts, the option writer decides to sell a call option. The most important point to note here is – the option seller is selling a call option because he believes that the price of Bajaj Auto will NOT increase in the near future. Therefore he believes that, selling the call option and collecting the premium is a good strategy.

As I mentioned in the previous chapter, selecting the right strike price is a very important aspect of options trading. We will talk about this in greater detail as we go forward in this module. For now, let us assume the option seller decides to sell Bajaj Auto’s 2050 strike option and collect Rs.6.35/- as premiums. 

Let us now run through the same exercise that we ran through in the previous chapter to understand the P&L profile of the call option seller and in the process make the required generalizations. The concept of an intrinsic value of the option that we discussed in the previous chapter will hold true for this chapter as well.

Before we proceed to discuss the table above, please note –

1. The positive sign in the ‘premium received’ column indicates a cash inflow (credit) to the option writer
2. The intrinsic value of an option (upon expiry) remains the same irrespective of call option buyer or seller
3. The net P&L calculation for an option writer changes slightly, the logic goes like this
   1. When an option seller sells options he receives a premium (for example Rs.6.35/). He would experience a loss only after he losses the entire premium. Meaning after receiving a premium of Rs.6.35, if he loses Rs.5/- it implies he is still in profit of Rs.1.35/-. Hence for an option seller to experience a loss he has to first lose the premium he has received, any money he loses over and above the premium received, will be his real loss. Hence the P&L calculation would be ‘Premium – Intrinsic Value’
   2. You can extend the same argument to the option buyer. Since the option buyer pays a premium, he first needs to recover the premium he has paid, hence he would be profitable over and above the premium amount he has received, hence the P&L calculation would be ‘ Intrinsic Value – Premium’.

The table above should be familiar to you now. Let us inspect the table and make a few generalizations (do bear in mind the strike price is 2050) –

1. As long as Bajaj Auto stays at or below the strike price of 2050, the option seller gets to make money – as in he gets to pocket the entire premium of Rs.6.35/-. However, do note the profit remains constant at Rs.6.35/-.
   1. Generalization 1 – The call option writer experiences a maximum profit to the extent of the premium received as long as the spot price remains at or below the strike price (for a call option)
2. The option writer experiences a loss as and when Bajaj Auto starts to move above the strike price of 2050
   1. Generalization 2 – The call option writer starts to lose money as and when the spot price moves over and above the strike price. Higher the spot price moves away from the strike price, larger the loss.
3. From the above 2 generalizations, it is fair to conclude that, the option seller can earn limited profits and can experience unlimited loss

We can put these generalizations in a formula to estimate the P&L of a Call option seller –

P&L = Premium – Max [0, (Spot Price – Strike Price)]

Going by the above formula, let’s evaluate the P&L for a few possible spot values on expiry –

1. 2023
2. 2072
3. 2055

The solution is as follows –

@2023

= 6.35 – Max [0, (2023 – 2050)]

= 6.35 – Max [0, -27]

= 6.35 – 0

= 6.35

The answer is in line with Generalization 1 (profit restricted to the extent of premium received).

@2072

= 6.35 – Max [0, (2072 – 2050)]

= 6.35 – 22

= -15.56

The answer is in line with Generalization 2 (Call option writers would experience a loss as and when the spot price moves over and above the strike price)

@2055

= 6.35 – Max [0, (2055 – 2050)]

= 6.35 – Max [0, +5]

= 6.35 – 5

= 1.35

Though the spot price is higher than the strike, the call option writer still seems to be making some money here. This is against the 2nd generalization. I’m sure you would know this by now, this is because of the ‘breakeven point’ concept, which we discussed in the previous chapter.

Anyway let us inspect this a bit further and look at the P&L behavior in and around the strike price to see exactly at which point the option writer will start making a loss.

Clearly even when the spot price moves higher than the strike, the option writer still makes money, he continues to make money till the spot price increases more than strike + premium received. At this point he starts to lose money, hence calling this the ‘breakdown point’ seems appropriate.

Breakdown point for the call option seller = Strike Price + Premium Received

For the Bajaj Auto example,

= 2050 + 6.35

= 2056.35

So, the breakeven point for a call option buyer becomes the breakdown point for the call option seller.

4.3 – Call Option seller pay-off

As we have seen throughout this chapter, there is a great symmetry between the call option buyer and the seller. In fact the same can be observed if we plot the P&L graph of an option seller.

The call option sellers P&L payoff looks like a mirror image of the call option buyer’s P&L pay off. From the chart above you can notice the following points which are in line with the discussion we have just had –

1. The profit is restricted to Rs.6.35/- as long as the spot price is trading at any price below the strike of 2050
2. From 2050 to 2056.35 (breakdown price) we can see the profits getting minimized
3. At 2056.35 we can see that there is neither a profit nor a loss
4. Above 2056.35 the call option seller starts losing money. In fact, the slope of the P&L line clearly indicates that the losses start to increase as and when the spot value moves away from the strike price

4.4 – A note on margins

Think about the risk profile of both the call option buyer and a call option seller. The call option buyer bears no risk. He just has to pay the required premium amount to the call option seller, against which he would buy the right to buy the underlying at a later point. We know his risk (maximum loss) is restricted to the premium he has already paid.

However, when you think about the risk profile of a call option seller, we know that he bears an unlimited risk. His potential loss can increase as and when the spot price moves above the strike price. Having said this, think about the stock exchange – how can they manage the risk exposure of an option seller in the backdrop of an ‘unlimited loss’ potential? What if the loss becomes so huge that the option seller decides to default?

Clearly, the stock exchange cannot afford to permit a derivative participant to carry such a huge default risk, hence it is mandatory for the option seller to park some money as margins. The margins charged for an option seller is similar to the margin requirement for a futures contract.

And here is the margin requirement for selling 2050 call option.

As you can see the margin requirements are somewhat similar in both the cases (option writing and trading futures). Of course there is a small difference; we will deal with it at a later stage. For now, I just want you to note that option selling requires margins similar to futures trading, and the margin amount is roughly the same.

4.5 – Putting things together

I hope the last four chapters have given you all the clarity you need with respect to call options buying and selling. Unlike other topics in Finance, options are a little heavy duty. Hence I guess it makes sense to consolidate our learning at every opportunity and then proceed further. Here are the key things you should remember with respect to buying and selling call options.

With respect to option buying

• You buy a call option only when you are bullish about the underlying asset. Upon expiry the call option will be profitable only if the underlying has moved over and above the strike price
• Buying a call option is also referred to as ‘Long on a Call Option’ or simply ‘Long Call’
• To buy a call option you need to pay a premium to the option writer
• The call option buyer has limited risk (to the extent of the premium paid) and an potential to make an unlimited profit
• The breakeven point is the point at which the call option buyer neither makes money nor experiences a loss
• P&L = Max [0, (Spot Price – Strike Price)] – Premium Paid
• Breakeven point = Strike Price + Premium Paid

With respect to option selling

• You sell a call option (also called option writing) only when you believe that upon expiry, the underlying asset will not increase beyond the strike price
• Selling a call option is also called ‘Shorting a call option’ or simply ‘Short Call’
• When you sell a call option you receive the premium amount
• The profit of an option seller is restricted to the premium he receives, however his loss is potentially unlimited
• The breakdown point is the point at which the call option seller gives up all the premium he has made, which means he is neither making money nor is losing money
• Since short option position carries unlimited risk, he is required to deposit margin
• Margins in case of short options is similar to futures margin
• P&L = Premium – Max [0, (Spot Price – Strike Price)]
• Breakdown point = Strike Price + Premium Received

Other important points

• When you are bullish on a stock you can either buy the stock in spot, buy its futures, or buy a call option
• When you are bearish on a stock you can either sell the stock in the spot (although on a intraday basis), short futures, or short a call option
• The calculation of the intrinsic value for call option is standard, it does not change based on whether you are an option buyer/ seller
• However the intrinsic value calculation changes for a ‘Put’ option
• The net P&L calculation methodology is different for the call option buyer and seller.
• Throughout the last 4 chapters we have looked at the P&L keeping the expiry in perspective, this is only to help you understand the P&L behavior better
• One need not wait for the option expiry to figure out if he is going to be profitable or not
• Most of the option trading is based on the change in premiums
• For example, if I have bought Bajaj Auto 2050 call option at Rs.6.35 in the morning and by noon the same is trading at Rs.9/- I can choose to sell and book profits
• The premiums change dynamically all the time, it changes because of many variables at play, we will understand all of them as we proceed through this module
• Call option is abbreviated as ‘CE’. So Bajaj Auto 2050 Call option is also referred to as Bajaj Auto 2050CE. CE is an abbreviation for ‘European Call Option’.

4.6 – European versus American Options

Initially when option was introduced in India, there are two types of options available – European and American Options. All index options (Nifty, Bank Nifty options) were European in nature and the stock options were American in nature. The difference between the two was mainly in terms of ‘Options exercise’.

European Options – If the option type is European then it means that the option buyer will have to mandatory wait till the expiry date to exercise his right. The settlement is based on the value of spot market on expiry day. For example if he has bought a Bajaj Auto 2050 Call option, then for the buyer to be profitable Bajaj Auto has to go higher than the breakeven point on the day of the expiry. Even not it the option is worthless to the buyer and he will lose all the premium money that he paid to the Option seller.

American Options – In an American Option, the option buyer can exercise his right to buy the option whenever he deems appropriate during the tenure of the options expiry. The settlement is dependent of the spot market at that given moment and not really depended on expiry. For instance he buys Bajaj Auto 2050 Call option today when Bajaj is trading at 2030 in spot market and there are 20 more days for expiry. The next day Bajaj Auto crosses 2050. In such a case, the buyer of Baja Auto 2050 American Call option can exercise his right, which means the seller is obligated to settle with the option buyer. The expiry date has little significance here.

For people familiar with option you may have this question – ‘Since we can anyway buy an option now and sell it later, maybe in 30 minutes after we purchase, how does it matter if the option is American or European?’.

Valid question, well think about the Ajay-Venu example again. Here Ajay and Venu were to revisit the agreement in 6 months time (this is like a European Option). If instead of 6 months, imagine if Ajay had insisted that he could come anytime during the tenure of the agreement and claim his right (like an American Option). For example there could be a strong rumor about the highway project (after they signed off the agreement). In the back of the strong rumor, the land prices shoots up and hence Ajay decides exercise his right, clearly Venu will be obligated to deliver the land to Ajay (even though he is very clear that the land price has gone up because of strong rumors). Now because Venu carries addition risk of getting ‘exercised’ on any day as opposed to the day of the expiry, the premium he would need is also higher (so that he is compensated for the risk he takes).

For this reason, American options are always more expensive than European Options.

Also, you maybe interested to know that about 3 years ago NSE decided to get rid of American option completely from the derivatives segment. So all options in India are now European in nature, which means the buyer can exercise his option based on the spot price on the expiry day.

We will now proceed to understand the ‘Put Options’.

Key takeaways from this chapter

1. You sell a call option when you are bearish on a stock
2. The call option buyer and the seller have a symmetrically opposite P&L behaviour
3. When you sell a call option you receive a premium
4. Selling a call option requires you to deposit a margin
5. When you sell a call option your profit is limited to the extent of the premium you receive and your loss can potentially be unlimited
6. P&L = Premium – Max [0, (Spot Price – Strike Price)]
7. Breakdown point = Strike Price + Premium Received
8. In India, all options are European in nature