Buying and Selling Call Options: Components of Option Premium

As we learnt in the previous chapters, a call option gives the option holder the right but not the obligation to buy the underlying at a predetermined price from the option writer.

So, a call option with a strike price of Rs 500 can be interpreted as an option that will give its buyer the right to buy the underlying instrument from the seller of the option for Rs 500 regardless of what the price of the underlying instrument might be at the time of exercise of the option.

To give the option holder the right to exercise the contract at will, the call option writer charges an amount called the premium from the buyer.

option premium is made up of two components:

1. Intrinsic Value of the Option

The Intrinsic value of an option is the difference between the spot and strike price, which is also the pay-off for the option.

For a call option the intrinsic value is calculated as spot price minus strike price.

2. Time Value of Option

The time value of an option is calculated as the difference between the option premium and its intrinsic value.

The longer the time to expiry, the higher the time value of an option as the probability of getting a favourable price movement is higher. For instance, if you are a call option buyer, the chances of the price of the underlying instrument going up would be higher if the period is one month as opposed to just a couple of days.

The time value of an option decays to zero on the expiry of the option.

Before moving on to the number crunching part, let us try and understand why are call options widely used and for what purposes.

As mentioned before, a call option gives its holder the right to buy the underlying at a certain price. The writer/seller of the call option is obligated to

sell the underlying to the option holder should the holder choose to exercise this right as per the option contract.

The buyer of the option expects the price of the underlying to rise and the seller expects the price to drop (at least not rise) based on their research and analysis of the underlying instrument.

In order for the call option contract to be profitable, the buyer expects the price of the underlying to rise above the strike price or else the buyer stands to suffer a loss limited to amount of premium paid.

Similarly, the seller of the option expects the price of the underlying won’t rise above the strike price or else the seller can suffer unlimited loss that will be reduced by the amount of premium received.

Let’s say you want to buy 100 shares of Company N which is currently trading for Rs 500 in the market with the following option contracts available:

LONG Call Option with Strike of Rs 480 with Premium of Rs 10 expiring in one month.

If the underlying price rises to Rs 510 after one month, this is how the payoff and profit scenarios will look for the parties involved:

• The option buyer will receive a payoff of Rs 30 per option. The payoff will be calculated as the difference between the spot price of Rs 510 and strike price of Rs 480. The buyer will receive a total payoff of Rs 3,000 (Rs 30 x 100 lot size per contract).
• The total profit for the option buyer will amount to Rs 2,000. To attain the total profit, the amount of premium paid is subtracted from the total payoff.
  Profit to buyer = Rs 3,000 – Rs 1,000 (100 contracts x premium of Rs 10 per share)
• The option seller will suffer a gross loss of Rs 30 per option. The payoff will be calculated as the difference between the strike price of Rs 480 and spot price of Rs 510. The seller will suffer a gross total loss of Rs 3,000 (Rs 30 x 100 contracts). This loss will be reduced by Rs 1,000 that is the amount of premium received.
• The net loss to the seller will amount to Rs 2,000.
  Loss to seller = Rs 1,000 (Premium received) – Rs 3,000 (loss due option exercise by buyer)

LONG Call Option with Strike of Rs 500 with Premium of Rs 5 expiring in one month.

If the underlying price rises to Rs 505 after one month, this how the payoff and profit scenarios will look for the parties involved:

• The option buyer will receive a payoff of Rs 5 per option. The payoff will be calculated as the difference between the spot price of Rs 505 and strike price of Rs 500. The buyer will receive a total payoff of Rs 500 (Rs 5 x 100 contracts).
• The profit for the option buyer will amount to Rs 0 after incorporating the amount of premium paid.
  Profit to buyer = Rs 500 – Rs 500 (100 contracts x premium of Rs 5 per share)
• The option seller will suffer a gross loss of Rs 5 per option. The payoff will be calculated as the difference between the strike price of Rs 500 and spot price of Rs 505. The seller will suffer a loss of Rs 0 as his loss will be reduced by Rs 500, the amount of premium received.
• The net loss to the seller will amount to Rs 0.
  Loss to seller = Rs 500 (Premium received) – Rs 500 (loss due option exercise by buyer)

Long Call Option with Strike of Rs 520 with Premium of Rs 2 expiring in one month.

If the underlying price rises to Rs 510 after one month, this how the payoff and profit scenarios will look for the parties involved:

• Since the option is out of the money, the option holder will not exercise their option to buy underlying.
• The loss to option buyer will be equal to amount of premium paid.
  Loss to buyer = Rs 200 (100 contracts x premium of Rs 2 per share)
• The option seller will make a profit of Rs 2 per option as the option was not exercised by the holder.
  Profit to seller = Rs 200 (Premium received)

An important point to note, in all above examples, the cost of brokerage and other statutory costs are assumed to be zero for the purpose of simplicity.