How to Calculate Payoffs in a Put Option

Calculation of put option payout

So, you’re wondering about how to calculate payoffs in a put option? Well, calculating the put option payout is quite similar to the process for computing payoffs in a call option. For the purpose of our calculations, we’ll take up a hypothetical put option contract of Infosys Limited. More specifically, we’ll analyse the INFY JUL 700 PE (here, the PE denotes put option) contract and see exactly how you can benefit from trading the said contract.  

That said, let’s first check out some preliminary details with respect to the stock and the contract.

• Assume that currently, Infosys Limited is trading at Rs. 750 in the spot (cash) market. 
• We have a buyer, Aditya, who expects that the share price of Infosys would fall by the date of expiry, which in this case is July 30, 2020. 
• Therefore, Aditya wants to have the option to sell the shares at a higher price in the future. 
• There’s a corresponding trader, Nikhil, who expects that the share price would actually rise by the date of expiry. 
• So, Nikhil wants to buy the shares of Infosys Limited at a lower price in the future. 
• Therefore, they both enter into the INFY JUL 700 PE contract on July 1, 2020. 
• Here, the buyer of the put option is Aditya and the seller of the put option is Nikhil.
• According to the put option contract, Nikhil essentially gives Aditya the right to sell 100 shares of Infosys Limited on July 30, 2020 for Rs. 750 per share.    
• In return for giving Aditya the right to sell, Nikhil charges a premium of Rs. 10 per share from Aditya, which comes up to Rs. 1,000 (Rs. 10 x 100 shares)

Clear with the specifics of the stock and the contract? Now, let’s take a look at four different scenarios and their respective put option payout calculations.   

Scenario 1: On the expiry date, say the shares of Infosys Limited are trading at Rs. 600 each.

Aditya’s point of view 

• Since the price of the share has decreased, just as per Aditya’s expectations, he chooses to exercise his put option. 
• In other words, he basically exercises his right to sell 100 shares of Infosys at Rs. 750 instead of at the current market price, which is just Rs. 600. 
• So, from this entire put option trade, Aditya makes a notional profit of Rs. 15,000 [(Rs. 750 - Rs. 600) x 100 shares]. 
• The total net profit that Aditya gets to enjoy if he buys the shares from the cash market and sells it to Nikhil in accordance with the put option contract is Rs. 14,000 (Rs. 15,000 - Rs. 1,000). Here, Rs. 1,00 is the premium Aditya paid Nikhil for buying the put option contract from him.

Nikhil’s point of view 

• Since Aditya exercised his right, Nikhil is obligated to buy 100 shares of Infosys Limited at Rs. 750 each from him even though the market price per share is Rs. 600. 
• Therefore, from this put option trade, Nikhil makes a notional loss of Rs. 15,000 [(Rs. 750 - Rs. 600) x 100 shares]. 
• The total net loss that Nikhil has to bear when he buys the shares sold by Aditya at Rs. 750 each instead of at the current market price is Rs. 14,000 (Rs. 15,000 - Rs. 1,000). Here, Rs. 1,00 is the premium received from Aditya for selling him the put option contract.

Let’s take a brief look at the cash flow of both Aditya and Nikhil as a consequence of this put option trade. 

Particulars	Aditya’s cash flow		Particulars	Nikhil’s cash flow
Premium paid on July 01, 2020 (A)	(Rs. 1,000)		Premium received on July 01, 2020 (A)	Rs. 1,000
Profit from the put option trade (B)	Rs. 15,000		Loss from the put option trade (B)	(Rs. 15,000)
Net profit (A + B)	Rs. 14,000		Net loss (A + B)	(Rs. 14,000)

Scenario 2: On the expiry date, say the shares of Infosys Limited are trading at Rs. 900 each.

Aditya’s point of view 

• Since the price of the share has increased and gone contrary to Aditya’s expectations, he chooses to walk away and not exercise his put option. 
• In other words, Aditya doesn’t exercise his right to sell 100 shares of Infosys Limited at Rs. 750 each to Nikhil. This is because Aditya would incur a loss if he sold the shares at Rs. 750 instead of the current market price of Rs. 900, which is higher.  
• So, from this entire put option contract, Aditya’s total loss is limited to only the premium he paid at the time of entering into the contract with Nikhil, which is just Rs. 1,000. 

Nikhil’s point of view 

• Since Aditya chose to not exercise his right, Nikhil cannot force him to sell the shares of Infosys Limited to him at Rs. 750 per share.  
• Therefore, on the expiry date, no trade occurs. 
• However, Nikhil gets to keep the premium that Aditya paid at the time of entering into the contract with him, which is Rs. 1,000. This premium amount is his profit from the put option contract. 

Let’s take a brief look at the cash flow of Aditya and Nikhil as a consequence of this put option contract. 

Particulars	Aditya’s cash flow		Particulars	Nikhil’s cash flow
Premium paid on July 01, 2020 (A)	(Rs. 1,000)		Premium received on July 01, 2020 (A)	Rs. 1,000
On the date of expiry (B)	Rs. 0		On the date of expiry (B)	0
Net loss (A + B)	(Rs. 1,000)		Net profit (A + B)	Rs. 1,000

Scenario 3: Before the expiry date, say on July 20, 2020, the shares of Infosys are trading at Rs. 600 each.

Aditya’s point of view

• In this case, Aditya’s expectations of the downtrend in the price of Infosys shares have come true.
• However, he does not want to wait till expiry to make a profit. He wants to profit off this downtrend right away.
• And so, he sells his put option contract to another trader named Pankaj through the stock exchange. This action is termed as squaring off a position.  
• Now, Aditya becomes the put option seller with Pankaj as the put option buyer.
• Since he’s the buyer here, Pankaj pays a premium to Aditya. And seeing as the price movements are in favor of Aditya’s views, he gets to charge a higher premium, say Rs. 3,000 (Rs. 30 per share x 100 shares).
• Once this trade is executed, Aditya is left with a profit of Rs. 2,000 (Rs. 3,000 that he got from Pankaj minus Rs. 1,000 that he paid to Nikhil).

Now let’s take a brief look at the cash flow of Aditya as a consequence of this put option trade.

Particulars	Aditya’s cash flow
Premium paid to Nikhil on July 01, 2020 (A)	(Rs. 1,000)
Premium received from Pankaj on July 20, 2020 (B)	Rs. 3,000
Net Profit (A + B)	Rs. 2,000

Scenario 4: Before the expiry date, say on July 20, 2020, the shares of Asian Paints Limited are trading at Rs. 900 each.

Aditya’s point of view 

• In such a scenario, Aditya senses that the price trend is going up, contrary to what he expected.
• Scared that it may go further up as the expiry date nears, Aditya wants to square off his position by selling off his contract right away, so that he can limit his losses. 
• And so, he sells his put option contract to Pankaj and squares off his position.
• As in the previous scenario, Aditya becomes the put option seller and Pankaj becomes the put option buyer.
• So, Pankaj ends up paying a premium to Aditya. 
• But since the price movements are not in favor of Aditya’s views, he doesn’t get to charge a very high premium. Let’s assume that he sells his put option contract to Pankaj for a premium of only Rs. 400 (Rs. 4 per share x 100 shares).
• Once this put option trade is done, Aditya is left with a loss of Rs. 600 (Rs. 1,000 that he paid to Nikhil minus Rs. 400 that he got from Pankaj). 
• This is less than the loss of Rs. 1,000, which he would have otherwise made had he waited till expiry.

Here’s how the cash flow of Aditya as a consequence of this put option trade looks like.

Particulars	Aditya’s cash flow
Premium paid to Nikhil on July 01, 2020 (A)	(Rs. 1,000)
Premium received from Pankaj on July 20, 2020 (B)	Rs. 400
Net Loss (A + B)	(Rs. 600)

Wrapping up

So, this is how to calculate payoffs with respect to put options. Now that we’ve seen quite a bit of the practical side of the options market, it’s time to get to know some of the important theoretical concepts, so you can understand these instruments better. This is where options theory becomes important. Head to the next chapter to be introduced to this essential concept.

A quick recap

• Calculating the put option payoff is quite similar to the process for computing payoffs in a call option.
• For the buyer of the put option, the maximum possible loss is limited to the premium paid. The maximum possible gain is potentially unlimited.
• For the seller of the put option, the maximum possible gain is limited to the premium paid. The maximum possible loss is potentially unlimited.
• The buyer of the put can choose to square off their position instead of holding it till expiry.