UNDERSTANDING  PAYOFF GRAPHS OF BUYER AND SELLER
 

In this chapter, we will explain the concepts of buying and selling call and put options, and then create payoff graphs from both the buyer’s and seller’s perspectives.

But before that, it's essential to understand the differences between European and American options. You might have noticed the terms CE (Call European) and PE (Put European) options. Why do we primarily use European options? Why not American options? Let’s explore this.

When options were first introduced in India, there were two types available: European and American options. These options differ primarily in terms of when the option can be exercised.

European Options

Imagine Aisha, an investor, who buys a HDFC 2500 Call option. European options can only be exercised on the expiration date, meaning Aisha must wait until the expiry to exercise her right. The settlement is based on the value of the spot market on the expiry day.

For Aisha to be profitable, HDFC must be trading above the breakeven point on that day. If HDFC is trading at Rs. 2550 on the expiration date, Aisha can exercise her option to buy at Rs. 2500 and immediately sell at Rs. 2550, making a profit (minus the premium paid). However, if HDFC is trading below Rs. 2500, the option is worthless, and Aisha loses the premium paid.

American Options

Now, consider Aisha's friend, Rohan, who buys a HDFC 2500 Call option, but this time it’s an American option. This flexibility allows Rohan to exercise his right anytime before the expiration date. 

Let's say HDFC is trading at Rs. 2400 when Rohan buys the option. The next week, news breaks that boosts HDFC’s price to Rs. 2600. Rohan can immediately exercise his option to buy at Rs. 2500, sell at Rs. 2600, and make a profit, without waiting for the expiration date. This ability to act on favourable market movements anytime introduces an additional layer of strategy and risk management.

Why the Difference Matters

The ability to exercise American options at any time introduces additional risk for the seller, who could be called upon to fulfil the option at any moment. This risk means American options generally have higher premiums compared to European options.

In India, all options are now European, meaning they can only be exercised on the expiration date. This change simplifies the market and reduces the premium costs, providing a more straightforward trading environment.

Now that we are clear with our understanding of european and american contracts .Let’s move forward and try to understand the Payoff graph of a call buyer -

As a call option buyer, your goal is to capitalise on the potential rise in the price of the underlying asset while limiting your downside risk to the premium paid. Buying a call option is a strategic move when you expect the price of the asset to increase. The maximum loss you can incur is the premium paid, which makes it a controlled risk with potentially unlimited upside.

Intrinsic Value (IV) and Break-even Point

To better understand your position as a call option buyer, it’s crucial to grasp the concept of intrinsic value.

The intrinsic value (IV) of the option upon expiry (specifically a call option for now)

is defined as the non – negative value which the option buyer is entitled to if he

were to exercise the call option. In simple words ask yourself (assuming you are the

buyer of a call option) how much money you would receive upon expiry, if the call

option you hold is profitable. Mathematically it is defined as –

IV = Spot Price – Strike Price

For example, if you have a call option with a strike price of Rs. 4150 and the spot price is Rs. 4300, the intrinsic value would be Rs. 150 (4300 - 4150). However, if the spot price is below the strike price, the intrinsic value is zero because exercising the option would not be profitable.

The break-even point for a call option is the point where the underlying asset's price equals the strike price plus the premium paid. This is the price at which the call option buyer starts to make a profit.

Formula for Break-even Point

Break-even Point=Strike Price+Premium Paid

For instance, if the strike price is Rs. 4150 and the premium paid is Rs. 42.20, the break-even point would be Rs. 4192.20.

To illustrate this, let’s use a detailed table with the provided data and see how the payoff changes with different spot prices:

Payoff Graph for Call Option Buyer

Now we can use the above data to plot a graph of a call buyer , and it would look something like this.

The payoff graph for a call option buyer shows potential profit and loss at different spot prices. Here’s a simplified explanation of how it works:

1. Maximum Loss : The maximum loss is limited to the premium paid. For example, if you paid a premium of Rs. 42.20, this is the most you can lose.( you can see a red straight line after the marked strike price , that represents that loss is limited to a fixed number)

2. Profit Potential: The profit potential is theoretically unlimited. As the spot price of the underlying asset increases above the break-even point, the profit increases. ( you can see a a green line steadily increasing that shows the increase in profit after the breakeven point)

3. Break-even Point: This is where the spot price equals the strike price plus the premium. Above this point, the call option buyer starts making a profit. ( the slope marked in red between the strike price and BEP is the line showing the shift in buyer’s P&L and finally buyer is about to make money.)

Summary from call buyer perspective

Being a call option buyer offers a strategic advantage in leveraging market movements with limited risk. By understanding the intrinsic value and break-even points, you can make informed decisions and potentially maximize your profits while keeping losses manageable. The payoff graph provides a visual representation of potential outcomes, helping you to plan your trades effectively. With the knowledge of how these elements work together, you are better equipped to navigate the market and capitalize on upward trends.

Call seller’s perspective

Now, Derivative has basic property i.e. it is a zero sum game.

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 to bear 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 understand your position as a call option seller, it’s crucial to grasp the concept of intrinsic value. The intrinsic value of a call option is the difference between the spot price (current market price) and the strike price, provided this difference is positive.

Formula for Intrinsic Value

IV=Spot Price−Strike Price

For example, if you have sold a call option with a strike price of Rs. 4150 and the spot price is Rs. 4300, the intrinsic value would be Rs. 150 (4300 - 4150). If the spot price is below the strike price, the intrinsic value is zero, as exercising the option would not be profitable for the buyer.

The break-even point for a call option seller is the point where the underlying asset's price equals the strike price plus the premium received. This is the price at which the call option seller starts to incur a loss.

Formula for Break-even Point

Break-even Point=Strike Price+Premium Received

For instance, if the strike price is Rs. 4150 and the premium received is Rs. 42.20, the break-even point would be Rs. 4192.20.

To illustrate this, let’s use a detailed table with the provided data and see how the payoff changes with different spot prices:

Payoff Graph for Call Option Seller

The payoff graph for a call option seller shows potential profit and loss at different spot prices. Here’s a simplified explanation of how it works:

1.  Maximum Profit : The maximum profit is limited to the premium received. For example, if you received a premium of Rs. 42.20, this is the most you can earn.

2. Loss Potential: The loss potential is theoretically unlimited. As the spot price of the underlying asset increases above the break-even point, the loss increases.

3. Break-even Point: This is where the spot price equals the strike price plus the premium. Above this point, the call option seller starts incurring a loss.

Summary

Being a call option seller offers the benefit of receiving immediate income through premiums. However, it comes with the risk of potentially unlimited losses if the underlying asset's price rises significantly but 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.

The payoff graph provides a visual representation of potential outcomes, helping you to plan your trades with a clear understanding of the risks and rewards. With this knowledge, you are better equipped to use call options as part of your trading strategy.



Now, Let’s understand P&L of a Put Option Buyer

As a put option buyer, your objective is to profit from a decline in the price of the underlying asset. Buying a put option gives you the right, but not the obligation, to sell the underlying asset at a predetermined strike price before the option expires. This strategy is typically used when you expect the price of the asset to fall. The maximum loss you can incur is the premium paid, making it a controlled risk with the potential for substantial profit if the asset's price drops significantly.

Intrinsic Value (IV) and Break-even Point

To understand your position as a put option buyer, it’s crucial to grasp the concept of intrinsic value. The intrinsic value of a put option is the difference between the strike price and the spot price (current market price), provided this difference is positive.

Formula for Intrinsic Value

IV=Strike Price−Spot Price

For example, if you have a put option with a strike price of Rs. 34000 and the spot price is Rs. 31000, the intrinsic value would be Rs. 3000 (34000 - 31000). However, if the spot price is above the strike price, the intrinsic value is zero because exercising the option would not be profitable.

The break-even point for a put option is the point where the underlying asset's price equals the strike price minus the premium paid. This is the price at which the put option buyer starts to make a profit.

Formula for Break-even Point

Break-even Point=Strike Price−Premium Paid

For instance, if the strike price is Rs. 34000 and the premium paid is Rs. 800, the break-even point would be Rs. 33200.

Example Table and Payoff Graph

To illustrate this, let’s use a detailed table with the provided data and see how the payoff changes with different spot prices:

Please note that the negative sign before the premium paid represents a cash out flow from the trading account.

Payoff Graph for Put Option Buyer

The payoff graph for a put option buyer shows potential profit and loss at different spot prices. Here’s a simplified explanation of how it works:

1.Maximum Loss: The maximum loss is limited to the premium paid. For example, if you paid a premium of Rs. 800, this is the most you can lose.

2. Profit Potential: The profit potential is substantial. As the spot price of the underlying asset decreases below the break-even point, the profit increases.

3.Break-even Point: This is where the spot price equals the strike price minus the premium. Below this point, the put option buyer starts making a profit.

Summary

Being a put option buyer offers a strategic advantage in leveraging market downturns with limited risk. By understanding the intrinsic value and break-even points, you can make informed decisions and potentially maximize your profits while keeping losses manageable. The payoff graph provides a visual representation of potential outcomes, helping you to plan your trades effectively. With the knowledge of how these elements work together, you are better equipped to navigate the market and capitalize on downward trends.

At last we have Put Option Seller

As a put option seller, your primary goal is to generate income through the premiums received from selling options. Selling put options can be a strategic move when you expect the price of the underlying asset to remain flat or increase. The major benefit is that you receive the premium upfront, providing immediate cash flow. However, selling put options comes with the risk of substantial losses if the underlying asset's price falls significantly.

Intrinsic Value (IV) Calculation

To understand your position as a put option seller, it’s crucial to grasp the concept of intrinsic value. The intrinsic value of a put option is the difference between the strike price and the spot price (current market price), provided this difference is positive.

Formula for Intrinsic Value:

IV=Strike Price−Spot Price

For example, if you have sold a put option with a strike price of Rs. 34000 and the spot price is Rs. 31000, the intrinsic value would be Rs. 3000 (34000 - 31000). If the spot price is above the strike price, the intrinsic value is zero, as exercising the option would not be profitable for the buyer.

The break-even point for a put option seller is the point where the underlying asset's price equals the strike price minus the premium received. This is the price at which the put option seller starts to incur a loss.

Formula for Break-even Point

Break-even Point=Strike Price−Premium Received

For instance, if the strike price is Rs. 34000 and the premium received is Rs. 800, the break-even point would be Rs. 33200.

Example Table and Payoff Graph

To illustrate this, let’s use a detailed table with the provided data and see how the payoff changes with different spot prices:

Payoff Graph for Put Option Seller

The payoff graph for a put option seller shows potential profit and loss at different spot prices. Here’s a simplified explanation of how it works:

1. Maximum Profit : The maximum profit is limited to the premium received. For example, if you received a premium of Rs. 800, this is the most you can earn.

2. Loss Potential: The loss potential is substantial. As the spot price of the underlying asset decreases below the break-even point, the loss increases.

3. Break-even Point: This is where the spot price equals the strike price minus the premium. Below this point, the put option seller starts incurring a loss.
 

Summary

Being a put option seller offers the benefit of receiving immediate income through premiums. However, it comes with the risk of substantial losses if the underlying asset's price falls significantly. By understanding the intrinsic value and break-even points, you can make informed decisions and potentially manage your risks more effectively. The payoff graph provides a visual representation of potential outcomes, helping you to plan your trades with a clear understanding of the risks and rewards. With this knowledge, you are better equipped to use put options as part of your trading strategy.


In the next chapter , we will understand something called moneyness of options.