Understanding the payoff to the buyer of an option

When you buy an option you get the right without the obligation. A call option is a right to buy without the obligation and a put option is a right to sell without the obligation. Since the option loss is restricted to the premium paid, the maximum loss is capped at that level. However, profits can be unlimited on the upside. That is what makes buying options attractive to traders and investors. When you buy options you need to understand the option payoff and break up the performance of the option under difference circumstances.

So, what exactly is the option payoff definition? It is the profitability of the option under different price conditions. There is a strike price at which you buy the option and that becomes the reference for evaluating your option pay-off. The call option payoff formula is nothing but the simulation of the option profitability under different price circumstances. How to calculate option payoff? Let us understand that with an example.

Understanding Option Payoff for buyer with a live example
Let us assume that X has purchased a 700 call option on Tata Steel at a premium of Rs.15 when the spot price is Rs.695. In this case, 700 becomes the strike price while Rs.15 is the premium or the option cost. The spot price is the price at which Tata steel is quoting at the time the option was purchased and this spot price will keep changing over time. The table below captures the pay-off of the option for the buyer of the option at different spot prices..
 

Price ScenarioProfit / LossOption CostOption P/LNet Pay offAction taken670015-15-15Left to expire680015-15-15Left to expire690015-15-15Left to expire700015-15-15Indifferent7101015-15-5Exercised7202015-155Exercised7303015-1515Exercised7404015-1525Exercised7505015-1535Exercised

 
As we can see in the table above there are 3 different payoff scenarios for the buyer of the option. The actual price of the option will vary with the market price but for sake of simplicity we have only considered the intrinsic value and not the time value of the option. Let us look at 3 such scenarios that emerge from the above table..

Scenario 1 – This scenario is shaded in yellow. In this scenario the price of Tata Steel is below the strike price of Rs.700. Such options are called Out of the Money (OTM) options. The option buyer will not see any point in exercising the option at Rs.700 when he can buy the stock at lower levels in the open market itself. So he will just let the option expire. But the Rs.15 paid is a sunk cost and so that is a fixed loss for the buyer of the option.

Scenario 2 – This scenario is shaded in light blue. This is when the stock price of Tata Steel is at or above the strike price of Rs.700 but it is still not covering the cost of the premium. For example when the market price of Tata Steel is Rs.710, he will exercise the option at Rs.700. In the process he is earning a profit of Rs.10 to partially offset his premium cost of Rs.15. In scenario 2, the buyer of the call option is still not making profits but he is reducing his losses due to the premium commitment.

Scenario 3 – This scenario is shaded in grey. In this scenario he is actually making a profit on the option position after considering his premium cost. In the above case of call option, the fixed premium cost is Rs.15, so above Rs.715, the buyer of the call option starts making net profits and this will continue without any limitations on the upside.

Understanding the payoff of the call option with charts



In the above chart the net payoff of the 700 call option is presented diagrammatically under different price scenarios. There are 3 phases in this chart. In the first phase when the market price of Tata Steel is below Rs.700, the diagram is a straight horizontal line as your losses are fixed at Rs.15. In the second phase (between the price of Rs.700 and Rs.715) you are gradually reducing the net cost of the premium that you have already sunk in. The point at which the graph intersects the X-axis is the breakeven point of Rs.715. In the third phase from Rs.715 onwards, the buyer of the option is making unlimited profits as the price also covers the premium cost.

Understanding option payoffs is the key to understand the extensive use of options in trading and hedging your risk in markets. A similar logic can be applied to put options too!

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