Pay off Diagrams for Options
This sub‑topic explains payoff diagrams for exchange‑traded currency options. It shows how profit and loss vary with the underlying exchange rate at expiry, and why understanding these graphs is essential for NISM Series I questions. The content links the visual diagram to the underlying payoff formulas used in SEBI‑regulated option contracts.
Learning Objectives
- 1Define a payoff diagram and identify its axes.
- 2Derive the profit formulas for long and short call and put positions.
- 3Interpret break‑even points, maximum profit and maximum loss from the diagram.
- 4Apply the concepts to a typical Indian currency‑option exam scenario.
What is a Payoff Diagram?
A payoff diagram is a graphical representation that plots the option holder’s profit or loss (Y‑axis) against the spot exchange rate of the underlying currency pair at expiry (X‑axis). In the Indian market, the underlying is often USD/INR or EUR/INR, and the diagram helps traders visualise how their position behaves as the rate moves.
The diagram consists of three key components: the strike price (the vertical line where the option becomes exercisable), the premium paid or received (shifts the whole curve up or down), and the shape of the curve which differs for calls and puts as well as for long versus short positions. SEBI’s definition of an exchange‑traded option requires the contract to be settled in cash, so the payoff is purely monetary.
For the exam, you will be asked to identify the correct diagram for a given position, compute the break‑even level, or recognise the maximum loss. A common trap is to ignore the premium and read the diagram as if it shows pure intrinsic value only. Remember: the diagram always reflects profit after accounting for the premium.
- Underlying price (S_T) – spot rate at expiry.
- Strike price (K) – predetermined rate at which the option can be exercised.
Many candidates draw the diagram correctly but forget to shift it by the premium paid or received. The exam expects the profit curve, not just the intrinsic value. Always subtract the premium for long positions and add it for short positions.
Payoff Formulas – Long Positions
Where:
S_T= Spot exchange rate at expiry (INR per USD)K= Strike price of the call option (INR per USD)P_c= Premium paid for the call option (INR per unit)Worked Example
Given S_T = 85, K = 80, P_c = 2: Step 1: Intrinsic = max(0, 85 - 80) = 5 Step 2: Profit = 5 - 2 = 3 Verification: max(0,85-80) - 2 = 3.
Where:
S_T= Spot exchange rate at expiry (INR per USD)K= Strike price of the put option (INR per USD)P_p= Premium paid for the put option (INR per unit)Worked Example
Given S_T = 70, K = 80, P_p = 2: Step 1: Intrinsic = max(0, 80 - 70) = 10 Step 2: Profit = 10 - 2 = 8 Verification: max(0,80-70) - 2 = 8.
The formulas above capture the net profit after the premium is accounted for. For a long call, profit starts only when the spot rate exceeds the strike; the break‑even point is therefore K + P_c. For a long put, profit begins when the spot falls below K, and the break‑even is K - P_p.
When you plot these equations, the long‑call curve is flat (loss equal to the premium) up to the strike, then rises linearly with a slope of +1. The long‑put curve mirrors this behaviour with a negative slope until the strike, after which it flattens. Both diagrams are bounded below by the premium paid, meaning the maximum loss cannot exceed the premium.
In NISM questions, you may be given the premium and asked to locate the break‑even price on the diagram, or you may be asked which curve represents a long put. Remember the direction of the slope: call profits rise with higher rates, put profits rise with lower rates.
Payoff Formulas – Short Positions
Where:
S_T= Spot exchange rate at expiry (INR per USD)K= Strike price of the call option (INR per USD)P_c= Premium received for writing the call (INR per unit)Worked Example
Given S_T = 90, K = 80, P_c = 2: Step 1: Intrinsic = max(0, 90 - 80) = 10 Step 2: Profit = 2 - 10 = -8 Verification: 2 - max(0,90-80) = -8.
Where:
S_T= Spot exchange rate at expiry (INR per USD)K= Strike price of the put option (INR per USD)P_p= Premium received for writing the put (INR per unit)Worked Example
Given S_T = 70, K = 80, P_p = 2: Step 1: Intrinsic = max(0, 80 - 70) = 10 Step 2: Profit = 2 - 10 = -8 Verification: 2 - max(0,80-70) = -8.
Short positions receive the premium up‑front, so the profit curve starts at +Premium. For a short call, the profit stays flat until the spot exceeds the strike, after which it declines with a slope of –1, leading to unlimited loss potential. The short‑put curve behaves oppositely: profit is flat until the spot falls below the strike, then it drops with a –1 slope, but the loss is limited to the strike minus premium.
Because the seller bears the risk of the option being exercised, SEBI requires higher margin requirements for short calls than for short puts. In exam questions, you may be asked to identify which position has unlimited loss – the answer is always the short call.
When drawing the diagram, remember to shift the entire curve upward by the premium received. The break‑even point for a short call is K + P_c, and for a short put it is K – P_p.
Comparative Summary
Payoff Characteristics for Currency Options
| Position | Payoff Direction | Maximum Profit | Maximum Loss |
|---|---|---|---|
| Long Call | Limited profit, Unlimited loss | Unlimited (theoretically) | Premium paid (P_c) |
| Long Put | Limited profit, Unlimited loss | Unlimited (theoretically) | Premium paid (P_p) |
| Short Call | Limited loss, Unlimited profit | Premium received (P_c) | Unlimited |
| Short Put | Limited loss, Unlimited profit | Premium received (P_p) | Strike – Premium (K - P_p) |
Visualising Payoffs – Sample Chart
Profit/Loss at Expiry for Different Option Positions (K=80, Premium=2)
Interpreting the Diagram for Exam Questions
When you look at a payoff chart, locate the point where the curve crosses the horizontal axis – this is the break‑even price. For the long call in the chart, the break‑even is at 82 (K + Premium). The region to the right of this point shows profit, while the left side shows a loss equal to the premium.
For short positions, the profit zone is on the opposite side of the strike. The short call’s profit remains at the premium until the spot reaches 82, after which the curve falls into loss territory. Recognising these zones helps you answer multiple‑choice questions that ask which price range yields a profit.
Remember the shape: calls have an upward‑sloping tail on the right, puts on the left. Unlimited loss appears as a line that continues indefinitely beyond the strike. These visual cues are frequently tested in NISM’s “identify the correct payoff diagram” items.
NISM‑Style Example
Scenario
An Indian exporter expects to receive USD 1,00,000 in three months. To protect against a fall in USD/INR, the exporter buys a USD/INR put option with strike 78 INR/USD, premium 1.5 INR/USD, and contract size 1,000 USD. At expiry, the spot rate is 73 INR/USD. Calculate the net profit from the option and comment on the hedging effectiveness.
Solution
Step 1: Intrinsic value = max(0, 78 - 73) = 5 INR/USD. Step 2: Gross profit = 5 × 1,000 = 5,000 INR. Step 3: Total premium paid = 1.5 × 1,000 = 1,500 INR. Step 4: Net profit = 5,000 - 1,500 = 3,500 INR. The exporter locks in a higher INR amount than the market rate, gaining 3,500 INR after premium, confirming the hedge worked as intended.
Conclusion
The example shows how the payoff formula translates into a real‑world profit figure. In the exam, you will be asked to compute net profit using the same steps.
Profit is positive, loss is negative. Many candidates mistakenly write the short‑call payoff as +max(0, S‑K) instead of Premium – max(0, S‑K). Keep the sign consistent with the direction of cash flow.
⭐Exam Takeaways
- Payoff diagram axes: underlying price (X) vs profit/loss after premium (Y).
- Long call profit = max(0, S_T‑K) ‑ premium; break‑even at K + premium.
- Long put profit = max(0, K‑S_T) ‑ premium; break‑even at K ‑ premium.
- Short call profit = premium ‑ max(0, S_T‑K); unlimited loss beyond K + premium.
- Short put profit = premium ‑ max(0, K‑S_T); loss limited to K ‑ premium.
- In diagrams, calls rise on the right side, puts rise on the left side.
- Always shift the curve by the premium to obtain the true profit line.
- For NISM questions, identify the correct curve, locate break‑even, and note unlimited loss positions.
Practice Questions
8 questions on Pay off Diagrams for Options
In a payoff diagram for an exchange‑traded currency option, what is plotted on the X‑axis and Y‑axis respectively?
What is the break‑even spot rate for a long call position?
A trader buys a long put with strike 85 INR/USD, premium 3 INR per unit. At expiry the spot rate is 78 INR/USD. What is the net profit per unit?
Which of the following option positions carries unlimited loss potential?
Refer to the sample payoff chart (K=80, Premium=2). What is the profit for a short put when the spot rate is 70 INR/USD?
If a short put has strike 80 INR/USD and premium received 2 INR per unit, at what spot rate does the position break even?
A common exam trap is to ignore the premium when drawing a payoff diagram. What effect does this have on the displayed profit line for a long position?
An Indian exporter buys a USD/INR put option with strike 78, premium 1.5 INR/USD, contract size 1,000 USD. Spot at expiry is 73 INR/USD. What is the net profit in INR?