Payoffs
Four lines on a chart settle most arguments about options. The buyer's loss is flat and their gain slopes; the seller's gain is flat and their loss slopes. Everything else is a combination of those four shapes.
Chapter 6 · Intermediate
A payoff diagram shows profit or loss at expiry against the price of the underlying. Four shapes, and they explain more than any amount of prose.
What you make, and lose, at expiry
Paid by the buyer, received by the seller.
- Break-even
- 24,150
- Maximum gain
- Unbounded
- Maximum loss
- ₹150
As the buyer you paid ₹150 and that is the most you can lose, however wrong you are. You need the underlying above 24,150 to be ahead — being right about direction is not enough, you have to be right by more than you paid, and before expiry.
Buying a call
You pay the premium. Below the strike the option expires worthless and you lose exactly the premium — a flat line. Above the strike it gains rupee for rupee with the underlying.
Break-even: strike + premium. A 24,000 call at ₹150 needs the index above 24,150 for the buyer to be ahead. At 24,100 the option is worth ₹100 and the buyer is still down ₹50.
That gap is the most commonly missed fact about options. Being right about direction is not enough; you have to be right by more than you paid.
Selling a call
The exact mirror. You receive the premium. Above the strike you lose rupee for rupee, without limit.
Maximum gain: the premium. Maximum loss: unbounded in principle, because there is no ceiling on how far the underlying can rise.
Put the two lines on one chart and the structure of the market is visible: they are reflections of each other. Every rupee the buyer makes, the seller loses.
Buying a put
You pay the premium. Above the strike it expires worthless and you lose the premium. Below the strike it gains as the underlying falls.
Break-even: strike − premium.
The gain is large but not infinite, because the underlying cannot fall below zero. That bound is the difference between a sold put and a sold call, and it matters in chapter 9.
Selling a put
You receive the premium and are obliged to buy at the strike if asked.
Maximum gain: the premium. Maximum loss: strike − premium, if the underlying goes to zero.
Bounded, and the bound is large. Selling a 24,000 put for ₹150 risks ₹23,850 a unit in the worst case, to earn ₹150.
The asymmetry, drawn
The table chapter 3 gave in words, now visible:
| Shape of gain | Shape of loss | |
|---|---|---|
| Buy a call | Sloping, unbounded | Flat, capped at premium |
| Sell a call | Flat, capped at premium | Sloping, unbounded |
| Buy a put | Sloping, large | Flat, capped at premium |
| Sell a put | Flat, capped at premium | Sloping, large |
The buyers have flat losses and sloping gains. The sellers have flat gains and sloping losses.
Neither side is better. The seller's higher probability of a small win is exactly compensated — in an efficiently priced market — by the size of the loss when it comes. That trade-off is the pricing, and chapter 9 is about why it feels different from how it is.
What the diagram leaves out
Three things, and each matters.
It is expiry only. Before expiry an option has time value, and its price moves for reasons the expiry diagram cannot show. Chapter 7.
It ignores margin along the way. A sold option's diagram shows the loss at expiry; chapter 5 showed that margin is demanded daily, and a position can be closed before it reaches the point the diagram describes.
It ignores costs. Brokerage, exchange fees and taxes shift every line down. For small premiums those costs are a large proportion, which is chapter 11.
Combinations
Every strategy with a name — spreads, straddles, condors — is two or more of these four lines added together. A bull call spread is buying one call and selling a higher one: the sloping gain gets a ceiling, and the premium paid is reduced.
Combinations change the shape; they do not change the arithmetic of chapter 1. Each leg has a counterparty, each leg costs money to trade, and more legs means more cost.
The point
A bought call loses the premium below the strike and gains above it, breaking even at strike plus premium; a sold call is the same line reflected, with a capped gain and an unbounded loss. Buyers have flat losses and sloping gains, sellers the reverse — and the diagram shows expiry only, ignoring time value, margin calls and costs.
Check yourself
4 questions. Every answer is explained afterwards, including the ones you get right — guessing correctly is not the same as knowing. Score 70% or more and the chapter is marked done.
Question 1 of 4
0 of 4 answered. You can submit with questions unanswered — they simply score zero.
Now do it with your own numbers
Draw the payoff for buying a 24,000 call at ₹150 and for selling the same call. Mark the break-even on each. Then say which one is holding the risk that cannot be bounded.
The two lines are mirror images across the horizontal axis, because every rupee one side makes is a rupee the other loses.