NISM PracticeOption payoffs: calls, puts, buyers and sellers
Every option question at expiry comes down to one comparison, between the strike price and the price of the underlying, and one subtraction, of the premium.
The four positions
| Position | Right or obligation | View | Maximum profit | Maximum loss |
|---|---|---|---|---|
| Buy a call (long call) | Right to buy at the strike | Price will rise | Unlimited | Premium paid |
| Sell a call (short call) | Obligation to sell at the strike if exercised | Price will not rise | Premium received | Unlimited |
| Buy a put (long put) | Right to sell at the strike | Price will fall | Strike − premium (if the price falls to zero) | Premium paid |
| Sell a put (short put) | Obligation to buy at the strike if exercised | Price will not fall | Premium received | Strike − premium |
Formulas at expiry
- Call payoff = the greater of (Spot − Strike) and 0.
- Put payoff = the greater of (Strike − Spot) and 0.
- Buyer's profit = Payoff − Premium.
- Seller's profit = Premium − Payoff.
- Break-even, call = Strike + Premium. Break-even, put = Strike − Premium.
The buyer's gain is always the seller's loss, rupee for rupee.
Call option: strike ₹100, premium ₹5
| Price at expiry (₹) | Option payoff (₹) | Buyer's profit or loss (₹) | Seller's profit or loss (₹) |
|---|---|---|---|
| 85 | 0 | -5 | +5 |
| 95 | 0 | -5 | +5 |
| 100 | 0 | -5 | +5 |
| 103 | 3 | -2 | +2 |
| 105 | 5 | +0 | +0 |
| 110 | 10 | +5 | -5 |
| 120 | 20 | +15 | -15 |
Below ₹100 the call expires worthless and the buyer loses the ₹5 premium. Between ₹100 and ₹105 the buyer exercises but does not recover the whole premium. At ₹105 the buyer breaks even. Above that, profit rises rupee for rupee with the price. The seller's column is the mirror image.
Put option: strike ₹200, premium ₹8
| Price at expiry (₹) | Option payoff (₹) | Buyer's profit or loss (₹) | Seller's profit or loss (₹) |
|---|---|---|---|
| 170 | 30 | +22 | -22 |
| 185 | 15 | +7 | -7 |
| 192 | 8 | +0 | +0 |
| 196 | 4 | -4 | +4 |
| 200 | 0 | -8 | +8 |
| 210 | 0 | -8 | +8 |
| 225 | 0 | -8 | +8 |
Above ₹200 the put expires worthless. Break-even is ₹192. Below that, the buyer's profit grows as the price falls.
Moneyness
| Call | Put | |
|---|---|---|
| In the money | Spot above strike | Spot below strike |
| At the money | Spot equal to strike | Spot equal to strike |
| Out of the money | Spot below strike | Spot above strike |
Intrinsic value and time value
Before expiry, an option's premium has two parts.
- Intrinsic value is what the option would be worth if exercised now: for a call, Spot − Strike if positive, otherwise zero; for a put, Strike − Spot if positive, otherwise zero.
- Time value = Premium − Intrinsic value. It reflects the chance that the option gains value before expiry.
Example. A call with strike ₹90 trades at ₹14 when the share is at ₹100. Intrinsic value = ₹10. Time value = 14 − 10 = ₹4. An out-of-the-money option has no intrinsic value; its whole premium is time value. At expiry, time value is zero.
What moves the premium before expiry
| If this rises | Call premium | Put premium | Greek |
|---|---|---|---|
| Price of the underlying | Rises | Falls | Delta |
| Volatility | Rises | Rises | Vega |
| Time to expiry | Rises | Generally rises | Theta (decay as time passes) |
| Interest rate | Rises | Falls | Rho |
Gamma, the fifth Greek, measures how fast delta itself changes.
Lot size
Exchange-traded options are traded in lots. Multiply the per-share figure by the lot size to get the rupee profit or loss. With a lot of 500 shares, the call buyer above who makes ₹7 a share at an expiry price of ₹112 earns 7 × 500 = ₹3,500. Lot sizes and contract specifications are set by the exchanges and are revised; a question will state the lot size to use.
Steps for any question
- Call or put? Buyer or seller?
- Compute the payoff from strike and expiry price.
- Subtract the premium for the buyer; subtract the payoff from the premium for the seller.
- Multiply by lot size and number of lots if a rupee total is asked.
- Check the sign: profit or loss.
Common slips
- Forgetting the premium and giving the payoff as the profit.
- Treating a put like a call.
- Giving the buyer's answer when the seller's is asked.
- Saying the seller of a call has limited loss. The loss is unlimited, because the price can rise without limit.
- Thinking an out-of-the-money option at expiry has some value. It has none.
Practise these in the Equity Derivatives question set, and see futures pricing for the other half of the paper's arithmetic.
Questions candidates ask
How do I calculate the profit on a call option?
At expiry, payoff = spot price minus strike price, if positive, otherwise zero. The buyer's profit is the payoff minus the premium paid.
What is the break-even of a put option?
Strike price minus the premium.
What is the maximum loss for an option buyer?
The premium paid. An option seller's loss can be much larger, and for a call seller it is unlimited.
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