Call Options
A call option gives the buyer the right (but not the obligation) to purchase the underlying asset at the strike price (K) on or before the expiry date.
Call Option Payoff at Expiry:
- Buyer's payoff = max(ST − K, 0) − Premium
- Seller's payoff = Premium − max(ST − K, 0)
The call buyer profits when the spot price (ST) exceeds the break-even point (K + Premium). The call writer profits if ST ≤ K (option expires worthless).
Put Options
A put option gives the buyer the right to sell the underlying at the strike price.
Put Option Payoff at Expiry:
- Buyer's payoff = max(K − ST, 0) − Premium
- Seller's payoff = Premium − max(K − ST, 0)
Break-even for put buyer = K − Premium. The put is useful for downside protection (portfolio insurance).
Moneyness
| Moneyness | Call | Put | Intrinsic Value |
|---|---|---|---|
| In-the-Money (ITM) | S > K | S < K | Positive |
| At-the-Money (ATM) | S ≈ K | S ≈ K | Zero |
| Out-of-the-Money (OTM) | S < K | S > K | Zero |
Option Premium Components
Option Premium = Intrinsic Value + Time Value
- Intrinsic Value: Amount by which the option is ITM. Always ≥ 0.
- Time Value: Premium attributable to the remaining time until expiry. Decreases as expiry approaches (Theta decay). Highest for ATM options.
Put-Call Parity
For European options on non-dividend-paying assets:
C − P = S − PV(K)
or equivalently: C + PV(K) = P + S
Where PV(K) = K × e−rT = present value of strike price.
This is a fundamental no-arbitrage relationship. If violated, riskless arbitrage profit is possible.
European vs American Options
- European: Can only be exercised at expiry. All index options (Nifty, Bank Nifty) in India are European.
- American: Can be exercised any time before expiry. All single-stock options in India are American-style.