Calls and puts look like opposite bets, but at the same strike and expiry they are tightly linked. Knowing the price of the call, the strike and the price of the futures contract is enough to work out what the put should cost. This relationship is called put-call parity. It is one of the most useful ideas in options because it explains how the whole option chain hangs together, and it lets you build a "synthetic" futures position out of options.
Parity holds exactly for European options, which can only be exercised at expiry. All index and stock options in India are European, so it applies directly.
The idea in plain words
Hold two positions at the same strike K, say 25,000, and the same expiry: you buy the call and sell the put. At expiry:
- If NIFTY ends above 25,000, the call is worth NIFTY − 25,000 and the put is worthless.
- If NIFTY ends below 25,000, the call is worthless and the put you sold costs you 25,000 − NIFTY.
In both cases the pair is worth exactly NIFTY − 25,000. That is the same payoff as buying a NIFTY future at 25,000. So the pair must cost the same as a future bought at 25,000, which means its price must equal the gap between the actual futures price and 25,000. Otherwise someone could buy the cheaper one, sell the dearer one and lock in a riskless profit.
Call − Put = (Futures price − Strike) × discount factor
The discount factor accounts for interest between now and expiry. For a month or less it is very close to 1, so in practice call − put ≈ futures − strike. Using the cash index instead of futures, the version taught in textbooks is call − put = spot − strike × e^(−rT), but in India the futures form is simpler because futures already include interest and expected dividends.
A worked NIFTY example
Suppose NIFTY spot is 25,000 and the current-month NIFTY future trades at 25,100 with about a month left. At the 25,000 strike:
| Item | Price |
|---|---|
| 25,000 call | ₹300 |
| 25,000 put | ₹201 |
| Call − put | ₹99 |
| Futures − strike | 100 points |
The difference of about one point is the interest on the 100 points for a month. Parity holds.
Now check the synthetic long future: buy the 25,000 call for ₹300 and sell the 25,000 put for ₹201, a net cost of ₹99.
| NIFTY at expiry | Synthetic long (call − put − 99) | Future bought at 25,100 |
|---|---|---|
| 24,700 | −300 − 99 = −₹399 | −₹400 |
| 25,100 | +100 − 99 = +₹1 | ₹0 |
| 25,400 | +400 − 99 = +₹301 | +₹300 |
Per unit, the two positions are the same apart from the small interest difference. Multiply by the lot size for a real trade (check the current NIFTY lot size on NSE).
Read parity on the live chain
You can test parity on today's NIFTY chain. Take the at-the-money strike, subtract the put price from the call price, and add the strike:
The result is the market's implied forward: the price NIFTY is expected to trade at by expiry after interest and dividends. It should land close to the NIFTY futures price for the same expiry, and usually a little above the spot index. If the call is worth more than the put at the ATM strike, that is mainly the forward premium, not a bullish signal.
The same check works for BANKNIFTY:
Try two or three strikes. Each should give almost the same forward. Bigger differences usually come from wide bid-ask spreads on less traded strikes rather than from a real mispricing.
Synthetic positions you can build
| Synthetic | Built from |
|---|---|
| Long future | Buy call + sell put, same strike and expiry |
| Short future | Sell call + buy put, same strike and expiry |
| Long call | Long future + buy put (a protective put) |
| Long put | Short future + buy call |
| Short put | Long future + sell call (a covered call has the same shape) |
This is why a covered call and a short put at the same strike have the same payoff, and why a protective put behaves like a long call. Traders sometimes pick whichever version is cheaper to trade or needs less margin.
Arbitrage: conversions and reversals
If parity breaks, professional traders lock in the gap:
- Conversion: when the call is too expensive relative to the put, they sell the call, buy the put and buy the future. At expiry the three cancel and the gap is profit.
- Reversal: when the put is too expensive, they do the opposite: buy the call, sell the put and sell the future.
Because many firms run these trades all day, gaps on liquid NIFTY strikes are usually smaller than the costs of trading them: brokerage, taxes, bid-ask spreads and margin funding. For a retail trader, parity is a tool for understanding, not a free-money machine.
Why parity matters for traders
- It explains the chain. Once you know the call price at a strike, the put price follows. Option prices are not two separate markets.
- Calls and puts share one implied volatility. Because parity ties them together, the call and put at the same strike must have roughly the same implied volatility. Differences in IV across strikes (the volatility skew) are about strikes, not about calls against puts.
- It shows the forward. The forward, not the spot, is the real centre of an option chain. Pricing models such as Black-Scholes use it.
- Delta of the pair is 1. A long call plus a short put at the same strike has a delta of about +1, like a future. Adding such pairs changes your direction exposure one-for-one.
Where parity bends a little
- Dividends. For stock options, an expected dividend before expiry lowers the forward price and so raises puts relative to calls. Futures prices already include this.
- Interest rates. Longer expiries carry more interest, so the discount factor matters more for options several months out.
- Liquidity. Last traded prices on thin strikes may be stale, so a "broken" parity is often just an old price.
- Margins. A synthetic future needs margin on the short option leg, which may differ from the margin on a future.
Common mistakes
- Reading calls costlier than puts as bullish. At the ATM strike this is mostly the forward premium from interest.
- Comparing with spot instead of futures. Use the future for the same expiry, or remember to add the interest and dividend effect.
- Chasing tiny parity gaps. Costs usually exceed them for retail traders.
- Forgetting the short put risk in a synthetic long. It carries the full downside of a future, not the limited risk of a bought call.