Look across an option chain and the put and call prices at each strike appear to be set independently — one by bearish demand, the other by bullish demand. They are not independent at all.
A single relationship ties them together, and understanding it explains several things on the chain that otherwise look like coincidences or opportunities.
The relationship, in words first
Take a call option and a put option on the same underlying, with the same strike and the same expiry. Consider two portfolios.
Portfolio A: buy the call option, and hold cash equal to the present value of the strike price — enough that, with interest, it becomes exactly the strike amount at expiry.
Portfolio B: buy the put option, and hold the underlying itself.
At expiry, work through what each is worth. If the underlying finishes above the strike, Portfolio A exercises the call using the cash and owns the underlying; Portfolio B lets the put expire and still owns the underlying. Both hold one unit of the underlying. If the underlying finishes below the strike, Portfolio A lets the call expire and holds cash equal to the strike; Portfolio B exercises the put and receives the strike. Both hold the strike in cash.
In every possible outcome the two portfolios end with the same value. And two things guaranteed to be worth the same at a future date must cost the same today, or somebody could buy the cheaper one, sell the dearer one, and collect the difference without risk.
Written compactly: call price + present value of strike = put price + price of underlying. That is put-call parity, stated for European-style options on an underlying that pays nothing in the meantime.
What it explains on an Indian option chain
Indian index and stock options are European-style, exercisable only at expiry, which is the setting where parity holds most cleanly. Several things you see on a chain follow directly from it.
The call and put at one strike share an implied volatility, roughly. If they did not, parity would be violated. Where the chain shows a meaningful difference between call and put implied volatility at the same strike, it is usually the effect of spreads, the rate assumption, dividends, or stale quotes rather than a genuine mispricing.
Futures and options are consistent with each other. Because a futures contract already embeds the cost of carry, parity can be expressed using the futures price in place of the underlying plus financing. That is why traders often read the synthetic futures price implied by a call and put at the same strike — and why it tracks the actual futures price closely.
At-the-money call and put prices differ for a reason. People sometimes expect them to be equal at the strike nearest the current price. Parity shows why they are not: the financing term and expected dividends shift the balance, so the call at the at-the-money strike is normally somewhat more expensive than the put when rates are positive and no large dividend is expected.
Dividends move the relationship. An expected dividend lowers the forward value of the underlying, which makes calls cheaper and puts dearer relative to each other than they would otherwise be. A chain that looks skewed around a dividend date often is simply reflecting this.
Synthetic positions
Rearranging the parity relationship shows that any one of the instruments can be recreated from the others. These combinations are called synthetic positions.
Synthetic long underlying: buy a call option and sell a put option at the same strike and expiry. The combined position gains and loses almost exactly like holding the underlying, or a long futures position.
Synthetic short underlying: sell a call option and buy a put option at the same strike and expiry.
Synthetic long call: hold the underlying and buy a put option — which is precisely the protective put, viewed from a different angle.
Synthetic long put: be short the underlying and buy a call option.
Knowing these is useful for understanding rather than for cleverness. A trader holding shares with a bought put already holds something that behaves like a call. A position combining a sold put and a bought call at one strike carries the full downside of owning the underlying, which is easy to miss when each leg is viewed separately. And the margin and cost of building a position one way versus another can differ, even when the payoff is the same.
Why it is rarely a free lunch
The obvious question is whether a violation of parity on the chain is an opportunity. For a retail participant, almost never, for four reasons.
Prices on the screen are not prices you can trade at. Parity uses a single price for each instrument. In reality you buy at the offer and sell at the bid, on four legs, and the spreads alone usually exceed any apparent gap.
Costs apply to every leg. Brokerage, statutory charges and exchange fees across multiple instruments quickly consume a small theoretical difference.
The inputs are assumptions. The financing rate and the expected dividends are estimates. A gap that appears under one set of assumptions can vanish under a slightly different, equally reasonable set.
Others are faster and cheaper. Participants with lower costs and automated execution close genuine gaps within moments. What remains visible to a retail screen is usually noise, a stale quote, or an illiquid strike where the gap cannot actually be captured.
So the value of parity for most people is not in trading it. It is in reading the chain correctly, recognising synthetic exposure in positions they already hold, and not mistaking an explained difference for a mistake by the market.
An account with the full chain
Call and put, bid and offer, side by side at each strike. Free to open
The relationship described is a simplified theoretical one; real markets include spreads, costs, dividends and financing differences. Contract specifications are set by the exchanges and revised periodically. This is educational material, not advice, and nothing here recommends any position. We run no tips group and no signal service, we manage nobody's money, and no return is promised. Options can lose their entire premium, and sold options can lose considerably more.
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Frequently Asked Questions
What is put-call parity?
The relationship that ties a call and a put with the same strike and expiry together: call price plus the present value of the strike equals put price plus the price of the underlying, for European-style options without dividends. Two positions with identical payoffs must cost the same.
Does put-call parity apply to Indian options?
Indian index and stock options are European-style, which is the setting where it holds most cleanly. In practice it is adjusted for financing, expected dividends and costs, and is often expressed using the futures price.
What is a synthetic long position?
Buying a call option and selling a put option at the same strike and expiry. The combined position behaves almost exactly like holding the underlying or a long futures contract, including carrying its full downside.
Why is the at-the-money call usually more expensive than the put?
Parity includes a financing term and expected dividends. With positive interest rates and no large dividend expected, the balance normally makes the call at the nearest strike somewhat dearer than the put.
Can I profit from a parity violation?
Rarely, as a retail participant. Bid-ask spreads on four legs, transaction costs, uncertain financing and dividend assumptions, and faster professional participants usually remove any gap. What looks like a violation is typically a stale quote or an illiquid strike.
Related Reading
- The options course, for Mumbai
- The financing term inside a futures price
- The protective put as a synthetic call
- Reading the chain this relationship explains
- Implied volatility and the Greeks
- The costs that close most apparent gaps
Disclaimer: TheFinBaba provides educational content only - this is not investment advice. Trading involves risk of loss.
