Guide · Derivatives · Updated 2026-09-23

Put-call parity is a band, not an equation, and most of its apparent breaks are prices from different moments

Most explanations of put-call parity stop at the formula and a promise that any violation is free money. The formula is the last line of an argument about two portfolios, and the argument says what the formula cannot: which trade enforces the relation and what that trade costs. Most free money turns out to be a price from a different moment, and the rest has a price of its own.

Two portfolios that cannot be priced differently

Hold two positions to the same expiry. Portfolio A is one call at strike K plus cash that grows to exactly K by expiry, worth K × DF today, where DF is the discount factor. Portfolio B is one put at the same strike and expiry plus one unit of the underlying.

If the index finishes above K, the call is worth the index less K, so A holds the index; the put expires worthless and B holds the index. If it finishes below K, the call is worthless and A holds K; the put is worth K less the index, so B holds K. In every state both are worth the larger of the index and the strike.

Two positions that pay the same in every state, with nothing paid between, must cost the same today, or buying the cheaper and selling the dearer locks in the difference with no exposure to the index. One unit of the index at expiry is worth F × DF today, so C + K × DF = P + F × DF, which rearranges to C − P = (F − K) × DF.

Three things are missing from that line. No volatility, so parity holds at any level of option prices provided the call and the put are priced together. No probability and no view, for the reason set out in the forward price is not a forecast. And no index level: the underlying enters through F, which already contains whatever the index distributes before expiry. The forward in a parity test on an Indian index should therefore be the traded future, not the index compounded at a money market rate, and the section on implied volatility measures what the second choice costs.

A synthetic is the same position, not an imitation of it

Rearranged, every position has a twin. A long call plus a short put at one strike is a long forward at that strike, the synthetic long; a short call plus a long put is the synthetic short; a long put plus a long future is a synthetic call; a long call plus a short future a synthetic put. Each matches its twin state by state at expiry: one claim in two wrappers.

On 18 September 2026 the 23,400 call on the monthly contract closed at 146.90 and the put at 172.85, so the synthetic long bought the index at 23,400 + (146.90 − 172.85) / DF = 23,374.00, against a future at 23,378.50. Why a gap of that size is not an opportunity, and what the gaps that remain are paying for, is the rest of this page. Three uses are genuine.

Replicating a futures exposure where no future exists. The exchange lists futures on the broad index in a three month cycle but options with four weekly expiries at any time (its contract specification for the index), so a position meant to settle on a weekly date can only be built from options. Since 1 April 2026 there is a second reason: STT falls on the seller at 0.15 per cent of an option's premium but 0.05 per cent of a future's whole price. Opened and closed before expiry at unchanged prices, the synthetic long at 23,400 costs 0.76 index points in statutory charges, 0.48 of it STT; the future costs 13.22, 11.69 of it STT. Under the earlier rates the figures were 0.60 and 6.21.

Getting out when one leg has stopped trading. On that session the 22,200 call did not trade once while the 22,200 put traded 15,632 times. A writer of the call does not need a buyer for it: buying the future and the 22,200 put completes a conversion with a fixed payoff, no STT is due on either purchase, and at expiry the call is assigned and its holder pays the exercise STT. A holder of the same call has the costlier mirror, a reversal that sells the future for 11.69 points of STT, worth it only where the dead leg's quoted spread is wider. The file holds no quotes, so that judgement is made on the screen.

Seeing that a short put is a covered call. A long future plus a short call at K pays the smaller of the index and K, less F: the short put's payoff plus the fixed sum K − F, and the premium difference today, C − P, is that sum discounted. It is one trade economically and two in the rulebook. NSE Clearing charges its extreme loss margin of 2 per cent of notional on a future and, separately, on a short option, so the covered call on a future carries ₹30,392 a lot more than the short put at these prices, and selling its future before expiry pays STT the short put never meets.

European exercise is what makes it an equation

The argument needs both portfolios to reach expiry intact. If the put could be exercised early, B would hold a right A lacks and the equality would split in two: for an underlying that pays nothing, American parity is only S − K ≤ C − P ≤ S − K × DF, and the space between the bounds is the value of early exercise, which prices alone do not reveal.

In India the contract settles it. NSE Clearing's settlement rules state that index options and options on individual securities are European, with automatic exercise at expiry. Index options have been European since trading began on 4 June 2001. Single stock options were American until contracts expiring from January 2011, after SEBI circular CIR/DNPD/6/2010 of 27 October 2010 let each exchange choose one style for all eligible stocks.

European exercise is what keeps a conversion locked: no leg can be assigned early, so the position holds until the settlement price is published, margin calls aside. It does not remove what follows exercise in single stocks, which have settled by delivery since the regulator's circular of December 2018 phased the segment across by the October 2019 expiry, the problem worked through in pin risk at expiry. Index options settle in cash on the closing value of the index on the last trading day, and the index future on the same number (NSE Clearing), which is what makes an index conversion exact.

The band is the price of the trade that enforces it

Two trades enforce parity. When the call is rich, sell it, buy the put and buy the future: a conversion, whose three legs sum at expiry to K − F in every state. When the call is cheap, do the reverse: a reversal, paying F − K. Both are riskless in payoff and neither is free, so the residual C − P − (F − K) × DF must beat one of their costs before anyone acts. Parity is a band from minus the reversal's cost to plus the conversion's, and inside it nothing pays.

The costs follow from published rates. STT from 1 April 2026 is 0.15 per cent of premium on the sale of an option, 0.15 per cent of intrinsic value on an option exercised, and 0.05 per cent of the traded price on the sale of a future (NSE circular NSE/FATAX/73524 of 31 March 2026, implementing the Finance Act 2026). The exchange's transaction charge with its IPFT contribution is ₹183 per crore on futures and ₹3,553 per crore of premium on options, each side (NSE/FA/73061, from 1 March 2026). The regulator's turnover fee is ₹10 per crore, stamp duty 0.002 per cent on the buyer of a future and 0.003 per cent on the buyer of an option, and GST 18 per cent on stock broking services (the exchange's page on SEBI turnover fees, STT and other levies), charged on brokerage, the exchange charge and the fee but not on STT or stamp duty. At the strike nearest the forward, held to expiry:

The asymmetry is the finding. STT falls on the seller: NSE Clearing's STT procedure lists sell trades, option exercise and physically settled stock derivatives, and a cash settled future that runs to final settlement is none of those. A conversion buys the future; a reversal must sell it, and 0.05 per cent of 23,378.50 is 11.69 points, about four times all the reversal's other costs together. The lower edge sits 14.53 points below zero and the upper 3.31 above. Under the rates in force until 31 March 2026 the reversal cost 7.43: the Finance Act roughly doubled one side of the band and left the other almost untouched.

The largest item in the conversion is not a tax but interest on margin, 1.91 points over 11 days at a stated 6.50 per cent, on capital a riskless position must still post. Brokerage and spread come on top as stated assumptions: ₹20 an executed order on one lot adds 1.09 points with GST, and half an assumed quoted spread of 0.20 on each option and 1.00 on the future adds 0.70. Both fall per unit with size, so the edges that bind are those of the cheapest participant, not of a single lot account.

Exercise is now taxed at the sale rate

A conversion or reversal held to expiry ends with one long option exercised automatically, so the exercise charge sits inside the band. It is also the subject of a warning repeated across Indian options material, that exercise is an STT trap. The warning was right once and has lost its basis in stages.

Until 31 August 2019 exercise was taxed at 0.125 per cent of the settlement price, the whole value of the underlying rather than the option's worth. Applied to today's index level, a contract 20 points in the money would have paid 29.22 points to be exercised against 0.01 to be sold. From 1 September 2019 the base became intrinsic value, the settlement price less the strike (NSE/FATAX/41919), leaving a rate gap of 2.5 times that narrowed to 2 in April 2023 and 1.25 in October 2024. From 1 April 2026 the rates are equal.

For a cash settled index option the comparison now runs the other way. A call 350 points in the money at the close on expiry day pays 0.525 points of STT if exercised. Sold for that value it pays the same STT plus the exchange charge on the premium and GST, 0.672 points in statutory charges, before brokerage and spread. Intrinsic value cannot exceed the price at the close, so exercise can no longer cost more STT than a sale; any broker fee on exercise appears separately on the contract note.

For single stock options the trap has moved rather than closed. They settle by delivery, and NSE Clearing applies the delivery based equity rate of STT to physically settled stock derivatives, payable by both giver and receiver on the value delivered: about 1.20 rupees a share on each side for a share near 1,200 with a call 10 rupees in the money, against 0.015 of exercise STT on the intrinsic value. Illustrative figures.

One session, strike by strike, and what each close really is

The test uses the exchange's derivatives file for 18 September 2026: the broad index contract expiring 29 September 2026, 11 days out, against the future expiring the same afternoon, the nearest expiry a listed future can hedge. The weekly contract expiring 22 September is nearer and serves the check in the last section. For each of the 128 strikes with a call and a put listed, the residual is C − P − (F − K) × DF, with F the future's close of 23,378.50 and DF at the stated 6.50 per cent.

A close is not a quote. An option that traded in the final half hour closes at that half hour's volume weighted average price, one that traded only earlier at its last trade, and one that did not trade takes a model price as its next base (the exchange's contract specification for the index's options). A future's daily settlement price is its last thirty minutes' volume weighted average (NSE Clearing), and since 3 August 2026 that half hour ends at 3:40 pm, when the derivatives session now closes (the exchange's closing auction session page). A residual means something only when all three legs are averages over the same window.

The file marks which closes those are, and the build measures the rule before using it. Of 35,313 option contracts, 7,908 traded and closed away from their last trade, so their close is a half hour average, and on every one the settlement column equals the close. All 21,739 that did not trade carry the previous close, and on 21,713 of them the settlement column holds a different, model value. A leg whose settlement column equals its close is a final half hour average; any other close is older.

Of the 128 strikes, 65 sit outside their band, and every one has a stale leg: 55 of the 56 with a leg that never traded and 10 of the 16 with a leg that last traded earlier. None of the 56 strikes whose closes are all final half hour averages is outside even the narrow floor band.

The stale prints are not subtle. The 22,350 call did not trade; its close of 1,150.00 is a price from an earlier session and produces a residual of +114.51 points, which a naive screen reads as a conversion paying over a hundred. The 21,950 call carries 1,800.00 and +368.65. A synthetic has a delta of one, so a stale leg is wrong by roughly the whole index move since it last traded.

The clean strikes are quieter. Their median residual is −4.36 points; across the 19 where both legs traded at least 1,000 times it is −4.19, every one between −5.93 and −1.34. The chain implies a forward of 23,374.30, four points under the future and well inside the band. One session says nothing about where the market usually sits, and this one turns out to be unusual.

Conversions, reversals and the capital a riskless trade consumes

A conversion has no payoff risk and a large margin, and the contradiction is only apparent. NSE Clearing's scanning margin is computed on the whole portfolio, and a locked position loses almost nothing in any scenario. Its extreme loss margin is different: 2 per cent of notional for index derivatives, defined on a future's contract value and, separately, on a short option's underlying value, with the only offset described for futures calendar spreads. A conversion holds one of each and pays twice.

Per lot of 65 at these prices that is ₹30,392 on the future and ₹30,350 on the short call, ₹60,742 in all, another ₹30,350 on expiry day when the extra 2 per cent on short index options applies, plus ₹1,687 of net premium at 23,400. The scanning component is not computed here; a live margin statement shows it. Interest on that capital at 6.50 per cent is ₹124 a lot over 11 days, the 1.91 points in the cost table, which is why the cheapest enforcer of the upper edge is whoever funds margin most cheaply, rarely an individual. The lower edge is expensive not for want of access, since any derivatives account can sell a future, but because of the tax on the sale. How spread margin behaves as expiry arrives is covered in spread margin and the expiry day.

Eighteen months of the same test: what survives is on the capital side

One session is an anecdote, so the test was repeated on every session from 1 April 2025 to 18 September 2026: 363 daily files from the exchange's public archive, the nearest monthly contract against its own future, each day at that day's statutory rates. The core is the cleanest strikes: both closes final half hour averages, at least 1,000 trades in each leg, within 2 per cent of the forward.

Stale legs account for 65 per cent of the 26,368 apparent breaks, and nine in ten stale strikes look broken, in both directions about equally, as random old prices would. The core is different in kind. 1,792 of its 5,391 strike sessions, 33.2 per cent, sit outside the floor band, 1,763 of them on the conversion side, where the synthetic is richer than the future by more than a conversion costs. The lean is not a closing artefact: recomputed from last traded prices, 33.6 per cent of core strike sessions are outside, and the day's core residual has a correlation of −0.01 with the gap between the future's last trade and its half hour average, a proxy for the market's direction in that half hour. Nor is it large: the median excess over the edge is 2.18 points, three quarters are under 4.74, and adding the assumed brokerage and spread leaves 18.7 per cent outside.

The lean grows with time to expiry, from 0.38 points in the final week to about 5.05 three to four weeks out, and from a fortnight out the return on margin it implies stays between 3.8 per cent and 4.9 per cent a year. A stale price does not scale with time and a tax is not charged by the day; interest on capital is. In the median core strike session that crosses the edge, the residual implies 12.7 per cent a year on the extreme loss margin after statutory costs, at closing averages. The widest month was March 2026, the financial year end, with a median core residual of 6.71 points and 70 per cent of core strike sessions outside. All of this fits a price for scarce margin rather than an unclaimed gift, though eighteen months cannot prove it, and a daily file cannot show whether the excess survives the spread at size or the scanning margin not modelled here.

The STT change is the control, and it returned a measured null. The reversal edge at the strike nearest the forward averaged 9.07 points before 1 April 2026 and 16.13 after, while the median core residual was 1.17 basis points of the future before and 1.17 after. Widening the side of the band the market never leaned on changed nothing observable, beyond the 29 core strike sessions that had crossed the old reversal edge and none that crossed the new one. The session of 18 September, at −4.47, sits below 96 per cent of sessions.

What parity is for on a retail screen

For someone who will never run a conversion, parity is a consistency check that needs no model. Every strike implies a forward, K + (C − P) / DF, and on a healthy chain they agree within a point or two, because a strike that disagreed by more would sit inside somebody's conversion. A strike off by tens of points has a stale leg. The weekly contract expiring 22 September, the nearest of all, has no future to test against, which makes it the natural case: its 23 liquid same window strikes imply a forward of 23,355.01, with a standard deviation of 0.93 points across them.

Carrying the monthly future back seven days at its own carry gives 23,358.07 for the weekly date, three points above the weekly chain, much like the monthly gap that session. On the weekly contract 48 of 96 strikes look outside their band, all with a stale leg, and none of its 47 same window strikes does.

Parity also explains a number that confuses most screens, the implied volatility of a call and a put at the same strike. Both have the same vega under the standard model, so a residual of e points appears as a volatility gap of e divided by vega: the band bounds the gap, and the gap widens as vega shrinks away from the money.

With the traded future as the forward, call and put volatility at 23,400 differ by 0.28 of a point, the −4.49 residual divided by a vega of 16.14. A tool that takes its forward from the index level compounded at 6.50 per cent, with nothing for distributions, lands at 23,392.18, about 14 points above the traded future, and shows a gap of 1.12 at the same strike and 2.66 at 24,000. That split describes the tool's forward, not the market. How the same options relate to a hedge ratio is covered in delta is not a probability.

What parity rewards is not a hunt for violations but the habit of asking which prices existed at the same moment, what the trade that would close a gap costs, and whose capital it would tie up. That is judgement a curriculum can teach and a screen cannot supply.