Conversion and Reversal Arbitrage: Put-Call Parity Trades Explained

Every option chain hides a small piece of arithmetic that ties the call, the put and the underlying together. When that arithmetic slips, even by a few rupees, a trader can lock in the gap without caring where the market goes next. The two trades built for that job are conversion and reversal arbitrage. One is used when calls look too expensive against puts, the other when puts look too expensive against calls.

Neither is a get-rich trade. The edges are thin, they vanish fast, and costs eat most of what is left. But understanding how they work tells you a lot about why option prices sit where they do, and why a call and a put at the same strike can never drift too far apart for long. We’ll build both trades from scratch, run the numbers on made-up examples, and then look at a real Nifty case from Zerodha Varsity, costs included.

The rule underneath: put-call parity

Both trades rest on put-call parity. The Options Industry Council (OIC) describes it as the pricing relationship between a put and a call on the same underlying, with the same strike and the same expiry. The price of the call implies a fair price for the put, and the other way round.

OIC also lists the “synthetic” equivalents that follow from this. Two that matter here:

• Long stock behaves like a long call plus a short put.
• Short stock behaves like a short call plus a long put.

Ignore interest and dividends for a moment, as OIC does in its simplest version. Then a long call plus a short put at strike K should cost exactly what it takes to own the stock at K. Put differently, call premium minus put premium should equal the stock price minus the strike. Investopedia’s page on conversion arbitrage writes the fuller version as Call − Put = Price of underlying − PV(Strike), where PV means present value. That PV term is how interest sneaks back in, and we’ll come to it.

When the two sides of that equation don’t match, one of the trades below can capture the difference.

How a conversion works

Investopedia defines a conversion as buying a put and selling a call at the same strike and expiry while holding the underlying stock. So the three legs are:

• Buy the stock.
• Buy a put at strike K.
• Sell a call at strike K, same expiry.

Look at what the last two legs are together. A long put plus a short call is a synthetic short stock. Add that to real long stock and the position has no direction left. If the stock falls, the put makes up the loss. If it rises, the short call gives back the gain. Whatever happens, at expiry you end up handing over the shares at exactly K.

That is why the trade is worth doing only when the call is rich compared with the put. You collect more on the call than you spend on the put, and that net credit, after the cost of the stock, is the locked-in profit.

Worked example 1: a conversion on a hypothetical stock

All numbers here are made up for illustration. Say a stock trades at ₹1,000. The ₹1,000 call with a month to expiry is quoted at ₹42 and the ₹1,000 put at ₹30.

Check parity first. Stock minus strike is ₹1,000 − ₹1,000 = 0. Call minus put is ₹42 − ₹30 = ₹12. The call side is ₹12 heavier than it should be, before thinking about interest. That points to a conversion.

Now run it to expiry at three prices:

• Stock ends at ₹900. The call expires worthless. The put is worth ₹100. Shares worth ₹900 plus a put worth ₹100 gives ₹1,000.
• Stock ends at ₹1,000. Both options expire worthless. You hold shares worth ₹1,000.
• Stock ends at ₹1,100. The put expires worthless. The short call costs you ₹100. Shares worth ₹1,100 minus ₹100 gives ₹1,000.

Every path ends at ₹1,000. You paid ₹988. That’s ₹12 a share, before costs, no matter what the stock did. On a hypothetical lot of 500 shares, ₹6,000.

A conversion doesn’t bet on the stock. It bets that a call and a put at the same strike have drifted out of line, and it gets paid when expiry forces them back together.

Don’t forget the money you tied up

Here is the part people skip. You put ₹988 a share into this trade for a month. That money could have earned interest somewhere else, or you may have borrowed it. OIC points out that interest is a real cost for anyone who borrows to buy stock, and that higher interest rates tend to push call premiums up and put premiums down.

Suppose your cost of money is a hypothetical 7% a year. Over 30 days, ₹988 × 7% × 30 ÷ 365 comes to about ₹5.68. So the true edge is closer to ₹12 − ₹5.68 = ₹6.32 a share, before brokerage and taxes. This is exactly why Investopedia’s version of parity uses the present value of the strike, not the strike itself. A call trading a little above the put isn’t automatically mispriced. Some of that gap is just the price of money.

How a reversal works

The reversal is the mirror image. Investopedia’s page on reverse conversions describes it as shorting the underlying, buying a call and selling a put, with the same strike and expiry. The long call plus short put is a synthetic long stock, which cancels the real short stock.

OIC lands on the same trade from the other direction. In its example, when the synthetic long can be built for less than the stock’s market price, traders would buy calls and sell puts, and might short the stock to lock in the difference. OIC notes that this is technically called a reversal.

You want this trade when the put is rich compared with the call.

Worked example 2: a reversal on a hypothetical stock

Same made-up ₹1,000 stock, but now the ₹1,000 call is quoted at ₹25 and the ₹1,000 put at ₹35. Call minus put is −₹10, while stock minus strike is still 0. The put is the expensive side.

At expiry, if the stock is below ₹1,000, the put you sold gets exercised and you buy shares at ₹1,000, which closes the short. If it is above ₹1,000, you use the call to buy at ₹1,000. Either way, the short gets covered at ₹1,000. You took in ₹1,010, so ₹10 a share stays with you before costs.

Investopedia adds a useful reality check. Puts are usually cheaper than the equivalent calls, not more expensive, so a genuine reverse conversion is rare. Its own example uses an overpriced put on a US stock and walks through how the trader pays the same amount to exit whether the stock falls or rises. Our numbers above are simply a rupee version of that logic.

The Indian version: swap the stock for futures

On NSE, the form most F&O traders will meet uses a futures contract in place of the stock. Zerodha Varsity’s chapter on synthetic long and arbitrage sets up the equation as long ATM call + short ATM put + short futures = 0. The synthetic long from the two options cancels the short future, so the expiry P&L should be zero. If it isn’t, there’s an arbitrage. Structurally, this is a reversal with futures standing in for the short stock.

Worked example 3: Varsity’s Nifty case

Varsity uses real January 2016 series prices from 21 January. Nifty spot was at 7304 and Nifty futures at 7316. The 7300 call traded at 79.5 and the 7300 put at 73.85. The trade:

• Buy the 7300 call at 79.5.
• Sell the 7300 put at 73.85.
• Sell Nifty futures at 7316.

The two options cost a net 79.5 − 73.85 = 5.65 points. That makes the synthetic long equal to buying Nifty at 7300 + 5.65 = 7305.65. The futures were sold at 7316. The gap is 7316 − 7305.65 = 10.35 points.

Varsity checks it at three expiry levels. At 7200, the call loses 79.5, the short put loses 26.15 and the short future gains 116, for a net of +10.35. At 7300, the call loses 79.5, the put keeps 73.85 and the future gains 16, again +10.35. At 7400, the call gains 20.5, the put keeps 73.85 and the future loses 84. Still +10.35. Direction doesn’t matter.

Where the “risk-free” profit leaks away

Varsity’s own verdict on that 10.35 points is the most useful part of the chapter. The costs it lists:

• Brokerage. With a traditional percentage-based broker, Varsity estimates 8 to 10 points could go in brokerage alone. With a discount broker, it puts the breakeven at around 4 to 5 points.
• STT at expiry. The profit is only realised at expiry, so the position has to be carried. Varsity warns that the long option will be in the money at expiry, and that brings a hefty STT bill.
• Other levies such as stamp duty and service tax, as Varsity calls the indirect tax in that chapter.

Its conclusion: a 10-point arbitrage may not be worth the effort after costs, but something like 15 or 20 points could be. With that kind of cushion, Varsity says you might even square off just before expiry to avoid the STT trap, giving up a few points to do it.

A few more risks are worth listing, because the textbook version assumes them away:

• Interest and carry. Investopedia flags that interest rates affect both carrying costs and what you earn on credit balances, and names a rate hike as a key risk to conversions.
• Dividends. OIC explains that higher dividends tend to reduce call prices and increase put prices. Investopedia lists the elimination of a dividend as another risk. If a dividend changes while the trade is on, the parity you calculated at entry is no longer the parity at expiry.
• Execution. Three legs have to fill at the prices you saw. Miss one by a couple of rupees and a small edge can turn into a small loss. OIC notes that bid-ask spreads and transaction costs affect whether these trades can be done at all.
• Expiry right at the strike. If the underlying closes almost exactly on the strike, it can be unclear which option ends in the money, and the neat “always K” outcome gets messy.

The arbitrage is real on paper. Whether it survives brokerage, STT, carry and a slipped fill is the only question that matters.

Why you rarely find conversion and reversal arbitrage

OIC is blunt about it. Arbitrage opportunities are fairly rare, and when they appear, buying and selling pressure quickly pushes prices back toward balance. It adds that traders with access to large amounts of capital, low fees and few borrowing restrictions are the ones who may occasionally catch them. Investopedia says the same about conversions: any chance at risk-free money gets acted on very quickly.

So for most retail traders, the real value of these trades is understanding, not income. A few practical takeaways we’d draw:

• Use parity as a sanity check. Before buying a call or a put, compare call minus put with spot (or futures) minus strike. If the gap looks odd, find out why before trading. There’s often a dividend or rate effect behind it.
• Read “mispricing” carefully. A call a few rupees above the put at the money is often just interest at work, as Worked example 1 showed.
• Know the family. Conversions and reversals sit next to the box spread, which applies the same parity logic across two strikes. Once you see one, the others make more sense.

If you’re still finding your feet with calls, puts and option chains, start with our guide to options trading for beginners in India. Then come back to parity trades. They’re one of the clearest windows into how option prices are actually held together.

Disclaimer: This article is for educational purposes only and is not investment advice. Examples 1 and 2 use hypothetical numbers; Example 3 is quoted from Zerodha Varsity. Derivatives trading carries significant risk; please do your own research or consult a SEBI-registered adviser before making investment decisions.