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Premium: Optionalysis: Put-Call Parity and Synthetic Long/Short Positions through Options



You could go “pure” long in a stock in two ways:

• Buy the stock, or buy the future

• Buy a call and sell a put at the same strike price (a “Synthetic” long)

The first is obvious. The concept of going long means you benefit when the stock goes up and lose when it goes down. A purchase (stock or futures) ensures that.

The second isn’t obvious. But let’s see how.


Buying a call gives you the right to receive all the upside benefit beyond the strike price, but no downside below. (other than the premium paid)

Sellling a put gives you no upside if the stock goes up, other than the premium received. But you get the full downside if the stock falls.

If you do both, then you get the full upside through the call, and the full downside through the put.

When you buy a call you pay premium. When you sell a put, you receive premium. Since the premiums will usually not be equal, the difference is either a payout (you have to pay) or a pay-in (you get money). This difference, when added to the strike price, gives you the “net cost” of the long position.


If you buy a 100 call at Rs. 10, and sell a 100 put at Rs. 15, then you net “receive” Rs. 5. You can subtract this from the strike and you get a net long price of Rs. 95.

Take the Nifty option chain:

Synth Longs

The 8100 call (on the left) is at Rs. 66.4, while the 8100 put is at 38.80. If you did the buy-call,sell-put piece you would net pay out (66.40-38.80) = Rs. 27.60.

That means your net synthetic long price is at 8127.60.

Similarly, to go short you could sell a call and buy a put at the same strike.

The Put-Call Parity Arbitrage

Technically, if you went long with futures, or you went long using the put-call, your effective price should be the same. If these prices differ, you could bridge the prices by purchasing one and selling the other.

The idea then may be:

• Future is at 8150

• “Synthetic” long through put-call is at 8126

• You lock in the difference by taking a synthetic long and shorting the future.

So you’ll go long the call, short the put option, and short the future. Since this is a fully hedged position, you will pay very little in terms of margins.

The arb can’t be done easily since there’s three legs. But an algorithm can be used to detect such opportunities, and do a three-legged trade when the opportunity is right. Still, since it is automated and has quite a bit of risk, you will learn quickly that other people quickly compete with you!

If you want to take advantage of this arb, you will need to do a “three way order” – where either all legs are executed or none are. You’ll have to use prices on the exchange (or even this can be done through an algorithm).

Extra Credit: The Advantage of Options Based Longs

If there’s no difference then why do two trades instead of one? Is the options trade in any way different?

One is in payouts and margins. The put-call combination have about the same margin (together) as a long position. But here’s what happens in a future:

When the stock goes down, for every day, you have to pay money out as a “mark-to-market” payment. (When it goes up, you receive the profit)

In an option based long, you have no payment to make since option margins have no daily mark to market payins or payouts. But your margins for the position will increase (or decrease) based on how the stock has moved.

So in effect, if you buy an 8000 long position through options, you might have seen an initial margin of Rs. 50,000 for 100 Nifty. If the Nifty falls to 7800, then your margin will increase to Rs. 70,000.

This is useful since you don’t need to pay the money out (and can earn interest on it). If you have a Rs. 100,000 deposit placed with the broker for margin, the deposit continues to earn you interest, and there is no paying out required until you close the position. (With a future, you would pay the Rs. 20,000 and have only Rs. 80,000 left in the deposit).

The second difference is in STT, in India. Securities transaction tax (STT) will apply on any “in the money” option position. This can drop the price by 0.1% (which translates to Rs. 8 on a Nifty contract when Nifty is 8000) Coming close to expiry you will end up with one position (either the long call or the short put) in the money.

Depending on which position that is, your “synthetic long” position can go out of what. The in-the-money position will lose premium by 0.1% (or whereabouts) on the day of expiry.

Lastly, it allows you to take a longer term future position. Nifty futures contracts are for 1, 2 and 3 months forward. But options positions can be as long as 3 years forward. If there is liquidity, you can take a 3 year forward position on the Nifty! (just buy that time’s call and sell the put)

At this time, when the Nifty is at 8127, you find the December 2015 put-call position give us a “synthetic” long at 8500 (1020 for the call, 320 for the put). Buying the Nifty for 8,500 today for a December 2015 position is equivalent to Rs. 370 premium for 15 months; this translates to less than 4% cost of carry!

A longer term view is made possible at a cheap only the Nifty allows long term options though.

Our View

• Put-Call parity is useful for brokers and entities where transaction costs are low. The put-call parity depends on transaction costs (brokerage)

• However, retail investors and HNIs can also use it to build algorithms to detect such opportunities and auto-trade. (Many brokers provide frameworks to do this)

• The put-call based Synthetic Long concept allows longer term investors to build positions through options, which have many advantages (including better utilization of margins and multi-year position potential)

More Arb Gyan

We will have more on this topic. Here’s the topic list:

• Cash Future Arb

• Inter-exchange arbitrage

• Stocks-Index Arb

• Put-Call Parity (This post)

• Higher Risk Arb: Mergers and Delisting

• Non-convergence: ADRs and Indian Stock

• Stat-arb: Pair Trading

Do let us know what you think. We aren’t recommending trades, and this is not portfolio advice. Please do understand the risks before you trade.



Nothing in this newsletter is financial advice and should not be construed as such. Please do not take trading decisions based solely on the matter above; if you do, it is entirely at your own risk without any liability to Capital Mind. This is educational or informational matter only, and is provided as an opinion. 

Disclosure: The authors at Capital Mind have positions in the market and some of them may support or contradict the material given above, or may involve a direction derived from independent analysis.

Capital Mind for ZD



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