Let’s say you come across a market place where there is a limejuice vendor selling you a glassful at Rs 15/-. Right next to him is a lime vendor giving away the fruit at Rs 3 a piece and in addition selling water at Rs 10 with complementary sugar and chaat masala (Remember its an exaggeration to prove a point!). We also assume that the limejuice vendor is willing to lend you empty glasses for free as the lime seller is his kin.

Now what do you do – you are entrepreneurial and possibly might want to possibly make the juice yourself and save Rs 2 (15-3-10) but would it be worth the effort? Let’s say the difference goes to 10 then a lot of people might start doing this till either one of the vendors begins migrating prices to remove this “arbitrage” and both options become almost similar except the effort bit which will still carry a small price!

The Put Call Parity theorem in options trading is similar in nature!

PUT CALL PARITY

Let’s say you want to buy a call in a stock. But the premium outflow makes you think twice and you begin to wonder how you could achieve the same result with another combination – and soon, Voila!, you understand that buying a futures contract and buying a put result in the same combination! (‘Put’ protects downsides, which is why you wanted to buy a call option and the futures contract gives you the upsides, right?)

In essence you have just learned what a synthetic option is! And this is where the parity theory is born!

Now, the Put Call theory can be interpreted as taking a short position in PE and simultaneous long position in CE of same expiration and strike price is equivalent to holding the same number of stocks (as in a futures contract) and ideally gives the same payoff. An arbitrage opportunity exists if this relationship does not hold true in any particular instance.

In short,

*CE – PE = Stock*

*or, C – P = S*

We can modify this formula and write,

*C = S + P*

If there is a deviation from put-call parity, then it would result in an arbitrage opportunity. Traders would take advantage of this opportunity to make riskless profits till the time the put-call parity is established again.

THE PUT CALL ARBITRAGE

In simple words, let’s say the 10800 Rs call option for Nifty is trading at 96 and the same strike/same month put option is trading at Rs 126. There is therefore a 30 Rs gap in both which presents an arbitrage opportunity.

You therefore want to go long the cheaper thing and short the expensive thing right?

Therefore, you might want to add a futures contract (let’s say its quoting at 10778) to the mix- now you may go short the futures, short the put and long the call– effectively, you have bought a cheaper call and sold a “synthetic call” (the difference in premium between the two options should be equal to the interest on the futures margin).

Let’s now see what happens to the payoffs

**Scenario 1 – Expiry at 10000**

- The 10800 CE would expire worthless, hence we lose the premium paid i.e.
**96** - The 10800 PE would have an intrinsic value of 800, but since we are short at 126, the net payoff would be 126– 800 =
**-674** - We are short on futures at 10778, which would result in a profit of 778 points
- Net payoff would be -96 – 726 + 778=
**+8**

** **

**Scenario 2 – Expiry at 11500**

- The 10800 CE would have an intrinsic value of 700, and therefore the payoff would be 700 – 96 = 604
- The 10800 PE would expire worthless, hence we get to retain 126
- We are short on futures at 10778, which would result in loss of 772 points
- Net payoff would be 604 + 126 – 772=
**+8**

You will get a similar value across strikes.

**Costs of the Trade**

Now Rs 8 in the example above may not be much of an arbitrage given the costs of the transaction and the interest on margins that you may borrow from your broker or bank – but what if the gap increased to 40. Would it be worth a look?

The above in essence is what is meant by the Put Call Parity principle and you can develop arbitrage strategies around it to benefit. Of course you should execute the arbitrage trade only if the P&L upon expiry makes sense after accounting for expenses/ STT etc.

This of course is not very easy to do as large institutional algorithms will make it difficult to do but you will often find smaller pockets of opportunity as large money cannot chase smaller trades — and here is where the learning may come into play!

The Options chain on Nifty is available for free at www.nseindia.com – Do have a look and see if you can spot any trades for the current expiry? And if you do, do write into us at advisory@plindia.com!