## Put Call Parity

Before we move on to further option trading strategies, we need to learn an important concept called ‘**Put-Call Parity**.’

The put-call parity helps you to understand the impact of demand and supply on the option price, and how option values are inter linked across different strikes and expirations, given that they belong to the same underlying security.

The term ‘**parity**’ refers to the state of being equal or having equal value. Options theory is structured in such an ingenious fashion that the calls and puts complement each other with regards to their price and value.

So, if you are aware of the value of a call option, you can easily calculate the value of the complimentary put option (which has the same expiration date and strike price). This knowledge is very essential for traders. Firstly because it can help you figure out profitable opportunities when the option premiums are not functional. A thorough understanding of put-call parity is also important because it helps you to work out the relative value of an option you are considering to add to your portfolio.

Suppose a trader holds a short put (European) and a long call (European) of the same class. According to the Put-call parity, this is equivalent to having one future contract of the same asset and same date of expiry, and future price that is the same as the strike price of the option.

In situations when the put price diverges from the call price, an arbitrage opportunity comes into existence. This means that traders can make a profit without taking any risk. However, as mentioned earlier, even in liquid markets, chances of this sort are a bit uncommon and have a small window.

**Put Call Parity is stated using this equation:**

**Call + Strike = Put + Futures**

Here,

Call means the price of the call option,

Put means the price of the put option,

Futures means the future price and

Strike means the price for which call and put are considered.

Having clarified that, let us understand how it works with the help of an example. Suppose Nifty is trading at 16940. So the ATM option will be 17000. You buy a call option and sell a put option of the same strike. The date of expiration is a month from the date of purchase. The call option costs ₹35 and the put option costs ₹90. So, the net inflow is (90-35) = ₹55/-

Let us consider a few scenarios to understand the trade better.

**Nifty expires 16000 (below ATM):**

Here the 17000 CE expires worthless because it is now OTM. Hence, we lose ₹35 which we had paid as its premium. For, put option, we suffered losses because we had sold the put option (bullish position) and the market went in the opposite direction on the downside. So, the loss here = (16000-17000 +90) = - ₹910/-

**Nifty expires at 17000 (ATM):**

In this case both the options expire worthless again. So we lose the premium paid for call and retain the premium received for put. So the difference of both the premium stays with us, i.e. ₹55/-

**Nifty expires at 18000 (above ATM):**

Here the call options start paying off because of the bullish position. So profit on call option = (18000-17000-35)= ₹965/-

The put option expires worthless because of being OTM. So we retain the premium of ₹90 from the put as well.

Hence, the total profit in this scenario = 965+90 = ₹1055/-

If you construct a graph by plotting the profit or loss one has on these positions for different prices of Nifty, some interesting things will come to light.

Suppose the long call’s profit/loss is combined with the short put’s profit/loss. We will make a profit or loss of the exact amount we would have if we just took a future contract of Nifty at 17000, which has a validity of one month. If Nifty trades lower than 17000, you will incur a loss. If it trades higher, you will make a profit.

Here, we are not taking transaction fees into consideration.

To understand the put-call parity better, you can also compare the performance of a fiduciary call and a protective put of the same class. Protective put is a combination of a long stock and a long put position. This limits the negative impact of holding the stock. A fiduciary call is the combination of a long call and stock which is equivalent to the strike price’s present value. This ensures that the investor gains enough money to make use of the option on its expiry.

Talking about the equation again,

**Call + Strike = Put + Futures**

In situations where one side of this equation is heavier than the other, this is when an arbitrage opportunity is present. A hassle-free profit is locked in when a trader sells the expensive side of the equation and buys the cheaper side. In real life, however, the occasions where one can take advantage of arbitrage are hard to come across and short-lived. Also, sometimes the margins offered by these are so tiny that you will need to invest a huge capital to use it advantageously.