Put-Call Parity

Options trading is one of the most sought-after asset classes that traders and investors leverage to make low risk and steady profits. Options are contracts that grant the holder the right but do not bind them, to either buy or sell an underlying asset at a fixed price on or before the contract expiration.

Although it's a little more complex than stock trading, Options yield comparatively greater returns if the security price goes up. This is because you do not have to pay the full premium for the insurance of an Options contract. Similarly, selling Options will reduce your losses if the security price goes down, which is also known as hedging. Investors that have allocated a portion of their capital to stocks enter Options as a short-term profit-making method.

However, new investors looking to enter the Options trading spectrum are confused about the types of Options, the underlying asset, and how they are priced. They never seem to understand the price relationship between Call and Put Options of the same class. This blog will shed light on this relationship and the Put-Call Parity.

But first, let’s understand the two types of Options Contracts:

Call Options

This is a contract wherein you win the right, but not the obligation, to buy a certain underlying asset at a decided-upon price and date between the contracting parties. Since there is no obligation to purchase as dictated by the Call Option, you do not need to execute it unless it is profitable to you.

Put Options

A Put Option works exactly opposite to the Call Option. While the Call Option equips you with the right to buy, the Put Option empowers you with the right to sell the stock on the date agreed upon by the contracting parties.

What is the Put-Call Parity?

Before moving on to the parity, it is important to know that European Options contracts can only be exercised at the time of the expiration date, while American contracts (which traders generally use) can be exercised at any date before the expiration date.

The term Put-Call Parity is defined as the relationship between the price of a European Call and Put Options of the same financial class. However, for the relationship between the Call and Put Options to work, they must have the same underlying asset, strike price, and expiration date. The central idea behind the Put-Call Parity is that returns of a portfolio that contain a short Put Option and long Call Option will be equal to a forwards contract with the same underlying asset, strike price, and expiration date. The Put-Call Parity is exclusively applicable for European Options and does not extend to any other Options class.

Note: A forward contract is when two parties agree to conduct the said transaction in the future, hence the term ‘forward’. Similar to a futures contract, the value of the forward contract is derived from the value of the underlying asset, which is why it acts as a derivative. However, unlike an Options contract, the two parties involved in forwards derivatives contracts are obligated to fulfill the specified transaction.

Understanding the Put-Call Parity

The Put-Call Parity suggests that an investor can hold a long European Call and a short European Put of the same class to mirror the returns that one forward contract will offer at the same strike price as the Options contract. The Put-Call Parity formula is as follows:

P + S= C + PV(x)

Here,

• P is the price of the European Put Option
• S is the spot price (current price) of the underlying asset
• C is the price of the European Call Option
• PV(x) is the strike price value, which is discounted from the expiration date’s value.

Here is an example to better understand the Put-Call Parity:

Let’s say you buy a Call Option with a premium of Rs 50 and a strike price of Rs 200 and simultaneously sell a Put Option with the same premium, strike price, the underlying asset, and same expiration date of six months. As per the Put-Call Parity, it is suggested that the returns will be equivalent to buying a forwards contract with the same terms.

At the end of six months, if the asset price goes up to Rs 250, you would exercise the Call Option. You will have to pay Rs 50 as a premium, get the asset at Rs 200, and sell the asset at Rs 250. Your profit here will be Rs 0 (250-200-50).

With the Put Option, it will not be exercised by the buyer as its price has increased, and it has become out-of-the-money. In this case, you will receive Rs 50 as a premium. This leaves you with Rs 50 as profit.

Now, as a forward contract must be exercised, you will pay Rs 200 (the predetermined price) and get the delivery of the asset. You can sell the asset at the current price of Rs 250 in the market and make a profit of Rs 50.

As you can see, under the Put-Call Parity, the profits using the Call and Put Options (Rs 50) are the same as exercising the forward's contract.

Put-Call Parity and arbitrage

Arbitrage is the simultaneous buying and selling of any of the securities, such as stocks, commodities, bonds, currencies, etc., in different markets to profit from the price difference. Under Put-Call Parity arbitrage, there are times when one side of the equation is greater in value than the other, resulting in arbitrage. Traders make the best out of this situation to buy on the cheaper side and sell the expensive side, making a risk-free profit.

Final Words

Put-Call Parity allows Options traders to understand the price relationship between the Options contract and a forward contract. Furthermore, it allows arbitrageurs to identify an arbitrage situation and make guaranteed profits with no risk. Using the Put-Call Parity, you are better equipped to choose between options and forward contracts.