Put Call Parity: Meaning, Example, Scope and Importance
11 November 2022
Trading in the derivatives segment of stock markets has gained immense popularity in recent years. A derivative options contract gives traders a choice to buy or sell the underlying asset on or before the expiry date. The call option gives buying rights, and the put option gives selling rights to traders.
Put call parity is a trading concept that shows a triangular relationship between a call option and a put option and the underlying security associated with them. However, for this relationship to fructify, the call and put options must have the same expiry date and strike price.
Read on to know more about put call parity and its implications on derivatives trading.
What Is Put Call Parity?
This investment theorem exhibits the relationship between a European class of call and put option contracts having the same derived asset, expiry date and strike price. Under this concept, a trading portfolio comprising long call options and short put option contracts is equal to a specific forward contract with the same strike price, underlying security and expiration date.
This theorem helps traders understand the impact of demand and supply on the price of various option contracts. Individuals can also understand the interlinking or relation between different options having the same strike price and underlying assets.
Parity means equality, and when call and put options are equal to each other, it does not lead to any arbitrage opportunity for traders. However, in case these two options of the same associated asset and strike price diverge from each other in terms of value, there arises a small window of arbitrage which is less risky and can generate significant returns.
How Does Put Call Parity Work?
One of the most important things regarding put call parity is that it works only in European options, which individuals can exercise only on the expiration date, unlike American contracts, which traders can exercise either on or before the settlement date.
For this theorem to work, there must be a call and put option contract, an asset or security, and cash or option premium. We can get a clearer idea about the functioning of put call parity by looking at a simple example which we will discuss in the next section.
Suppose you have bought a call options contract by paying a premium amount of Rs. 100, and the strike price of the said contract is Rs. 300. At the same time, you buy a put option having the same premium amount, the same underlying asset, strike price and expiry date of three months.
You must remember that as per put call parity, gains earned from exercising the put and call options will be equal to gains earned from selling a forward contract having the same terms and conditions.
At the end of the expiry period of three months, the price of the underlying security increases to Rs. 450. You can exercise your call option by paying a premium of Rs. 100. You will receive the asset at Rs. 300, and you can further sell the same at Rs. 450. Therefore, your net profit will be Rs. [450 – (300+100)] = Rs. 50.
In this case, the put contract will not be exercised, and it will expire. This is because the spot price of the asset has gone above the strike price. Hence, you will have to bear the premium amount as the loss, which is Rs. 100. Therefore, the total loss from exercising put and call options will be Rs. (100-50) = Rs. 50.
According to put call parity theory, you should exercise a similar forward contract having the same structure. In that case, you must pay Rs. 300, which is predetermined and receive physical delivery of the underlying security. Now, as the price of this asset has increased to Rs. 450, you can sell the same at Rs. 450 and earn a total profit of Rs. (450-50) = Rs. 400.
As seen from the above example, the put call parity theory is used to earn profits from both the put and call options as well as the forward contract.
Why Is Put Call Parity Important?
Some reasons exhibiting the importance of this theorem are given below:
This concept allows traders to estimate or compute the value of call or put options contracts in regard to their other components.
Any divergence in the value of put and call options may open a window of opportunity to undertake arbitrage. Traders can buy and sell these contracts simultaneously in different stock exchanges and earn risk-free gains.
Individuals have the flexibility to generate synthetic trading positions.
Any difference between synthetic option position and actual option position allows opportunities for traders to earn profits.
What Is the Put Call Parity Formula?
One can easily determine the value of his/her put and call options in relation to their components with the help of the following formula:
PV(x) + C = P + S
P stands for price or value of put options;
S stands for current market value or spot price of a derived asset;
C is the price of call options;
PV(x) is the current value of x. The variable x stands for present market value of strike price discounted from the value of strike price as on the expiry date. It is the risk-free rate.
Traders must remember that this formula based on put call parity is only valid and applicable for the European class of options. A major characteristic of this options class is that market participants can exercise this only on the expiry date and not before that.
Opportunity for Arbitrage in Put Call Parity
Arbitrage is a trading technique in which an individual will take advantage of the price differential of an asset in two different markets. A trader will buy the asset at a lower price in one market and sell the same at a higher price in another market. This transaction happens simultaneously.
As per the put call parity concept, the value of the call and put option must be equal to a forward contract having the same underlying asset, expiry date and strike price. Any deviation in this relationship and violation of parity creates opportunities for arbitrage.
The formula for put call parity for a perfectly efficient market is P+S = C+PV(x); therefore, any mismatch in the value of either side, with one side being higher or lower than the other, will create a possibility for arbitrage. Traders will carry out risk-free trade by purchasing the cheaper side and selling the expensive side of the equation simultaneously.
This may be true when individuals opt to buy call options and risk-free assets and at the same time sell put options and short that stock. However, it must be noted that in a practical scenario, the window for carrying out arbitrage is short-lived with very fine margins. This means that traders will have to invest huge amounts of capital in order to attain any meaningful profit.
European Call Example under Put Call Parity
Let’s understand how the European call option works under put call parity through a simple example:
You bought a European options contract having the underlying asset as gold. The strike price of this contract is €100, and let’s say, the current trading market price of gold is €25. We need to find the put premium amount if the risk-free rate of interest is 2% and the spot price of gold is €120. Moreover, the expiry period of the contract is six months.
The formula for put premium is:
P = C + (X/[1+R] ^T) – S
Putting in the values at their respective place, we get the put premium as €5. You can also use various accounting and software tools to simplify this calculation and compute the put premium. This will help traders determine the prices of the options contracts and the forward contracts if they wish to use the theorem of put call parity.
How Can Dividends Impact Put Call Parity?
Till now, we have assumed that stock concerning put call parity does not pay any dividend. Now, if this changes and the underlying stock pays a dividend, it will lead to a minor tweak in the put call parity formula.
Individuals borrowing funds will have to pay the interest, and it will be a cost for them. At the same time, investors who short the stock and invest their money in securities will receive the interest. Market participants will adjust that particular equation with the current value of the dividend.
The total amount that an investor puts in the market will be equal to the summation of the current value of dividend and the current value of the strike price of that contract. This adjustment happens on a particular fiduciary call option. The tweaked formula is as follows:
P + S = C + (D + X*e^-r*t)
Things to Know about Put Call Parity
Here are some points that traders should keep in mind regarding put call parity:
The put call parity holds true only for the European options contracts that have to be exercised only on the expiration dates.
The formula for put call parity is also referred to as the “Fiduciary Call is equal to Protective Put” formula. In the formula, P = C + (X/[1+R] ^T) – S, the left side is called the Protective Put, and the right side is called the Fiduciary Call.
When the value of one side of the put call parity formula is greater than the other, it gives rise to an arbitrage opportunity.
Put call parity is a trading philosophy that entails equality between options contracts and a forward contract, with all having the same underlying assets, strike prices and expiry dates. Any disparity in prices of put and call options and the price of the forward contract will open a window for arbitrageurs. This detailed guide will help readers understand the nitty gritty of this trading philosophy and assist them in taking an informed decision.
Q1. What do you understand by protective put?
Ans. It acts as a shield protecting traders from the downsides of holding stocks. A protective put is a trading position having a long put along with a long stock position. Analysts compare the performance between fiduciary call and protective put and determine put call parity.
Q2. What is a fiduciary call?
Ans. This trading position ensures that a combination of long call option and cash has parity with the current value of strike price after adjustment with prevailing discount rates. It shows whether an investor has adequate cash to execute options contracts on their maturity date.
Q3. How can put call parity be advantageous?
Ans. The most crucial benefit of put call parity is that it helps ascertain the value of an options contract with respect to its other components. It also helps arbitrageurs to identify arbitrage opportunities.
Q4. What are the assumptions on which put call parity is based?
Ans. There are certain assumptions that must be satisfied for this theorem to work. They are as follows: The rate of interest is constant. Traders have full knowledge about dividends received on these stocks. The underlying asset has high liquidity and is easily transferable.
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This article has been prepared on the basis of internal data, publicly available information and other sources believed to be reliable. The information contained in this article is for general purposes only and not a complete disclosure of every material fact. It should not be construed as investment advice to any party. The article does not warrant the completeness or accuracy of the information and disclaims all liabilities, losses and damages arising out of the use of this information. Readers shall be fully liable/responsible for any decision taken on the basis of this article.
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