# What is Put-Call parity in option trading?

Authored by
Team Espresso
November 12 2022
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Stock Options in the derivatives market typically fall into one of two categories, "Call" or "Put." To speculate on a price increase, a Call option is purchased. And when you believe prices will go down, buy a Put option.

However, Warren Buffett warns that derivatives can be as destructive as nuclear weapons.

Options are derivative contracts that are worthless in and of themselves and instead derive their worth from the value of the underlying asset. Shares, commodities, and currencies, among others, can all serve as the underlying asset.

Buyers of options contracts have the right, but not the obligation, to sell or buy the underlying asset on or before the contract's expiration date and at the predetermined price outlined in the contract (known as the strike price).

When purchasing an options contract, the buyer also acquires the right to put the option into effect or cancel it. The buyer of an option bears no more risk than the amount of the option's premium paid.

## What is Call Option?

A call option gives the option buyer the right but not the obligation to buy the underlying asset at a predetermined price, also known as a strike price, on or before the option's expiration date. The seller of an option is called an option writer.

## What is Put Option?

A put option gives the option buyer the right but not the obligation to sell the underlying asset at a predetermined price.

## Put-call parity calculator

The link between a European call option (CE), a European put option (PE), and the underlying asset are displayed via this put-call parity calculator. You may examine what values each of these variables should take on if parity were to be maintained by entering data.

When the forward market determines the price, this theory describes the connection between a call option and a put option.

If both options are forward "for money," then the intrinsic value of a call option in one currency should be equivalent to the value of a put option in another currency, given that both options have the same strike price and expiration date.

As opposed to its synonym, purchasing power parity (PPP), which holds that the price of a good in one country should be equal to that of an interest in another country after applying the applicable exchange rate, Put-Call-Forward Parity (PCFP) uses a different formula. Not all cases involve PPP.

The concept of put-forward parity for European options is central to options pricing. You'll need to buy a put option and a forward contract for the underlying asset with the same expiration date as the put option to acquire a call and bonds (trust call) and synthetic protective put.

## Understanding put-call parity

Investors should not hesitate to buy a call contract and hold a forward contract with the same expiration date and special price or buy a stock and long for a European put option for protection, assuming put-call parity.

If the price of one asset deviates from the parity relationship, then an arbitrage opportunity arises. Traders can profit from this by purchasing the bargain and selling the inflated asset.

European options are subject to the principle of put-call parity. The strike price, underlying asset, and expiration date are all consistent across all of these options because they belong to the same class. Consequently, since American options can be exercised at any moment before the expiration date, this logic does not apply to them.

According to the principle of the put-call parity formula, if you hold a short European put and an extended European call of the same class, you will receive the same return as if you had a single forward contract on the same underlying asset, with the same expiration and a forward price equal to the option's strike price.

Suppose this correlation breaks down, as arbitrage can be pursued when the prices of put and call options diverge. Therefore, experienced traders can theoretically make money without taking any risks. In liquid markets, such chances are rare and don't last long.

An arbitrage opportunity exists when the put or the call side of the put-call parity formula is more significant. You can generate a risk-free profit by selling the costlier half of the equation and buying the less expensive side.

## How does put-call parity work?

When an asset has put-call parity, both Put Options and Call Options on the same asset can be utilised to achieve the same portfolio objective. It also indicates that Put Options and Call Options have the same implied volatility (IV) for a given underlying asset.

Assuming Put Options and Call Options with the same underlying assets have the same value, the put-call parity calculator ensures that investors end up with a net zero return.

A common understanding of option prices and related tactics relies heavily on the concept of put-call parity. Its ease of use is a plus as well as a minus.

While it helps learn about the most common options contracts and their values, it may produce poor results when applied to more complex options strategies. Models such as the Black-Scholes approach and the Monte Carlo method are ideally suited for analysing such complex variations.

The value of a put or call can be estimated using the put-call parity strategy. An arbitrage opportunity arises if the parity is broken, which occurs when the values of the put and call options diverge to the point where this relationship no longer holds. Even though such openings are rare and temporary in liquid markets, expert traders can theoretically make a profit with no downside risk. In addition, it allows for the easy production of artificial postures.

## Conclusion

Any attempt to gain a holistic knowledge of the pricing of Options and related techniques must account for the put-call parity strategy. Its ease of use is both a strength as well as a weakness. While it helps learn about the fundamentals of Options contracts and prices, it can fall short when applied to more nuanced options. Models, including the Black-Scholes and Monte Carlo approaches, are superior for analysing complex variations.

## FAQs

### Q. Do all options follow the put-call parity rule?

Put-call parity does not hold for American options; it’s good for only European options. Unlike American options, which can be exercised any time before a specific date, European options can only be used on the specified date.

### Q. What is the definition of arbitrage?

The trading method known as "arbitrage" aims to generate a profit by simultaneously purchasing and selling assets in different markets. This tactic seeks a short-term advantage by taking advantage of mispriced assets in different markets.

### Q. What is market friction?

Frictions in the market are the hidden expenses of making a trade. When a deal is made, these fees are often hidden in the fine print. These include taxes, commissions, and the spread between buying and selling prices, among others.

### Q. How do you define a synthetic position in Put-Call Parity?

The so-called synthetic positions are a part of many option arbitration methods. There is an artificial analogue for every material stake in the underlying stock or its options.

Every position's risk profile (potential profit or loss) can be precisely replicated with other, more complex methods. For a synthetic position to be valid, all of its constituent parts, including the execution price, expiration date, call, and put, must be the same.

The expiration date is the single most critical consideration when trading options. Let's see what happens if you don’t square off your option contract position.