## Definition

Put-call parity is a principle in options pricing which shows the relationship between the value of European put and call options of the same class with identical strike prices and expiration dates. It states that the combined value of these options will be equal to the difference between the strike price of the options and the current spot price. In other words, the value of a call option is equal to the value of a put option when they both have the same strike price and expiry, plus the present value of the strike price.

### Phonetic

**The phonetics of the keyword “Put-Call Parity” is:Put: /pʊt/Call: /kɔːl/Parity: /ˈpærɪti/**

## Key Takeaways

Sure, here are three main points about Put-Call Parity:“`html

- Put-Call Parity Principle: This is a principle that defines a price relationship between a call option, put option and the underlying asset. The principle states that the portfolio of a long call option and a short put option should yield the same return as holding the asset.
- Arbitrage Opportunities: If the put-call parity is not as it should be, it presents an opportunity for arbitrage. This is where traders can take advantage of price differences between markets to make a profit. So, put-call parity helps keep the options market efficient.
- Applies to European Options: An important thing to note about put-call parity is that it only applies to European style options. European options can only be exercised at the expiry date. If you have American style options, that can be exercised at any time before expiry, the put-call parity concept cannot be applied in the same way.

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## Importance

Put-call parity is a vital principle in options pricing that sets a relationship between the price of a call option, a put option, and the underlying stock. This principle is significant as it prevents the opportunity for arbitrage. In a properly functioning market, opportunities for risk-free profits, or arbitrage, should not exist. Therefore, if the prices of the options drift so that this relationship gets out of balance, arbitrageurs can initiate trades that will profit and generate risk-free returns until the prices are back in sync. This serves as a self-correcting system to sustain fairness and equilibrium in the options market. Put-call parity is also helpful in pricing options and helps traders strategize their trading by understanding the value and potential return of an option.

## Explanation

The Put-Call Parity concept serves a critical role in the options pricing theory, acting as a guiding principle for the pricing of options. Essentially, it establishes an equivalence relationship between a portfolio consisting of a call option, a bond that pays the strike price at the expiration of the option, and a portfolio consisting of a put option and the underlying asset. In relation to derivatives and options markets, it can help traders and investors identify arbitrage opportunities. If the parity condition does not hold through, it means that the prices of these instruments are out of sync, and there is an opportunity to gain a risk-free profit through arbitrage.Moreover, it is utilized in generating synthetic positions in an asset. With the help of Put-Call Parity, investors can create a synthetic long or short position in assets using a combination of puts, calls and bonds. This gives market participants flexibility, allowing them to take a position in an asset without holding the asset itself. This is particularly beneficial in the derivatives market where there can be restrictions or higher costs associated with owning the underlying asset, at the same time, it impacts the strategy for financial derivative trading and risk management. Understanding the principle of Put-Call Parity is fundamental for both options pricing and financial market integrity.

## Examples

Put-Call Parity is an essential principle in options pricing that defines a relationship between the price of a European call option and European put option, both with the same strike price and expiration date. Here are three real-world examples which can help illustrate this confidence:1. Stock Investing: Imagine a stock of a company is trading at $100. An investor who believes the price might go down can buy a put option with a strike price of $100 and expiry in one month. Simultaneously, if the investor also buys a call option with the same strike price and expiry, he/she can hedge their bets, utilizing the put-call parity. If the stock price goes up, they profit from the call option, and if it goes down, they profit from the put option.2. Commodity Markets: Say a trader wishes to benefit from price movements of a certain commodity, like gold. The trader can buy a put option if they believe prices will fall and a call option if they believe prices will rise, with both options having the same strike price and expiry date. This strategy, enforced by put-call parity, enables the trader to avoid huge losses if the prediction about price movement is incorrect.3. Currency Exchange: A forex trader is considering options on a currency pair, say, USD/EUR. If the trader predicts the EUR will strengthen (and USD will weaken), they might buy a call option. Conversely, if the trader thinks the EUR will weaken (and USD will strengthen), they might buy a put option. Through put-call parity, the trader could buy both the put and call options with the same strike price and expiry date to cover all bases. In all these real-life scenarios, put-call parity provides opportunities to create strategies for hedging risks or profiting from predicted price movements while offsetting potential losses from inaccurate predictions.

## Frequently Asked Questions(FAQ)

## What is Put-Call Parity?

Put-Call Parity is an important principle in options pricing, providing a relationship between the price of European put and call options with the same strike price, expiry, and underlying asset. It helps in determining the theoretical value of options.

## Why is Put-Call Parity important in financial markets?

Put-Call Parity is essential in financial markets as it provides a framework for arbitrage opportunities. If the Put-Call Parity doesn’t hold, traders can simultaneously buy undervalued options and sell overvalued options to take advantage of risk-free profit opportunities.

## How is Put-Call Parity calculated?

The formula for Put-Call Parity is C + PV (X) = P + S, where C is the price of the European Call Option, PV(X) is the present value of Strike price (X), P is the price of the European Put Option, and S is the spot price of the underlying asset.

## Can Put-Call Parity be used for American options?

Technically, the Put-Call Parity concept is derived from assuming European options. However, it still brings some useful insights into the connection between put and call prices for American options.

## What happens if the Put-Call Parity relationship is violated?

If the Put-Call Parity relationship is violated, it implies there exists an arbitrage opportunity, i.e., an opportunity to make a risk-less profit. The arbitrageur can purchase the cheaper portfolio (put or call option) and sell the more expensive one to make a profit.

## What factors can affect the Put-Call Parity?

Many factors can affect this relationship, including price variations, market volatility, interest rates, dividends, and the expiration date of the options. It assumes no brokerage fees or transaction costs and that markets are perfectly efficient, which might not always be the case.

## Does Put-Call Parity hold in a binomial model?

Yes, the Put-Call Parity principle holds in a binomial model. The binomial model is flexible enough to adjust itself to maintain the parity.

## Related Finance Terms

- Options Trading
- Strike Price
- Expiration Date
- Arbitrage
- European Options

## Sources for More Information