How does Put-Call Parity work?

Put-Call Parity relates to the principle that in rational and efficient markets, the price of a put option should always be equal to the price of a call option plus the present value of the strike price. This means that if an investor has a call option and a puts option with identical underlying assets, strike prices and expiration dates, it is impossible for one to be more valuable than the other.

Are there any risks associated with Put-Call Parity?

While Put-Call Parity is a useful tool for hedging and arbitrage trading, there is always a possibility of mispricing and losses if the market moves in an unexpected direction. Investors should be aware of these risks before trading with Put-Call Parity.

What Is Put-Call Parity? | Importance, Formula, Pros & Cons

Q: What is Put/Call Parity?

Put Call Parity is defined as the equality between Put and Call prices, or equivalently, Put/Call=Stock price. Put-call parity allows investors to calculate the intrinsic value of their option based on the intrinsic value of its related security.

Q: How to Calculate P/C Parity?

The formula for P/C parity is: C + PV(x) = S + PN(x)

Put-call parity is a principle of derivatives pricing that says the premium an investor receives for a call option should equal a similar put option. It focuses on European options, which can only be exercised at expiry.

Put-call parity states that the price of a put and a call with the same strike and expiration must have the same implied volatility.

Put-call parity is a useful formula for pricing options because it allows you to price an option by looking at the prices of other related options.

Understanding this principle can help you make better investment decisions and makes practicing sound risk management a little easier.

Importance of Put-Call Parity

Put-call parity is the most basic option pricing model because it allows you to calculate the value of a call or put by computing the value of a related option.

It says that a stock option should be worth at least as much as its corresponding position in the underlying security. Put-call parity is also a method to assess the market for pricing discrepancies.

Put-call parity explains that traders aren't willing to risk their capital unless there is sufficient compensation, making it much easier to manage your portfolio.

How Put-Call Parity Works

Put-call parity says that if you buy a call option on a stock then sell a put option on that same stock, the premium received from buying the call must be equal to the premium paid for the shot put.

Put-call parity says that there should also be equality between premiums and strikes when you write an option in your portfolio and buy its related option.

The Formula for P/C Parity

The figure below shows how to calculate P/C parity. The equation that expresses put-call parity is:

Put-call parity is the most important tool in your derivatives pricing toolbox because it allows you to compare options across strikes, tenors, and issuers.

Benefits and Drawbacks of P/C Parity

The greatest advantage of put-call parity is that it's a great tool for risk management.

It also makes it easier to compare the prices of different options written on the same security because you can calculate them in terms of their intrinsic value, which is simply the difference between the strike and the current price.

However, Put-Call parity does have some drawbacks. Put-call parity typically only works near the money and when trading options on individual stocks.

Put-call parity also doesn't work as well without money options.

Why It’s Important to Understand Put-Call Parity

Helps better diversify your portfolio by limiting the company or sector that you invest in
Allows you to use options as a hedge, which means you can buy them instead of owning the stock itself. This is typically an easier way to manage volatility because it doesn't require keeping track of dividends and other issues associated with being a direct shareholder.
Helps identify when security is overpriced. Put-call parity will show, for example, that you have to pay more for an option than it's worth. So if put-call parity shows that the premium on a stock option is too expensive then it probably means that the security can't find buyers and might be a good opportunity because its price is expected to fall.
Helps you better manage your portfolio by limiting the company or sector that you invest in, making it easier to diversify, and identifying when expensive options might mean other stocks are also overpriced.

The Bottom Line

Put-Call Parity is a major tool in derivatives pricing because it tells you the combined premium of Put and Call options for a security trading at or around strike price.

In addition to its uses as a risk management tool, Put-Call parity can help you better diversify your portfolio by limiting which companies or sectors you invest in.

It also aids you in identifying opportunities when Put-Call parity shows Put option prices are too expensive and helps identify overpriced securities.

Put-Call Parity FAQs