Putcallparity

A call gives the right to buy an asset at a fixed price and a put gives the right to sell it at that same price. At first sight they look like opposites, but combining them with the asset and some cash shows they are tightly connected.

Two different portfolios can be built that pay exactly the same amount at expiry, so they must cost the same today. The first portfolio holds a call option and enough cash to pay the strike price at expiry.

The second holds a put option and one unit of the asset. Whatever the asset price turns out to be, both portfolios are worth the same at expiry, which is the logic behind the rule.

This matters in practice because it lets traders and risk managers spot mispriced options. If a call looks cheap compared with the matching put, an arbitrageur (someone who profits from price gaps) can buy the call, sell the put, and take an offsetting position in the asset.

The trade earns a certain profit until the gap closes. The relationship is also used to create synthetic positions.

A trader who cannot trade a particular option directly can build the equivalent from the other option and the asset. Option dealers use it daily to check that their quotes are consistent.

The standard formula applies to European options, which can be exercised only on the expiry date. It assumes no dividends and no trading costs.

In real markets, dividends, borrowing costs and early exercise rights for American options adjust the formula, so small gaps are normal and do not always mean a free profit. A useful nuance is that interest rates enter through the present value of the strike price.

When rates rise, the cash needed today to cover the strike falls, which shifts the balance between call and put prices. This is why calls tend to be a little more expensive than puts when rates are higher, all else equal.