Parity price refers to the level at which the price of an asset is directly linked to a related price. The concept exists with several types of assets and varies slightly with each. Parity price can also refer to a theory about how international exchange rates fluctuate and settle.
Some uses of parity price simply refer to an intrinsic relationship. One example would be with foreign currencies that, rather than having their exchange rates float freely on the market, are fixed to a particular level in relation to another currency. This often happens with developing nations that fix their currency rate in terms of the US dollar. This rate is the parity price.
Parity price can also be used with options. These are financial products that give the holder the right to choose to purchase another asset at a set price on a set date in the future. Holding such an option can end up being profitable, depending on what the market price of the asset is on that future date. If it is higher than the price the option holder is allowed to buy it at, he will make an immediate profit.
The option itself can be bought and sold before its due date. The price people will pay for the option will vary over time, depending on how likely it looks that the option will wind up being profitable. The parity price of the option is when the market price for selling and buying the option is equal to its intrinsic value, which is the amount of profit somebody holding the option today would wind up making if the market price for the underlying asset remains unchanged between now and the option's due date.
The term parity price can also be used to refer to purchasing power parity. This is the theory that in the long-run, currency exchange rates will find and maintain a level position. The theory is that this position is the one by which the same amount of money will be enough to buy the same goods in both countries. For example, the exchange rate between the United States and Japan might settle at $1 (USD) to 100 yen. The theory would state that, for example, a hamburger that cost $2 in the US would then cost 200 yen in Japan.
In reality, there are several reasons why this theory is not literally borne out. One is that it works on the basis that both countries, and indeed all countries, make up a single market. But in the hamburger example, a hamburger offered for sale in Tokyo is clearly not going to be of any interest to a buyer in New York. Another issue is that demand for products is not universal. A hamburger seen as a low-quality snack in the US may be seen as a luxury food in other countries, and thus command a relatively higher price.