Where e is the exchange rate, that is, how many units of country A's currency can be converted into one unit of country B's currency (direct quotation); P a stands for the general price index of country a; P b stands for the general price index of country B.
The above formula implies an important assumption that under the condition of free trade, the price of the same commodity is equivalent all over the world. Because different countries use different monetary units, the price of the same commodity expressed in different currencies is finally equal after the equilibrium exchange rate conversion, that is, P a=? Public radio station. In fact, law of one price is a manifestation of purchasing power parity theory.
Law of one price provided a basic method for exchange rate calculation. If a Big Mac sells for $3 in the US and HK$ 24 in Hong Kong, excluding other factors, US$ 3 should be equivalent to HK$ 24, that is, the exchange rate of US$ to HK$ 65,438 +0/HKD 8. This method was put forward by economists in the American magazine Economics, and it is called the Big Mac Index. Other similar indexes have also been proposed, such as ipod using Apple computers and Starbucks coffee. This kind of products have three commonalities. First, they are all sold in many countries at the same time. Second, they are all standardized products, and manufacturers strive to provide differentiated products at any point of sale; Third, they are all representative best-selling products. Law of one price is also used for pricing financial products.
Financial assets traded in the financial market have a single buying price and selling price. There is a price difference between the buying price and the selling price, which applies to law of one price. Theoretically, no dealer is willing to sell financial assets at a price lower than the market maker is willing to sell. Similarly, no one wants to buy financial assets at a price higher than the market maker is willing to pay. Otherwise, a market participant who buys high and sells low can't find a suitable counterparty, or his business is equivalent to doing charity and benefiting others.
Law of one price in the derivatives market is different. Derivatives are not concerned with the consistency of similar prices, but with the consistency of the same commodity price with different time differences.
Futures and spot prices are an example. Whether buying goods from the futures market or the spot market, excluding transaction costs such as handling fees and transportation fees, the current prices of the two commodities should be the same. Otherwise, investors may buy from the lower-priced market and then sell in the higher-priced market. For example, he buys soybeans from the spot market at a cheaper price, and at the same time establishes a soybean futures short contract, trades at a price higher than the current price in the futures market, and delivers them three months later, which has an arbitrage opportunity. However, arbitrage will also attract other investors to participate in similar transactions, so this arbitrage behavior cannot exist for a long time, and eventually the futures price and spot price will be consistent on the maturity date, reflecting the convergence nature of prices [1].
The InvestorWorld website points out that:
A security must have a single price, no matter how it is generated. For example, if an option can be generated by two securities belonging to different targets, then the prices of the two securities must be the same, or there is an arbitrage opportunity between them.
Bodie, Kane and Marcus also pointed out that:
The same securities or portfolio of securities should have the same price, otherwise arbitrage will occur.
A similar discussion can also be found in Arrow and Debru's discussion about Arrow Securities.