Anyone who has exchanged money in a foreign country understands that the same wealth viewed from opposite sides of an exchange rate market looks different. For example, the wealth associated with one U.S. dollar might be the same wealth associated with 1.5 British pounds. At any given instant the exchange rate between two currencies determines the amount of wealth units one receives for a specific amount of abstract wealth.

The same is true with any other asset, although usually it is not viewed in this way. An electric power plant exchanges its "domestic currency" — the electricity — for a "foreign currency" — the US Dollar. Or we can say that it purchases US Dollars using its electric power. The case is exactly similar to the one of exchange rate markets for currencies. In fact, any economic situation where the change of one asset against any other asset takes place is a situation where the symmetry relationships described in this booklet apply.

PAT technology is especially useful for hedgers who operate in terms of "currencies" other than the US Dollar. For example some electric power producers hedge their electricity producing capacity against the market prices of Natural Gas or Heating Oil. If this kind of hedging is not done from the standpoint of symmetry relationship between these markets, unexpected and initially invisible risk may arise. PAT, functioning from the level of symmetry, will eliminate such risk by always producing financially equivalent payoffs from the perspective of different assets.

Options act the same as insurance policies. They pay off under certain future conditions. If the payoff schedule of an option is relatively simple (essentially a call or a put option), then the financially equivalent payoff on the opposite side of a market is simple to calculate. However, if an option's payoff is more complex, it is impossible to calculate the financially equivalent payoff on the other side of the market without PAT.

Based on a no-arbitrage tenet in a two-asset market, every option must have a financially equivalent reciprocal, or opposite, on the opposite side of the market. As we explained above, every situation where one asset is exchanged against any other asset can be viewed as a foreign exchange market because of the mechanics of the transactions. Hence, the same option parity must be true in the case of any other market as well. For every option payoff on Natural Gas in terms of US Dollars there must be a financially equivalent option payoff on the other side of the market — an option on US Dollars in terms of Natural Gas.

As shown in this section, payoffs on the opposite sides of the market can look substantially different from the original payoff. If a manufacturer or a trader with assets such as Electricity or Natural Gas (or with the ability to convert one into another) is measuring his profitability and risk in terms of a currency foreign to him (US Dollar), his hedging operations may produce completely random results. And this may happen (and does happen) without the producer himself ever noticing! In order to make his decisions from the viewpoint of his own assets, he has to operate in terms of his own assets, not in terms of a foreign currency. We admit that this total change of perspective is somewhat drastic compared to current practice. However, the diagrams presented in this section will display the reasons why such a switch is necessary for accurate risk reporting and management.

In the following pages we present reciprocal payoff schedules for European and American contingent claims. On the left-hand side of the diagrams, titled "Asset 1", we present original payoffs on Asset 2 denominated in Asset 1. This can be, for example, a put option on Natural Gas denominated in US Dollars. Or it can be a barrier option on Heating Oil denominated in BTU units.

The right-hand side diagram, titled "Asset 2", represents the reciprocal payoff on the original Asset 1 denominated in Asset 2. For example, this could be a call option on US Dollars denominated in Electricity units (MWh). Or it could have some unrecognizably shaped payoff on Natural Gas denominated in Heating Oil.

We will see that the payoff on the opposite side of the exchange rate market does not always resemble the shape of the original payoff, or even the shape of any well-known financial instrument. Often the original and reciprocal payoffs look completely different. This is why it is almost impossible to identify such financially equivalent payoffs without PAT. And this is also the reason why every manufacturer or market participant has to operate in terms of his own assets and not in terms of any other asset. Otherwise, although intending to hedge his assets against US Dollars, he is actually hedging the US Dollars against his assets which, as we will see, may turn out to provide a completely different result.