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.

Large investment banks and other international businesses face risk and opportunity in the daily fluctuations of international exchange rates. Sophisticated currency traders use both simple and exotic options to shape their portfolio's risk profile. The Payoff Advantage Tool instantly provides financially equivalent option payoffs on the opposite side of any currency environment for any option.

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 opposite payoff on the other side of the exchange rate 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 exchange rate market without PAT.

Based on a no-arbitrage tenet in a two-currency environment, every option must have a financially equivalent reciprocal (or opposite) on the opposite side of the foreign exchange market. However, current technology, though sophisticated, can only calculate financially equivalent payoffs on the opposite side of an exchange rate if those payoffs are simple. PAT is capable of calculating financially equivalent payoffs on the opposite sides of an exchange rate for any option. Therefore, PAT not only proves that physics-based technologies provide a greater benefit, it also validates the use of physics-based operators in finance.

In the following pages we present reciprocal payoff schedules for European and American contingent claims. On the left-hand side of the diagrams, titled "Domestic Payoff", is the original payoff. This can be, for example, a put option on the Swiss Franc denominated in US Dollars. Or it can be a barrier option on British Pound denominated in Japanese Yen.

The right-hand diagram, titled "Foreign Payoff", represents the reciprocal payoff on the original domestic currency, denominated in the foreign currency. For example, this could be a call option on US Dollar denominated in Swiss Francs. Or it could have some unrecognizably shaped payoff on Japanese Yen denominated in British Pound.

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 using tools other than PAT. However odd the diagrams may look, the payoffs on the left-hand side and the payoffs on the right-hand side of the page always are financially equivalent at every point along the exchange rate. This is due to the symmetry relationship that is the basis for PAT.