In this document we saw how PAT functions in the two- and three-currency environments. A direct extension from here would be applying PAT in a truly multi-currency environment. There are no limits to the number of currencies that PAT can handle; PAT will always identify financially equivalent payoffs, no matter how complex the environment. In a world where offshore investments, import-export businesses and tourism flourish, we believe that PAT will become a major tool for managing such a vast and rapid flow of wealth.

This document has been written for currency traders. One potentially unlimited application for PAT becomes clear when we stop viewing portfolios as currencies, and start viewing them as assets or wealth units. In this way, PAT can be applied to basically any derivatives markets: stocks, commodities, and interest rates to name just a few.

For example, an electric power producer might want to view their operations as input (fuels), output (electricity) and the currency (US Dollar) used by the markets. In this way, the power producer could manage hedging of its operations based on the underlying symmetry between the input and output of its production process. This should clearly be a vastly more efficient method than managing these risks based on the statistical analysis of various risk factors separately; a process in which the underlying symmetry gets broken.

The level of complexity caused by trading or hedging with exotic options can be enormous. There are numerous exotic options at traders' and risk-managers' disposal. Without properly analyzing the impact of such instruments on the portfolio as a whole, the risks assumed can be much greater than originally expected. Using wrong or inadequate tools for analyzing potential risks creates only an illusion that risks have been managed or profitable positions entered. Such an illusion can be even more dangerous than simply ignoring risk.

In the two sections about PAT in the two- and three-currency environments we looked at American and European options. PAT is equally applicable to any other type of exotic options, such as Asian options, Correlation options, and others. There are almost no limits to the applications for PAT. We invite everyone to use this unique and powerful tool to increase their own profitability, and in this way to benefit the entire financial community.