In this section we saw how PAT functions in a two-currency environment. We saw that PAT offers new opportunities-- opportunities that have not been previously available—for finding financially equivalent payoffs on the opposite sides of currency exchange markets. The diagrams in this section showed how PAT can provide the benefits that were explained in the introduction:

• PAT in a two-currency environment provides new true arbitrage opportunities by identifying financially equivalent payoffs that do not seem to be equivalent if the proper tools are not used for identifying them (for example, Asset or Nothing Call and Cash or Nothing Put options). If such instruments are being traded at different values, traders can enter the arbitrage position by going short one and going long the other, taking a profit in the process. Because the payoffs are financially equivalent, they will cancel each-other out at expiration. For risk-management professionals, this situation can provide more economical hedge positions using alternate options that are financially equivalent to the originally desired options but that cost less.

• PAT in a two-currency environment provides a screen for testing the consistency of existing option pricing models by correctly identifying financially equivalent payoffs on the opposite sides of the exchange rate market. If a model used to independently generate prices for financially equivalent options does not provide financially equivalent results, this reveals an inconsistency in the model. For example, pricing models used to calculate financially equivalent Supershare 1 and Supershare 2 option prices on the opposite sides of the foreign exchange market must yield financially equivalent results. If that is not the case, the pricing models need to be re-evaluated.

• PAT also provides a unifying way to manage an entire comprehensive portfolio by enabling a manager to convert various different payoffs in different currencies back into one single payoff in the domestic currency (Sophisticated Portfolio Example). Using PAT in the three-currency environment, which is further explained in the next section, further enhances this feature.

There are probably more uses for PAT in a two-currency environment than were identified in this section. The world of finance is in a state of constant evolution and new needs and new tools are coming up continuously. PAT is one such tool which, when properly employed, can provide substantial benefits. Applying PAT in a three-currency environment, which is the topic of the next section, will open up some new avenues for working with financially equivalent alternative payoffs.