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

• PAT in a two-asset environment provides new true arbitrage opportunities by identifying financially equivalent payoffs that do not seem to be equivalent unless the proper tools are used to identify 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. As 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-asset environment provides a screen for testing the consistency of existing option pricing models by always accurately identifying financially equivalent payoffs on the opposite sides of the market. If a model used independently to generate option prices for these financially equivalent payoffs does not provide financially equivalent results, this reveals an inconsistency in the model. This inconsistency must then be fixed.

• PAT also provides a unifying way to manage an entire comprehensive portfolio by enabling a manager to convert various different payoffs in different assets back to one single payoff in terms of assets most essential to the business. For example, electric power producers could view energy markets from the perspective of their ability to produce electricity, not from the perspective of the US Dollar, which would be a "foreign currency" for them (see page 3). Using PAT in the three-asset environment, which is explained in the next section, further enhances this feature.

There are probably more uses for PAT in a two-asset environment than those 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-asset environment, which is the topic of the next section, will open up new avenues for working with financially equivalent alternative payoffs and options.