ABSTRACT
Asian options are contracts that depend on underlying assets X and Y and upon the average of the price process XY (t). The average price process is captured by a no-arbitrage contract A called the average asset. The payoff of the average asset is defined as
AT =
[∫ T 0
XY (t)µ(dt)
] · YT . (9.1)
The average asset is a contract that pays off a number of units of an asset Y , where the number of units is the weighted average price of an asset X with respect to the asset Y . The weights are determined by the weighting measure µ which can represent both continuous or discrete averaging. Our definition of the average asset guarantees that its price is always positive, and thus the average asset can be used as a numeraire. The average asset is analogous to the maximal asset M∗ that appears in pricing of lookback options. The important difference is that the average asset A turns out to be a no-arbitrage asset in contrast to the maximal asset M∗.
