ABSTRACT
American options have the same payoff as their European option counterparts but an American option can be settled at any time τ before the maturity time T . American options pay off either fY (XY (τ)) units of an asset Y , or fX (YX(τ)) units of an asset X at the exercise time τ ∈ [0, T ]. The exercise time is chosen by the holder of the option. When these two payoffs correspond to the same contract, they are related by the perspective mapping
fY (x) = fX ( 1 x
) · x, or fX(x) = fY ( 1x) · x. (7.1) We will distinguish two cases: when the underlying assets are no-arbitrage assets, and when one of the underlying assets is an arbitrage asset.
