Suppose we have invested in a US asset that pays us USD$10m every 6 months for 2 years and the cashflow is completely risk free in USD. We are an Australian based investor so we have exposure to foreign exchange risk and our cashflow is not risk free We receive a cashflow of $10m USD and atthe current exchange rate of 1 USD = 2 AUDthat converts to $20m AUD per half year.

The Australian Dollar value of the combination of the cashflow from the US asset and the payoff fromthe putoption portfolio at time T_iis cashflow=S_Ti+ max (X- S_Ti, 0) = max (S_Ti, X), whereS_Tiis the Australian dollar value of $1m USD at time T_i

Show that this is equivalent tocashflow =X +max (S_Ti- X, 0) and thatX +max (S_Ti- X, 0) > X

S_{Ti I}is the value of AUD of $1m USD at time T_i( which is random) and X is $2m which is constant.