Consider the European continuously monitored arithmetic average Asian option with terminal payoff: max(A T X 1

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Consider the European continuously monitored arithmetic average Asian option with terminal payoff: max(AT − X1ST − X2, 0), where

AT T 1 =-=-6 T Su du.

At the current time t > 0, the average value At over the time period [0,t] has been realized. Let V (S,τ ; X1,X2) denote the price function of the Asian option at the start of the averaging period. Show that the value of the in-progress Asian option is given by

T-t XT XT T7V (S.T-t. -V St, T-ti T-t' T-t t;  At t - =). T-t

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