We define Show that the price functions of various European barrier put options are given by where

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We define

and d d3 = = In + (r+)T K 2 O 2 In ot d=d - 0 t, +d, d4 d3 - 07, 8 = V(S, t; K) = [Xe N(-d) - SN(-d)] 8-1r BShow that the price functions of various European barrier put options are given by

Puo (S, t; X, B) = V(S, t; min(X, B)) Pdo (S, T; X, B) = max(V (S, t; X)  V (S, t; B), 0) - Pui (S, T; X, B)

where pE(S, τ ; X) is the price function of the European put option, B is the barrier and X is the strike price.

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