We define

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

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

Transcribed Image Text:

and d₁ d3 = = In + (r+)T K 2 O 2 In o√t d₂=d₁ - 0 √t, +d₁, d4 d3 - 0√√7, 8 = V₁(S, t; K) = [Xe¯¹¹ N(-d₂) – SN(-d₁)] - 8-1r B - ( 13 ) ₁ -1 [ X e-™™ N Xe¯¹¹ N(-d₁) - S B² S 2r มะ N(-d₂)].