Consider a contingent claim whose value at maturity T is given by min(S_T0 ,S_T ), where T₀ is some intermediate time before maturity, T₀ T and S_T0 are the asset price at T and T₀, respectively. Assuming the usual Geometric Brownian process for the price of the underlying asset that pays no dividend, show that the value of the contingent claim at time t is given by

Transcribed Image Text:

V = S[1 - N(d₁) + e¯r(T-To) N (d₂)], where S is the asset price at time t and d₁ r (T – To) + (T – To) - - o√T - To d₂=d₁ - o√T - To.