Perpetual Put Option For T it is sufficient to analyze the ODE 2 2 S2

Perpetual Put Option For T → ∞ it is sufficient to analyze the ODE

σ2 2 S2 d2V dS2 + (r − δ)S dV dS − rV = 0 .

Consider an American put with high contact to the payoff V = (K − S)+ at S = Sf . Show:

a) Upon substituting the boundary condition for S → ∞ one obtains V (S) = c

 S K

λ2

,