Exercises 9.1 Symmetry 1. For a LVM dened by dft = C(ft)dWt, prove that the intrinsic fair value of a European call option dened as G(; f0;K)  C(;K) ???? max(f0 ???? K; 0)

is G(; f0;K) =

p C(K)C(f0)

p 2

Z 

0 P(t0; s(K))dt0 where the fundamental solution P(t0; s(K)) satises an Euclidean Schrodinger equation.

2. Deduce the symmetry G(; f0;K) = G(;K; f0)