(b) Assume that for a continuously sampled arithmetic average asset price the option value V(S,1,t) can be written as V(S,1,t) = F (5,1) for some function F and some constant a. Then the transformation 1 R= ' V=SCHR,t) (3) reduces the problem from three to two dimensions. (1) Write the path dependent Black-Scholes equation in the case when a continuously sampled arithmetic average asset price is considered. av av 22v (ii) Find the derivatives if V is given by (3) t'as as2 aHaH ? (iii) Find the derivatives and al' as 232 (iv) Hence show that the partial differential equation for the value of the option (3) is ? aH +(1+oR(1 a) rR) 1 H=0. R2 at aR [2] and [3] 1 [3] +302125 (1a) (20*a+r) [2]