(b) Assume that for a continuously sampled arithmetic average asset price the option value I V(S,1,1) can be written as V(S,1,1) = sF (r) for some function F and some constant V=sH(R,1) a. Then the transformation R= (3) reduces the problem from three to two dimensions. [ [2] [3] . (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 and 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 22H aH +-o at (1-a) R2 + (1+0-R(1 a) rR) 2 IR H. [3] 1 OR JR? (jo+a+r)h=0 [2]