Hi, I have to change the variable in the following eqn, although I know the answer I cannot see how the answer was arrived at: We start with a p.d.e in F(S,t) -dF = -rF + (r- delta)SdF+0.5(theta^2)(S^2)d^2F dt dS dS^2 We then want to change to X=1/S F(S,t)=Sf(X,t) The answer is: -df = -deltaf + (delta- r)Sdf+0.5(theta^2)(S^2)d^2f dt dS dS^2 Now the way I see it: -dF = -Sdf part 1 dt dt -rF = -r.S.f not sure how this becomes delta? part 2 (r-delta)SdF=(r-delta)S^2df. dX=(delta-r)S^2df . 1 dS dX dS dX S^2 =(delta-r)df .1 (when you divide through with the S from part 1) dX S =(delta-r)df. X part 3 dX Lastly .5(theta^2)S^2d^2F=.5(theta^2)S^3d^2 .dX^2 dS^2 dX^2 dS^2 =(.5*theta^2).S^3.d^2f . -2 dX^2 X^3 =theta^2.d^2f .X where the .X comes from dividing through by S from part 1 dX^2 = part 4 Part 4 clearly is wrong but I'm not sure where I've made the mistake?