(dV/dt) + 0.5 * (sigma)^2 * S^2 * (d2V/dS2) + r * S * (dV/dS) - r * V =
0
Then change the variables: F = e^( r * (T-t)) * S and V(S,t) = U(F,t)
The book gives me the answer as in the following:
(dU/dt) + 0.5 * (sigma)^2 * F^2 * (d2U/dF2) - r * U = 0
I have tried several times, but can't reproduce the solution. Can
anyone help me on the derivation of the solution?
Thanks in advance.
A standard derivation could be found in
http://www.rotman.utoronto.ca/%7Ehull/Technical%20Notes/TechnicalNote7.pdf