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Heston model
Dear Nanette,if you would like to use a global optimizer use Differential Evolution. You can download a C(++) and a matlab version for instance from the website of Rainer Storn. He is one of the inventors of the algo...But for the first try you could use a newton solver like lfbgs or sqp method. To be sure you get the real min you may vary the starting params randomly and choose the best outcome...Hope this helps, Ciao Lapsi
Heston model
Have you tried gatheral's approximations for initial guesses? They have worked very well for me.
Heston model
The C++ version from the website of Rainer Storn has problem to work.