Hot answers tagged calibration
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I highly recommend you to stick with the error function (RMSE) value minimization approach. I love MC techniques for this and related problem solving and thus do not recommend you to use anything else because of its simplicity and transparency. It comes down to using the right discretization function and to possibly implement variance reduction approaches.
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Doesn't the Heston model have some Fourier transform formulae for pricing vanillas? I think one could use those to calibrate to the vanillas. Can't provide references at this moment, on the road.
Edit: check out http://www.visixion.com/dok/Visixion_Calibrating_Heston.pdf -- I haven't read this closely but it sounds familiar
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Jim Gatherals Book deals with the models you mention and gives an intuitive understanding about calibration and issues that arise. Mostly basic stuff, but very useful if you're just starting out. Also very understandable without an extensive math background.
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You can find the derivation of the Heston characteristic function (its Fourier Transform) in Gatheral (2006).
Using the characteristic function, you can optimize the model on the prices. There are multiple approaches to optimize, among others pattern search (which is very slow) and stochastic optimization (randomly jump around and stop after n iterations), ...
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Here's a decent study of calibration performance using fast fourier transforms versus other techniques. It concludes Gaussian quadrature works better than other techniques.
http://www.frankfurt-school.de/dms/publications-cqf/CPQF_Arbeits6.pdf
Edit: AZhu points out the link above is dead and that a working link is ...
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Dealing with model error under stochastic volatility (in a more formal way) you could use the UVM (Uncertain Volatility Framework). Here are what i think are the most seminal references:
Avellenada et al (1995) Pricing And Hedging Derivative Securities In Markets With Uncertain Volatilities
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.3736
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