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The HestonModelHelper in QuantLib expects a spot value, strike and BlackVol. In theory, you could convert the strike of your FX Options (which are normally quoted in Delta terms) into an absolute strike (Check this post for details), and then calibrate the model as if the instruments were options on an equity where the foreign rate would be the dividend. I ...

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The best solution is to compute the implied volatility for a call that matures in two years then the implied volatility for one year call one year from now will be equal to: $$\sqrt{2*vol^2_{2y}-vol^2_{1y}}$$ You can find this formula in the wikipedia article about forward volatility: Forward volatility Now in order to generate many volatilities, the ...

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In this (extremely technical) paper by Duffie et al it is shown that a Markov process is infinitely decomposable if and only if it is a regular affine process. So their results establishes a correspondence between Markov processes and regular affine processes. Okay, that (the paper) is too technical for me, but if I look at the characteristic function of ...

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I am not providing a full proof but a reference for you to read up the details. The key step is mentioned below. Most models used in finance are Markovian which is kind of in line with the efficient market hypothesis. The key step of of seeing that the Heston process is Markovian is the following theorem. Let $f$ be a bounded Borel function from \$\mathbb{...

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A stochastic process with independent increments is a markov process. the proof is available in the following document: (Lemma 1.1) http://statweb.stanford.edu/~adembo/math-136/Markov_note.pdf

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