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I'm interested in calibrating the Heston model so I was reading about it online. All procedures I could find was using market prices for European call options and using the (semi-)closed-form expression to obtain parameters that would've yielded these call option prices.

However, the Heston dynamics tell us something about how the stock price behaves. Wouldn't it make more sense to use the stock price trajectory and infer reasonable parameters based on that information? I could not find anything similar in the literature but maybe I haven't searched thoroughly enough yet.

Does anyone know anything about this or has even tried it? I'm interested to hear your thoughts.

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    $\begingroup$ You can. You could do some maximum likelihood or filtering estimation. But this gives you Heston parameters under $\mathbb{P}$. For option pricing, you need risk-neutral parameters though. Thus, directly calibrating the model to option prices is easier. $\endgroup$
    – Kevin
    Apr 6 at 8:46
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    $\begingroup$ Stoch vol models now are LSV, and use historical series of spot and implied vols to calibrate the general model dynamics of spot/vol and vol/vol covariances, and european vanilla options to calibrate today's smile. $\endgroup$ Apr 6 at 13:21

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