How do we estimate parameters in a continuous time stochastic volatility model? I've seen the usage of EMM, GMM, SMM algorithms. But how do you extract a time series of those parameters such as correlation? Also, why do people sometimes estimate parameters in SDE by time series analysis while other times they use cross sectional fitting to calibrate the model? What are their advantages and disadvantages? Those questions are really bothering me right now. Any response will be greatly appreciated.
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