Optimal adaptive sequential calibration of option models

Option models needs to be recalibrated as new data becomes available. The updated model parameters will depend on previous parameters and new data, making adaptive sequential calibration a suitable choice. We introduce a method for optimally tuning the parameter adaptivity when non-linear filters are used for calibration, as well as extending the dynamics of the parameters. The adaptivity is optimized by defining a statistical model, including both the option models and the adaptivity parameters. It turns out the corresponding (log-)likelihood function can be optimized through the EM algorithm, which ensures that the optimization is robust. We evaluate the method on simulated data and S&P 500 index options, seeing that we can track variations in the model parameters well. The likelihood framework is also used for model selection where we find support for both complex option models as well as non-trivial adaptivity. This is made feasible with the optimal tuning presented in this chapter.