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Title: L1 regularized smoothing with changepoints applied to implied volatility surfaces Authors:  Matus Maciak - Charles University (Czech Republic) [presenting]
Abstract: Nonparametric models with changepoints gain on their popularity because of the overall flexibility which they offer. On the other hand, the theoretical background of such models is quite challenging and many problems need to be solved to correctly apply these models in real life situations. The idea is to introduce a direct method to estimate the implied volatility function (the implied volatility surface respectively) in option pricing by adopting the nonparametric smoothing together with the sparsity principle and recent developments in the area of atomic pursuit techniques. We propose the L1 regularized nonparametric estimation with possible changepoints (structural breaks) in the underlying dependence structure. Moreover, conditional quantiles can be obtained instead of the conditional mean and various hierarchical concepts can be used to specify the unknown model and the occurrence of hypothetical changepoints in it. Some theoretical results are derived and the consistency of the proposed method is proved with respect to the model estimation and the changepoint detection too. Empirical performance is investigated via a simulation study and some real implied volatility surface estimation.