Abstract
In this paper we present an option pricing model based on the assumption that the underlying asset price is an exponential Mixed Tempered Stable Lévy process. We also introduce a new R package called PricingMixedTS that allows the user to calibrate this model using procedures based on loss or likelihood functions.
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Notes
We refer the interested reader to Rroji and Mercuri (2015) for a more complete analysis on the shape of MixedTS distribution and on the behaviour of skewness and kurtosis for varying \(\alpha \) and different combinations of \(\lambda _+\) and \(\lambda _{-}\).
In the PricingMixedTS the dumping parameters can be selected by the user, the default value is 0.75.
Recall that APE and RMSE yield the same estimates as explained in Sect. 4.
The uniform density has bounded support and the bounds depends on the model parameters. Consequently asymptotic results cannot be derived trivially (see Lehmann and Casella 1998, for more details).
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Mercuri, L., Rroji, E. Option pricing in an exponential MixedTS Lévy process. Ann Oper Res 260, 353–374 (2018). https://doi.org/10.1007/s10479-016-2180-x
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DOI: https://doi.org/10.1007/s10479-016-2180-x