Abstract: The driven processes of Wiener and Lévy are known
self-standing Gaussian-Markov processes for fitting non-linear
dynamical Vasciek model. In this paper, a coincidental Gaussian
density stationarity condition and autocorrelation function of the
two driven processes were established. This led to the conflation
of Wiener and Lévy processes so as to investigate the efficiency
of estimates incorporated into the one-dimensional Vasciek model
that was estimated via the Maximum Likelihood (ML) technique.
The conditional laws of drift, diffusion and stationarity process
was ascertained for the individual Wiener and Lévy processes as
well as the commingle of the two processes for a fixed effect
and Autoregressive like Vasciek model when subjected to financial
series; exchange rate of Naira-CFA Franc. In addition, the model
performance error of the sub-merged driven process was miniature
compared to the self-standing driven process of Wiener and Lévy.
Abstract: German electricity European options on futures using
Lévy processes for the underlying asset are examined. Implied
volatility evolution, under each of the considered models, is
discussed after calibrating for the Merton jump diffusion (MJD),
variance gamma (VG), normal inverse Gaussian (NIG), Carr, Geman,
Madan and Yor (CGMY) and the Black and Scholes (B&S) model.
Implied volatility is examined for the entire sample period, revealing
some curious features about market evolution, where data fitting
performances of the five models are compared. It is shown that
variance gamma processes provide relatively better results and that
implied volatility shows significant differences through time, having
increasingly evolved. Volatility changes for changed uncertainty, or
else, increasing futures prices and there is evidence for the need to
account for seasonality when modelling both electricity spot/futures
prices and volatility.