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.
Abstract: With the implied volatility as an important factor in
financial decision-making, in particular in option pricing valuation,
and also the given fact that the pricing biases of Leland option pricing
models and the implied volatility structure for the options are related,
this study considers examining the implied adjusted volatility smile
patterns and term structures in the S&P/ASX 200 index options using
the different Leland option pricing models. The examination of the
implied adjusted volatility smiles and term structures in the
Australian index options market covers the global financial crisis in
the mid-2007. The implied adjusted volatility was found to escalate
approximately triple the rate prior the crisis.