3,875 research outputs found
Interpolation of equation-of-state data
Aims. We use Hermite splines to interpolate pressure and its derivatives
simultaneously, thereby preserving mathematical relations between the
derivatives. The method therefore guarantees that thermodynamic identities are
obeyed even between mesh points. In addition, our method enables an estimation
of the precision of the interpolation by comparing the Hermite-spline results
with those of frequent cubic (B-) spline interpolation.
Methods. We have interpolated pressure as a function of temperature and
density with quintic Hermite 2D-splines. The Hermite interpolation requires
knowledge of pressure and its first and second derivatives at every mesh point.
To obtain the partial derivatives at the mesh points, we used tabulated values
if given or else thermodynamic equalities, or, if not available, values
obtained by differentiating B-splines.
Results. The results were obtained with the grid of the SAHA-S
equation-of-state (EOS) tables. The maximum difference lies in the range
from to , and difference varies from to
. Specifically, for the points of a solar model, the maximum
differences are one order of magnitude smaller than the aforementioned values.
The poorest precision is found in the dissociation and ionization regions,
occurring at K. The best precision is achieved at
higher temperatures, K. To discuss the significance of the
interpolation errors we compare them with the corresponding difference between
two different equation-of-state formalisms, SAHA-S and OPAL 2005. We find that
the interpolation errors of the pressure are a few orders of magnitude less
than the differences from between the physical formalisms, which is
particularly true for the solar-model points.Comment: Accepted for publication in A&
Extracting expectations from currency option prices: a comparison of methods
This paper compares the goodness-of-fit and the stability of six methods used to extract risk-neutral probability density functions from currency option prices. We first compare five existing methods commonly employed to recover risk-neutral density functions from option prices. Specifically, we compare the methods introduced by Shimko (1993), Madan and Milne (1994), Malz (1996), Melick and Thomas (1997) and Bliss and Panigirtzoglou (2002). In addition, we propose a new method based on the piecewise cubic Hermite interpolation of the implied volatility function. We use data on 12 emerging market currencies against the US dollar and find that the piecewise cubic Hermite interpolation method is by far the method with the best accuracy in fitting observed option prices. We also find that there is a relative tradeoff between the goodness-of-fit and the stability of the methods. Thus, methods which have a better accuracy in fitting observed option prices appear to be more sensitive to option pricing errors, while the most stable methods have a fairly disappointing fitting. However, for the first two PDF moments as well as the quartiles of the risk-neutral distributions we find that the estimates do not differ significantly across methods. This suggests that there is a large scope for selection between these methods without essentially sacrificing the accuracy of the analysis. Nonetheless, depending on the particular use of these PDFs, some methods may be more suitable than othersRisk-neutral probability density functions, option pricing, exchange rate expectations
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