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We suggest an intermediate currency approach that allows us to price options on all FX markets simultaneously under the same risk-neutral measure which ensures consistency of FX option prices across all markets. In particular, it is sufficient to calibrate a model to the volatility smile on the domestic market as, due to the consistency of pricing formulas, the model automatically reproduces the correct smile for the inverse pair (the foreign market). We first consider the case of two currencies and then the multi-currency setting. We illustrate the intermediate currency approach by applying it to the Heston and SABR stochastic volatility models, to the model in which exchange rates are described by an extended skewed normal distribution, and also to the model-free approach of option pricing, Comment: An updated version with changes through out and an additional calibration example

Micrometeoroid impacts, solar wind plasma interactions, and regolith gardening drive the complicated and nuanced mechanism of space weathering (or optical maturation); a process by which a material’s optical properties are changed as a result of chemical and physical alterations at the surface of grains on airless bodies. Reddened slopes, attenuated absorption bands, and an overall reduction in albedo in the visible and near-IR wavelength ranges are primarily the result of native iron nanoparticle (npFe0) production within glassy rims that form from sputtering and vaporization. The sizes and abundance of these particles provide information about the relative surface exposure age of a particular grain. In addition, many studies have indicated that composition greatly affects the rate at which optical maturation occurs. Despite our understanding of how npFe0 affects optical signatures, the relative roles of micrometeoroid bombardment and solar wind interactions remains undetermined. To simulate the early effects of weathering by the solar wind and to determine thresholds for optical change with respect to a given mineral phase, we irradiated a fine-grained lunar basalt with 1 keV H+ to a fluence of 6.4 x 1016 H+ per sq.cm. Surface alterations within four phases have been evaluated using transmission electron microscopy (TEM). We found that for a given fluence of H+, the extent of damage acquired by each grain was dependent on its composition. No npFe(0) was produced in any of the phases evaluated in this study. These results are consistent with many previous studies conducted using ions of similar energy, but they also provide valuable information about the onset of space weathering and the role of the solar wind during the early stages of optical maturation.

We have collected laboratory thermal IR spectra of the mineraloid allophane and aluminosilicate gels. Using those spectra to model regional TES spectra, we suggest that several areas of Mars contain significant amounts of allophane-like weathering products. The presence of allophane on Mars indicates that 1) significant Al sources, such as feldspar or glass, were weathered; 2) weathering on Mars produced poorly-crystalline aluminosilicates, rather than easily identifiable crystalline minerals; and 3) some Martian weathering proceeded under moderate pH environments, suggesting acid weathering is not the only major alteration mechanism on Mars.

Allophane is an alteration product of volcanic glass and a clay mineral precursor that is commonly found in basaltic soils on Earth. It is a poorly-crystalline or amorphous, hydrous aluminosilicate with Si/Al ratios ranging from approx.0.5-1 [Wada, 1989]. Analyses of thermal infrared (TIR) spectra of the Martian surface from TES show high-silica phases at mid-to-high latitudes that have been proposed to be primary volcanic glass [Bandfield et al., 2000; Bandfield, 2002; Rogers and Christensen, 2007] or poorly-crystalline secondary silicates such as allophane or aluminous amorphous silica [Kraft et al., 2003; Michalski et al., 2006; Rogers and Christensen, 2007; Kraft, 2009]. Phase modeling of chemical data from the APXS on the Mars Exploration Rover Spirit suggest the presence of allophane in chemically weathered rocks [Ming et al., 2006]. The presence of allophane on Mars has not been previously tested with IR spectroscopy because allophane spectra have not been available. We synthesized allophanes and allophanic gels with a range of Si/Al ratios to measure TIR emission and VNIR reflectance spectra and to test for the presence of allophane in Martian soils. VNIR reflectance spectra of the synthetic allophane samples have broad absorptions near 1.4 m from OH stretching overtones and 1.9 m from a combination of stretching and bending vibrations in H2O. Samples have a broad absorption centered near 2.25 microns, from AlAlOH combination bending and stretching vibrations, that shifts position with Si/Al ratio. Amorphous silica (opaline silica or primary volcanic glass) has been identified in CRISM spectra of southern highland terrains based on the presence of 1.4, 1.9, and broad 2.25 m absorptions [Mustard et al., 2008]; however, these absorptions are also consistent with the presence of allophane. TIR emission spectra of the synthetic allophanes show two spectrally distinct types: Si-rich and Al-rich. Si-rich allophanes have two broad absorptions centered near 1080 and 430 cm-1 from Si(Al)-O stretching and Si(Al)-O bending vibrations, respectively, and Al-rich allophanes have three broad absorptions centered near 950, 540, and 430 cm-1. We used a spectral library commonly used to deconvolve TES spectra and four allophane spectra to model nine spectrally distinct regions on Mars [from Rogers et al., 2007]. Regions previously modeled with high-silica phases contain significant amounts of allophane (>10 vol.%) in our models. Our models of northern Acidalia, the type locality for surface type 2 materials, contain 40 vol.% Si-rich allophane. The presence of allophane in multiple surface regions of Mars indicates a more widespread occurrence of low-temperature aqueous alteration at moderate pH than has been previously recognized. The regional variations in modeled abundances and the types of allophane (Si- vs. Al-rich) suggest regional differences in Mars weathering processes.

It has been suggested that allophane or related poorly crystalline aluminosilicates are present on Mars, and that they comprise the high-silica phase detected by the Thermal Emission Spectrometer (TES) in Surface Type 2 materials (Michalski et al., 2005). Using new laboratory spectra of allophanic materials, we (Rampe et al., this meeting) have detected allophane on the Martian surface via spectral modeling of TES data. We find that ST2 materials in the Northern Plains are consistent with a significant amount of high-silica allophane-like materials. In addition, we find that allophane may be present in some areas of ancient highlands (TES surface type 1), but spectra of those regions are more consistent with aluminous allophane. The presence of allophane and its chemical variability have important implications for chemical weathering and soil development on Mars. Allophane-like materials are amorphous or poorly crystalline hydrous aluminosilicates formed from chemical weathering of glasses, feldspars, and other silicates (cf. Parfitt, 2009). True allophane is a combination of SiO2, Al2O3 and H2O where Al:Si ranges from ~0.5-2. Aluminosilicate gels are amorphous and chemically similar to allophane but can have higher SiO2 contents. The presence of allophane indicates low-temperature chemical weathering and provides constraints on alteration conditions, limiting pH to circum-neutral (~4.5-8). Our model results indicate that weathering occurred in the relatively young northern plains of Mars. The high-silica allophane-like material present there implies little silica mobility through the soil column, which suggests that weathering involved small amounts of liquid water, consistent with our previous models of weathering in ice-rich soils (Kraft et al., 2007). The aluminous allophane indicated by our spectral models to be present in the highlands suggest that those regions experienced greater amounts of SiO2 leaching and weathering in those soils may have involved much larger amounts of water. The presence of allophane-like materials suggests that these weathering regimes were not influenced by the acidic weathering that appears to have affected other areas of Mars and has been proposed as a planetwide alteration process (Hurowitz and McLennan, 2007). Soil development in basaltic material (typically tephra) on Earth usually leads to formation of andosols. Although we do not suggest a one-to-one analogy between dark basaltic Martian soils and andosols, there may be important similarities, as andosols are typified by significant production of allophane as well as poorly crystalline Fe-hydroxides. The detection of allophane on Mars suggests a positive utility of an andosol model for Martian soils, particularly when coupled with the ubiquitous presence of Feoxide materials on Mars. An andosol model of soil formation is mineralogically consistent with palagonite models for the formation of Martian dust (cf. Banin et al., 1992; Morris et al., 2001), which suggests a possible genetic relationship of dust and bright soils to the broader soil layer of Mars.

Allophane is a poorly-crystalline, hydrous aluminosilicate with variable Si/Al ratios approx.0.5-1 and a metastable precursor of clay minerals. On Earth, it forms rapidly by aqueous alteration of volcanic glass under neutral to slightly acidic conditions [1]. Based on in situ chemical measurements and the identification of alteration phases [2-4], the Martian surface is interpreted to have been chemically weathered on local to regional scales. Chemical models of altered surfaces detected by the Mars Exploration Rover Spirit in Gusev crater suggest the presence of an allophane-like alteration product [3]. Thermal infrared (TIR) spectroscopy and spectral deconvolution models are primary tools for determining the mineralogy of the Martian surface [5]. Spectral models of data from the Thermal Emission Spectrometer (TES) indicate a global compositional dichotomy, where high latitudes tend to be enriched in a high-silica material [6,7], interpreted as high-silica, K-rich volcanic glass [6,8]. However, later interpretations proposed that the high-silica material may be an alteration product (such as amorphous silica, clay minerals, or allophane) and that high latitude surfaces are chemically weathered [9-11]. A TIR spectral library of pure minerals is available for the public [12], but it does not contain allophane spectra. The identification of allophane on the Martian surface would indicate high water activity at the time of its formation and would help constrain the aqueous alteration environment [13,14]. The addition of allophane to the spectral library is necessary to address the global compositional dichotomy. In this study, we characterize a synthetic allophane by IR spectroscopy, X-ray diffraction (XRD), and transmission electron microscopy (TEM) to create an IR emission spectrum of pure allophane for the Mars science community to use in Martian spectral models.

Siderophile elements in the Earth.s mantle are depleted relative to chondrites. This is most pronounced for the highly siderophile elements (HSEs), which are approximately 400x lower than chondrites. Also remarkable is the relative chondritic abundances of the HSEs. This signature has been interpreted as representing their sequestration into an iron-rich core during the separation of metal from silicate liquids early in the Earth's history, followed by a late addition of chondritic material. Alternative efforts to explain this trace element signature have centered on element partitioning experiments at varying pressures, temperatures, and compositions (P-T-X). However, first results from experiments conducted at 1 bar did not match the observed mantle abundances, which motivated the model described above, a "late veneer" of chondritic material deposited on the earth and mixed into the upper mantle. Alternatively, the mantle trace element signature could be the result of equilibrium partitioning between metal and silicate in the deep mantle, under P-T-X conditions which are not yet completely identified. An earlier model determined that equilibrium between metal and silicate liquids could occur at a depth of approximately 700 km, 27(plus or minus 6) GPa and approximately 2000 (plus or minus 200) C, based on an extrapolation of partitioning data for a variety of moderately siderophile elements obtained at lower pressures and temperatures. Based on Ni-Co partitioning, the magma ocean may have been as deep as 1450 km. At present, only a small range of possible P-T-X trace element partitioning conditions has been explored, necessitating large extrapolations from experimental to mantle conditions for tests of equilibrium models. Our primary objective was to reduce or remove the additional uncertainty introduced by extrapolation by testing the equilibrium core formation hypothesis at P-T-X conditions appropriate to the mantle.

Among the most important discoveries made during the Mars Global Surveyor (MGS) mission was that the rocky materials of Mars are broadly divisible into two distinct rock types. The geological significance of this finding is dependent on the mineralogy of these rock types as well as their geographic and stratigraphic positions. Much work has yet to be done to understand these relationships and the small-scale variability of these units. For now, it is worth considering various scenarios that could have resulted in Mars global-scale mineralogical dichotomy. Such work will make clearer what must be looked for in Thermal Emission Spectrometer (TES) and Thermal Imaging Spectrometer (THEMIS) data, what to test with other data sets, and what geological processes can be considered or ruled out as we advance with interpreting Martian geologic history. Here, we suggest that exogenic coatings of secondary silica on basaltic rocks may provide a plausible explanation for the newly discovered distribution of rock types.

For over a decade, the oldest evidence for life on this planet has been microfossils in the 3.5 Ga Apex Chert in Western Australia. Recently, the biogenicity of these carbon-rich structures has been called into question through reanalysis of the local geology and reinterpretation of the original thin sections. Although initially described as a stratiform, bedded chert of siliceous clasts, the unit is now thought to be a brecciated hydrothermal vein chert. The high temperatures of a hydrothermal environment would probably have detrimental effects to early non-hyperthermophilic life, compared to that of a shallow sea. Conversely, a hydrothermal origin would suggest that if the microfossils were valid, they might have been hyperthermophilic. Apex Chert controversy. The Apex Chert microfossils were originally described as septate filaments composed of kerogen similar in morphology to Proterozoic and modern cyanobacteria. However new thin section analysis shows that these carbonaceous structures are not simple filaments. Many of the original microfossils are branched and have variable thickness when the plane of focus is changed. Hydrothermal alteration of organic remains has also been suggested for the creation of these strange morphologies. Another point of contention lies with the nature of the carbon material in these proposed microfossils. Kerogen is structurally amorphous, but transforms into well-ordered graphite under high pressures and temperatures. Raman spectrometry of the carbonaceous material in the proposed microfossils has been interpreted both as partially graphitized kerogen and amorphous graphite. However, these results are inconclusive, since Raman spectrometry cannot adequately discriminate between kerogen and disordered graphite. There are also opposing views for the origin of the carbon in the Apex Chert. The carbon would be biogenic if the proposed microfossils are indeed the remains of former living organisms. However, an inorganic Fischer- Tropsch-type synthesis is also a possible explanation for the formation of large-aggregate carbonaceous particles and could also account for the depletion of (13)C observed.

The Sample Collection for Investigation of Mars (SCIM) mission, presently a finalist for flight as a Mars Scout, proposes to return martian atmospheric dust to Earth for mineralogical, chemical, isotopic, and other studies. The returned sample will consist of least 1000 martian dust particles =10 m in diameter plus millions of smaller particles. Here we discuss the science gained from analyzing such a sample in terrestrial laboratories. An accompanying abstract discusses the SCIM atmosphere sample return science.