2017
DOI: 10.4236/jmf.2017.73030
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Nonparametric Model Calibration for Derivatives

Abstract: Consistently fitting vanilla option surface is an important issue in derivative modelling. In this paper, we consider three different models: local and stochastic volatility, local correlation, hybrid local volatility with stochastic rates, and address their exact, nonparametric calibration. This calibration process requires solving a nonlinear partial integro-differential equation. A modified alternating direction implicit algorithm is used, and its theoretical and numerical analysis is performed.

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Cited by 6 publications
(11 citation statements)
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“…As mentioned in the several Planck papers [16][17][18] the DL07 and GNILC-derived SEDs are compatible with MBB spectrum, which is obtained empirically from Planck observations of dust. For optically thin sources (like M31) the MBB function is as follows…”
Section: The Modified Blackbody Spectrumsupporting
confidence: 74%
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“…As mentioned in the several Planck papers [16][17][18] the DL07 and GNILC-derived SEDs are compatible with MBB spectrum, which is obtained empirically from Planck observations of dust. For optically thin sources (like M31) the MBB function is as follows…”
Section: The Modified Blackbody Spectrumsupporting
confidence: 74%
“…There is anti-correlation between T d and β reported by Planck collaboration. 16,17 The spectral index of dust increases with radius, which means, that dust emission properties depend on the temperature, and the heating rate of dust depends on the spectral index. The corresponding values of the optical depth in this case are given in Table 3 and Table 4.…”
Section: Dust Emission Optical Depthmentioning
confidence: 99%
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“…The algorithm utilizes the GW localization map, an estimate of the event distance, and a model of the expected optical emission (e.g., Barnes & Kasen 2013). This information is folded in with observational information, including a map of sky brightness (using the DES sky brightness model; Neilsen 2012), the atmospheric transmission (using information on airmass and the interstellar dust extinction from Planck; Abergel et al 2014), the expected seeing (from scaling laws with airmass and wavelength), and the confusion-limit probability (based on stellar density maps) to produce a full source-detection probability as a function of sky location. We used this map to observe the highest probability region that included area both inside and outside the DES footprint.…”
Section: Observing Strategymentioning
confidence: 99%
“…It is notable generalization of Yang-Mills theories instead of using an addition auxiliary field to the gauge field, one can use the non-local action and cause to useful results in gauge field theories scenario [56]. We should emphasise for such mechanism in comparison to the canonical and local scalar field approach, by considering observations includes of Planck 2013 [59], W M AP 9 + eCM B + BAO + H 0 data sets in addition to BICEP 2 data surveying [57,58], our results are in good agreement. The paper has been planned in the following form: In Sec.1 which includes of above discussions we have introduction.…”
Section: Introductionmentioning
confidence: 99%