2,912 research outputs found
European Securitisation : a GARCH model of CDO, MBS and Pfandbrief spreads
Asset-backed securitisation (ABS) is an asset funding technique that involves the issuance of structured claims on the cash flow performance of a designated pool of underlying receivables. Efficient risk management and asset allocation in this growing segment of fixed income markets requires both investors and issuers to thoroughly understand the longitudinal properties of spread prices. We present a multi-factor GARCH process in order to model the heteroskedasticity of secondary market spreads for valuation and forecasting purposes. In particular, accounting for the variance of errors is instrumental in deriving more accurate estimators of time-varying forecast confidence intervals. On the basis of CDO, MBS and Pfandbrief transactions as the most important asset classes of off-balance sheet and on-balance sheet securitisation in Europe we find that expected spread changes for these asset classes tends to be level stationary with model estimates indicating asymmetric mean reversion. Furthermore, spread volatility (conditional variance) is found to follow an asymmetric stochastic process contingent on the value of past residuals. This ABS spread behaviour implies negative investor sentiment during cyclical downturns, which is likely to escape stationary approximation the longer this market situation lasts
Nonlinear quantile mixed models
In regression applications, the presence of nonlinearity and correlation
among observations offer computational challenges not only in traditional
settings such as least squares regression, but also (and especially) when the
objective function is non-smooth as in the case of quantile regression. In this
paper, we develop methods for the modeling and estimation of nonlinear
conditional quantile functions when data are clustered within two-level nested
designs. This work represents an extension of the linear quantile mixed models
of Geraci and Bottai (2014, Statistics and Computing). We develop a novel
algorithm which is a blend of a smoothing algorithm for quantile regression and
a second order Laplacian approximation for nonlinear mixed models. To assess
the proposed methods, we present a simulation study and two applications, one
in pharmacokinetics and one related to growth curve modeling in agriculture.Comment: 26 pages, 8 figures, 8 table
Estimating Smooth Transition Autoregressive Models with GARCH Errors in the Presence of Extreme Observations and Outliers,
This paper investigates several empirical issues regarding quasimaximum likelihood estimation of Smooth Transition Autoregressive (STAR) models with GARCH errors, specifically STAR-GARCH and STAR-STGARCH. Convergence, the choice of different algorithms for maximising the likelihood function, and the sensitivity of the estimates to outliers and extreme observations, are examined using daily data for S&P 500, Heng Seng and Nikkei 225 for the period January 1986 to April 2000.
Comparison on the Bayesian Estimation of Gompertz Distribution Based on Type I Censored Data
The paper depicts assessment of the Bayesian methodology utilizing Gaussian quadrature formulas and Markov Chain Monte Carlo of the Gompertz distribution based on type I censored data with two loss functions, the Square Error loss function and the Linear Exponential loss function. In Markov Chain Monte Carlo, the full conditional distributions for the scale and shape parameters, survival and hazard functions are acquired by means Gibbs sampling and Metropolis- Hastings algorithm. The strategies for the Bayesian methodology are contrasted with maximum likelihood estimation regarding the Mean Square Error (MSE) to decide the best assessing of the scale and shape parameters, survival and hazard functions of the Gompertz distribution based on type I censored data. Keywords: Gompertz distribution, Bayesian estimation, Type I censored data, Gaussian Quadrature Formulas, Markov Chain Monte Carlo
Nonlinear Beam Propagation in a Class of Complex Non-PT -Symmetric Potentials
The subject of PT-symmetry and its areas of application have been blossoming
over the past decade. Here, we consider a nonlinear Schr\"odinger model with a
complex potential that can be tuned controllably away from being PT-symmetric,
as it might be the case in realistic applications. We utilize two parameters:
the first one breaks PT-symmetry but retains a proportionality between the
imaginary and the derivative of the real part of the potential; the second one,
detunes from this latter proportionality. It is shown that the departure of the
potential from the PT -symmetric form does not allow for the numerical
identification of exact stationary solutions. Nevertheless, it is of crucial
importance to consider the dynamical evolution of initial beam profiles. In
that light, we define a suitable notion of optimization and find that even for
non PT-symmetric cases, the beam dynamics, both in 1D and 2D -although prone to
weak growth or decay- suggests that the optimized profiles do not change
significantly under propagation for specific parameter regimes
Velocity vector reconstruction for realâtime phaseâcontrast MRI with radial Maxwell correction
Purpose To develop an auto-calibrated image reconstruction for highly accelerated multi-directional phase-contrast (PC) MRI that compensates for (1) reconstruction instabilities occurring for phase differences near urn:x-wiley:07403194:media:mrm29108:mrm29108-math-0003 and (2) phase errors by concomitant magnetic fields that differ for individual radial spokes. Theory and Methods A model-based image reconstruction for real-time PC MRI based on nonlinear inversion is extended to multi-directional flow by exploiting multiple flow-encodings for the estimation of velocity vectors. An initial smoothing constraint during iterative optimization is introduced to resolve the ambiguity of the solution space by penalizing phase wraps. Maxwell terms are considered as part of the signal model on a line-by-line basis to address phase errors by concomitant magnetic fields. The reconstruction methods are evaluated using simulated data and cross-sectional imaging of a rotating-disc, as well as in vivo for the aortic arch and cervical spinal canal at 3T. Results Real-time three-directional velocity mapping in the aortic arch is achieved at 1.8 Ă 1.8 Ă 6 mm3 spatial and 60 ms temporal resolution. Artificial phase wraps are avoided in all cases using the smoothness constraint. Inter-spoke differences of concomitant magnetic fields are effectively compensated for by the model-based image reconstruction with integrated radial Maxwell correction. Conclusion Velocity vector reconstructions based on nonlinear inversion allow for high degrees of radial data undersampling paving the way for multi-directional PC MRI in real time. Whether a spoke-wise treatment of Maxwell terms is required or a computationally cheaper frame-wise approach depends on the individual application
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