Modelling default correlations in a two-firm model with dynamic leverage ratios

University of Technology, Sydney. School of Finance and Economics.Default correlations have been an important research area in credit risk analysis. This thesis aims to extend the one-firm structural model of default to the two-firm situation for valuing default correlations. In the structural approach, default happens when the firm value falls below a default threshold. In the fundamental model of Merton (1974), the default threshold is simply the face value of the bond. Collin-Dufresne & Goldstein (2001) related the default threshold to the firm's debts and modelled it as mean-reverting to a constant long-term target. Hui et al. (2006) generalized the Collin-Dufresne & Goldstein (2001) model to consider the default threshold as stochastic and the long-term target as time-dependent. In these models, the corporate bond price is a function of the leverage ratio - a ratio of the firm's debt to its asset value. For this combined measure of the firm's default risk, Hui et al. (2007) proposed a dynamic leverage ratio model, where default happens when the leverage ratio falls below a certain level. The aim of this thesis is to extend the one-firm dynamic leverage ratio model of Hui et al. (2007) to incorporate the default risk of two firms and interest rate risk. The model will be based on the consideration of a financial instrument (a credit linked note) that is exposed to the default risk of the two firms. Initially, the dynamic leverage ratios will be assumed to follow geometric Brownian motions and the stochastic interest rate assumed to follow a Vasicek (1977) process. The pricing problem will then be reduced to that of solving the first-passage-time problem that plays an important part in the valuation of default correlations. In order to study the impact of the capital structures of firms on default correlations, the two-firm model is extended by allowing the dynamic leverage ratios to follow mean-reverting processes, so as to capture the behaviour of firms when they adjust their capital structures to a long-term target. Then in order to capture the effect of external shocks on default correlations, the model is further extended to consider the situation in which the dynamic leverage ratios follow jump-diffusion processes. Finally, the numerical results of default correlations based on the two-firm model are studied and compared when the firm's leverage ratios follow these three types of processes. The thesis concludes by pointing to some future research directions. These includes further development of the method of images approach for the solution of the first passage time problem to the time varying coefficients case by use of the multi-stage approximation. Development of approximate analytical methods to extend the range of applicability of the method of images approach. Extension of Fortet's integral equation approach for the solution of first passage time problem to the two-dimensional situation. The estimation and calibration of leverage ratio models, including estimation of market prices of risk. The main contributions of the thesis are: • The setting up the two firm leverage ratio framework for evaluation of default correlations. • The extension of the method of images approach to the two-dimensional situation for solving the first passage time problem with constant coefficients and the time varying barrier approach for time-dependent coefficients. • Extension of the leverage ratio framework to incorporate jumps in both the one and two firm cases. • A comparative study of the impact on default correlations and joint survival probabilities of the different types of processes for the leverage ratio dynamics

Determination of AGC capacity requirement and regulation strategies considering penalties of tie-line power flow deviations

2003-2004 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Biomechanical study of the funnel technique applied in thoracic pedicle screw replacement

Background: Funnel technique is a method used for the insertion of screw into thoracic pedicle.Aim: To evaluate the biomechanical characteristics of thoracic pedicle screw placement using the Funnel technique, trying to provide biomechanical basis for clinical application of this technology.Methods: 14 functional spinal units (T6 to T10) were selected from thoracic spine specimens of 14 fresh adult cadavers, and randomly divided into two groups, including Funnel technique group (n=7) and Magerl technique group (n=7). The displacement-stiffness and pull-out strength in all kinds of position were tested and compared.Results: Two fixed groups were significantly higher than that of the intact state (P<0.05) in the spinal central axial direction, compression, anterior flexion, posterior bending, lateral bending, axial torsion, but there were no significant differences between two fixed groups (P>0.05). The mean pull-out strength in Funnel technique group (789.09±27.33) was lower than that in Magerl technique group (P<0.05).Conclusions: The Funnel technique for the insertion point of posterior bone is a safe and accurate technique for pedicle screw placement. It exhibited no effects on the stiffness of spinal column, but decreased the pull-out strength of pedicle screw. Therefore, the funnel technique in the thoracic spine affords an alternative for the standard screw placement.Keywords: Thoracic; Pedicle screws; Biomechanics; Funnel techniqu

Direct Integration and Non-Perturbative Effects in Matrix Models

We show how direct integration can be used to solve the closed amplitudes of multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, we give explicit expressions for the ring of non-holomorphic modular objects that are needed to express all closed matrix model amplitudes. This allows us to integrate the holomorphic anomaly equation up to holomorphic modular terms that we fix by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg--Witten curve and the ring reduces to the non-holomorphic modular ring of the group $\Gamma(2)$. On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. We use these results to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, we argue that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model.Comment: 51 pages, 8 figure

Studies on critical issues related to operating reserves in deregulated electricity market environment

2002-2003 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

MelodicBrush : a cross-modal link between ancient and digital art forms

Author name used in this publication: Stephen ChanRefereed conference paper2011-2012 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe

Survey on operating reserve procurement and pricing in deregulated electricity market environment

2003-2004 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Procurement and pricing of operating reserves based on the Peak-Load Pricing Theory

2002-2003 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Examining the Effects of One- and Three-Dimensional Spatial Filtering Analyses in Magnetoencephalography

Spatial filtering, or beamforming, is a commonly used data-driven analysis technique in the field of Magnetoencephalography (MEG). Although routinely referred to as a single technique, beamforming in fact encompasses several different methods, both with regard to defining the spatial filters used to reconstruct source-space time series and in terms of the analysis of these time series. This paper evaluates two alternative methods of spatial filter construction and application. It demonstrates how encoding different requirements into the design of these filters has an effect on the results obtained. The analyses presented demonstrate the potential value of implementations which examine the timeseries projections in multiple orientations at a single location by showing that beamforming can reconstruct predominantly radial sources in the case of a multiple-spheres forward model. The accuracy of source reconstruction appears to be more related to depth than source orientation. Furthermore, it is shown that using three 1-dimensional spatial filters can result in inaccurate source-space time series reconstruction. The paper concludes with brief recommendations regarding reporting beamforming methodologies in order to help remove ambiguity about the specifics of the techniques which have been used

Non-perturbative effects and the refined topological string

The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P1xP1, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.Comment: 38 pages, 5 figure