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You searched for +publisher:"University of Manchester" +contributor:("EVATT, GEOFFREY GW"). Showing records 1 – 2 of 2 total matches.

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University of Manchester

1. Li, Wang. Default Contagion Modelling and Counterparty Credit Risk.

Degree: 2017, University of Manchester

This thesis introduces models for pricing credit default swaps (CDS) and evaluating the counterparty risk when buying a CDS in the over-the-counter (OTC) market from a counterpart subjected to default risk. Rather than assuming that the default of the referencing firm of the CDS is independent of the trading parties in the CDS, this thesis proposes models that capture the default correlation amongst the three parties involved in the trade, namely the referencing firm, the buyer and the seller. We investigate how the counterparty risk that CDS buyers face can be affected by default correlation and how their balance sheet could be influenced by the changes in counterparty risk.The correlation of corporate default events has been frequently observed in credit markets due to the close business relationships of certain firms in the economy. One of the many mathematical approaches to model that correlation is default contagion. We propose an innovative model of default contagion which provides more flexibility by allowing the affected firm to recover from a default contagion event.We give a detailed derivation of the partial differential equations (PDE) for valuing both the CDS and the credit value adjustment (CVA). Numerical techniques are exploited to solve these PDEs. We compare our model against other models from the literature when measuring the CVA of an OTC CDS when the default risk of the referencing firm and the CDS seller is correlated.Further, the model is extended to incorporate economy-wide events that will damage all firms' credit at the same time-this is another kind of default correlation. Advanced numerical techniques are proposed to solve the resulting partial-integro differential equations (PIDE). We focus on investigating the different role of default contagion and economy-wide events have in terms of shaping the default correlation and counterparty risk.We complete the study by extending the model to include bilateral counterparty risk, which considers the default of the buyer and the correlation among the three parties. Again, our extension leads to a higher-dimensional problem that we must tackle with hybrid numerical schemes. The CVA and debit value adjustment (DVA) are analysed in detail and we are able to value the profit and loss to the investor's balance sheet due to CVA and DVA profit and loss under different market circumstances including default contagion. Advisors/Committee Members: EVATT, GEOFFREY GW, Johnson, Paul, Evatt, Geoffrey.

Subjects/Keywords: Default Contagion Modelling; Counterparty Credit Risk; CVA and DVA; Finite-difference Numerical Schemes; PDE and PIDE; Hybrid Numerical Schemes

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Li, W. (2017). Default Contagion Modelling and Counterparty Credit Risk. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:308577

Chicago Manual of Style (16th Edition):

Li, Wang. “Default Contagion Modelling and Counterparty Credit Risk.” 2017. Doctoral Dissertation, University of Manchester. Accessed September 24, 2020. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:308577.

MLA Handbook (7th Edition):

Li, Wang. “Default Contagion Modelling and Counterparty Credit Risk.” 2017. Web. 24 Sep 2020.

Vancouver:

Li W. Default Contagion Modelling and Counterparty Credit Risk. [Internet] [Doctoral dissertation]. University of Manchester; 2017. [cited 2020 Sep 24]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:308577.

Council of Science Editors:

Li W. Default Contagion Modelling and Counterparty Credit Risk. [Doctoral Dissertation]. University of Manchester; 2017. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:308577


University of Manchester

2. Johnson, Peter. Optimal detection of hidden targets.

Degree: 2015, University of Manchester

The main contribution of this thesis is the full characterisations and solutions to the sequential testing and quickest detection problems for Bessel processes.These are the first known solutions for problems considering well-studied diffusions with a non-constant signal-to-noise ratio (SNR) process which are inherently two-dimensional. Chapter 3 is a base for a joint paper with G. Peskir which describes the solution to the sequential testing problem for Bessel processes, of dimension greater than or equal to two, through a method of stochastic time-change. This passes the problem in to the time-space domain, meaning the auxiliary problem is well suited to being considered for a finite time horizon. This is then fully characterised and solved using local time-space calculus on curves, before letting this horizon tend to the infinite horizon case. This solution is followed by a description of general diffusion processes that this method will also work for.Chapter 4 is the base for a paper in which the solution to the sequential testing of the dimension of a Bessel process is used to give the solution to a natural optimal stopping problem concerning the sequential testing of the mean of the CIR process with exponential time costs through a time-space change. The CIR process considered has a non-constant SNR but the optimal stopping problem is also time inhomogeneous meaning that the problem also requires knowledge of the running time making the problem three-dimensional. The optimal surfaces are calculated for a given example.The quickest detection problem considered in Chapter 6 is based on the joint paper with G. Peskir. This paper characterises and finds solution to the Bayesian quickest detection problem for a Bessel process of dimension greater than or equal to two. It contains many results that are applicable to all quickest detection problems of this type and particularly when the observed processes have a non-constant SNR process. This includes a description of a change of measure which allows the sufficient statistics to become uncoupled in the second component, also abandoning the need to include the innovation process. This simplifies the problems and allows for subsequent analysis. Additionally, a change-of-variable formula is shown to reduce the sufficient statistic in such problems to the observed process and a process of bounded variation. In combination with the measure change this also removesany mixed derivatives in the resulting partial differential equation (PDE) formulation. The methodologies used in providing the solution to problem concerning Bessel processes also address a number of key issues in dealing with fully two-dimensional problems of optimal stopping for diffusions and their connections with (locally) parabolic PDEs. This makes the work of general probabilistic interest.The remaining chapters include (i) a review in detection theory (Chapter 2), (ii) a connection between the observed processes of traditional disorder problems andself-exciting processes via a stochastic time change… Advisors/Committee Members: EVATT, GEOFFREY GW, Evatt, Geoffrey, Peskir, Goran.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Johnson, P. (2015). Optimal detection of hidden targets. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:277660

Chicago Manual of Style (16th Edition):

Johnson, Peter. “Optimal detection of hidden targets.” 2015. Doctoral Dissertation, University of Manchester. Accessed September 24, 2020. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:277660.

MLA Handbook (7th Edition):

Johnson, Peter. “Optimal detection of hidden targets.” 2015. Web. 24 Sep 2020.

Vancouver:

Johnson P. Optimal detection of hidden targets. [Internet] [Doctoral dissertation]. University of Manchester; 2015. [cited 2020 Sep 24]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:277660.

Council of Science Editors:

Johnson P. Optimal detection of hidden targets. [Doctoral Dissertation]. University of Manchester; 2015. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:277660

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