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Structural Model For Credit Default In One And Higher Dimensions

Shi, Bo (2012) Structural Model For Credit Default In One And Higher Dimensions. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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In this thesis, we provide a new structural model for default of a single name which is an extension in several directions of Merton's seminal work [41] and also propose a new hierarchical model in higher dimensions in a heterogeneous setting.

Our new model takes advantage of the fact that currently much more data is readily available about the equity (stock) markets, and through our analysis, can be translated to the much less transparent credit markets. We show how this can be used to provide volatilities for the default indices in structural models for these same stocks. More importantly, we use the equity data to obtain an implied probability distribution for the firms' liabilities, a quantity that is only reported quarterly, and often with questionable reliability. This completes the structural model for a single firm by specifying (probabilistically) the absorbing
default barrier. In particular, we can then obtain the default probability of this firm and capture its Credit Default Swap(CDS) spreads. For several companies selected from different industry sectors, the values that our model obtain are in good agreement with the credit market data. Furthermore, we are able to extend this approach to higher dimensional models (e.g., with 125 firms) where the correlations among the firms are essential. Specifically,
we use hierarchical models for which each firm’s default boundary a linear combination of a systematic factor (e.g, the Dow Jones Industrial Average) and an idiosyncratic factor, with firm-to-firm correlations obtained through their correlations with the systemic factor. Once again the parameters for these high dimensional structural models are obtained from equity data and the resulting values for the tranche spreads for the CDX: NAIG Series 17 Collateralized Debt Obligations (CDO) compare favorably with actual market data.

In the course of this work we also provide results for the probabilistic inverse first passage problem for a Brownian motion default index: given a default probability, find the probability distribution for linear default barriers (equivalently initial distributions) that reproduce the given default probability.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Shi, Bobos6@pitt.eduBOS6
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairChadam, JohnCHADAM@pitt.eduCHADAM
Committee MemberManfredi, Juanmanfredi@pitt.eduMANFREDI
Committee MemberSwigon, Davidswigon@pitt.eduSWIGON
Committee MemberIyengar, Satishssi@pitt.eduSSI
Date: 3 July 2012
Date Type: Publication
Defense Date: 12 January 2012
Approval Date: 3 July 2012
Submission Date: 18 January 2012
Access Restriction: 3 year -- Restrict access to University of Pittsburgh for a period of 3 years.
Number of Pages: 58
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Credit Default, Structural Models, Intensity Models, Credit Default Swap, Call Option, Black-Scholes Equation, Large Homogeneous Model, Heterogeneous Model
Date Deposited: 03 Jul 2012 14:02
Last Modified: 15 Nov 2016 13:58

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