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A factor model for joint default probabilities, pricing of CDS, index swaps and index tranches

Cantia, Catalin, Tunaru, Radu (2016) A factor model for joint default probabilities, pricing of CDS, index swaps and index tranches. Insurance: Mathematics and Economics, 72 . pp. 21-35. ISSN 0167-6687. (doi:10.1016/j.insmatheco.2016.10.004)

Abstract

A factor model is proposed for the valuation of credit default swaps, credit indices and CDO contracts. The model of default is based on the first-passage distribution of a Brownian motion time modified by a continuous time-change. Various model specifications fall under this general approach based on defining the credit-quality process as an innovative time-change of a standard Brownian motion where the volatility process is mean reverting Lévy driven OU type process. Our models are bottom-up and can account for sudden moves in the level of CDS spreads representing the so-called credit gap risk. We develop FFT computational tools for calculating the distribution of losses and we show how to apply them to several specifications of the time-changed Brownian motion. Our line of modelling is flexible enough to facilitate the derivation of analytical formulae for conditional probabilities of default and prices of credit derivatives.

Item Type: Article
DOI/Identification number: 10.1016/j.insmatheco.2016.10.004
Uncontrolled keywords: Time-change; Mean-reverting process with jumps; CDS pricing; Time-change; Time change, Mean-reverting process with jumps,CDS pricing,Credit index pricing,Tranche pricing
Subjects: H Social Sciences > HA Statistics > HA33 Management Science
H Social Sciences > HG Finance
Divisions: Faculties > Social Sciences > Kent Business School > Accounting and Finance
Depositing User: Radu Tunaru
Date Deposited: 19 Oct 2016 09:55 UTC
Last Modified: 29 May 2019 18:00 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/57915 (The current URI for this page, for reference purposes)
Tunaru, Radu: https://orcid.org/0000-0002-5623-9876
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