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

Cantia, Catalin and Tunaru, Radu (2017) 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

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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
Keywords: Time-change; Mean-reverting process with jumps; CDS pricing; Credit index pricing; Tranche pricing
Schools and Departments: University of Sussex Business School > Accounting and Finance
Research Centres and Groups: Quantitative International Finance Network
Subjects: H Social Sciences > HG Finance > HG0101 Theory. Method. Relation to other subjects > HG0106 Mathematical models
H Social Sciences > HG Finance > HG3691 Credit. Debt. Loans
Depositing User: Radu Tunaru
Date Deposited: 23 Jan 2020 12:14
Last Modified: 31 Jan 2020 09:00
URI: http://sro.sussex.ac.uk/id/eprint/89499

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