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A factor model for joint default probabilities. Pricing of CDS, index swaps and index tranches
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.
History
Publication status
- Published
File Version
- Accepted version
Journal
Insurance: Mathematics and EconomicsISSN
0167-6687Publisher
ElsevierExternal DOI
Volume
72Page range
21-35Department affiliated with
- Accounting and Finance Publications
Research groups affiliated with
- Quantitative International Finance Network Publications
Full text available
- Yes
Peer reviewed?
- Yes