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

Catalin Cantia and Radu Tunaru

Insurance: Mathematics and Economics, 2017, vol. 72, issue C, 21-35

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.

Keywords: Time-change; Mean-reverting process with jumps; CDS pricing; Credit index pricing; Tranche pricing (search for similar items in EconPapers)
JEL-codes: C51 C63 G12 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:72:y:2017:i:c:p:21-35

DOI: 10.1016/j.insmatheco.2016.10.004

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