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Abstract. This paper analyzes a family of multivariate point process models of correlated event timing whose arrival intensity is driven by an affine jump diffusion. The components of an affine point process are self-and cross-exciting and facilitate the description of complex event dependence structures. ODEs characterize the transform of an affine point process and the probability distribution of an integer-valued affine point process. The moments of an affine point process take a closed form. This guarantees a high degree of computational tractability in applications. We illustrate this in the context of portfolio credit risk, where the correlation of corporate defaults is the main issue. We consider the valuation of securities exposed to correlated default risk and demonstrate the significance of our results through market calibration experiments. We show that a simple model variant can capture the default clustering implied by index and tranche market prices during September 2008, a month that witnessed significant volatility.

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We propose a flexible framework for pricing single-name knock-out credit derivatives. Examples include Credit Default Swaps (CDSs) and European, American and Bermudan CDS options. The default of the underlying reference entity is modelled within a doubly stochastic framework where the default intensity follows a CIR++ process. We estimate the model parameters through a combination of a cross sectional calibration-based method and a historical estimation approach. We propose a numerical procedure based on dynamic programming and a piecewise linear approximation to price American-style knock-out credit options. Our numerical investigation shows consistency, convergence and efficiency. We find that American-style CDS options can complete the credit derivatives market by allowing the investor to focus on spread movements rather than on the default event.Credit derivatives, Credit default swaps, Bermudan options, Dynamic programming, Doubly stochastic Poisson process, Cox process,

We introduce a simple extension of a shifted geometric Brownian motion for modelling forward LIBOR rates under their canonical measures. The extension is based on a parameter uncertainty modelled through a random variable whose value is drawn at an infinitesimal time after zero. The shift in the proposed model captures the skew commonly seen in the cap market, whereas the uncertain volatility component allows us to obtain more symmetric implied volatility structures.We show how this model can be calibrated to cap prices. We also propose an analytical approximated formula to price swaptions from the cap calibrated model. Finally, we build the bridge between caps and swaptions market by calibrating the correlation structure to swaption prices, and analysing some implications of the calibrated model parameters. * We are extremely grateful to Gianvittorio Mauri from Banca IMI for his helpful assistance in running the numerical tests. We are also grateful to John Weyant from Stanford University for his helpful comments. Useful discussions with Dariusz Gatarek from Numerix and helpful assistance from Andrea Pallavicini from Banca IMI are gratefully acknowledged.1 A different approach, but similar in spirit, was introduced by Santa-Clara and Sornette (2001) and Goldstein (2000) who proposed "String-Shocks" type of models to describe the evolution of forward rates.