We develop a new approach to approximating asset prices in the context of continuous-time models. For any pricing model that lacks a closed-form solution, we provide a closed-form approximate solution, which relies on the expansion of the intractable model around an “auxiliary” one. We...

In [4], the authors introduced a Markov copula model of portfolio credit risk. This model solves the top-down versus bottom-up puzzle in achieving efficient joint calibration to single-name CDS and to multi-name CDO tranches data. In [4], we studied a general model, that allows for stochastic...

We study a model for default contagion in intensity-based credit risk and its consequences for pricing portfolio credit derivatives. The model is specified through default intensities which are assumed to be constant between defaults, but which can jump at the times of defaults. The model is...

We study default contagion in large homogeneous credit portfolios. Using data from the iTraxx Europe series, two synthetic CDO portfolios are calibrated against their tranche spreads, index CDS spreads and average CDS spreads, all with five year maturity. After the calibrations, which render...

We value CDS spreads and kth-to-default swap spreads in a tractable shot noise model. The default dependence is modelled by letting the individual jumps of the default intensity be driven by a common latent factor. The arrival of the jumps is driven by a Poisson process. By using conditional...

We value synthetic CDO tranche spreads, index CDS spreads, kth-to-default swap spreads and tranchelets in an intensity-based credit risk model with default contagion. The default dependence is modelled by letting individual intensities jump when other defaults occur. The model is reinterpreted...

We model dynamic credit portfolio dependence by using default contagion in an intensity-based framework. Two different portfolios (with 10 obligors), one in the European auto sector, the other in the European financial sector, are calibrated against their market CDS spreads and the corresponding...

Certain commodity producers face uncertain output and price, but can trade financial derivatives on price. I consider how best to use a put option on price. I introduce the variance surface, which is a data visualization technique that shows the level of variance across a grid of values for the...