A jump model for credit default swaps with hierarchical clustering

The return time series of Credit Default Swaps (CDS) display possibly the highest excess kurtosis and skewness of any asset class in capital markets. Capturing this requires a departure from classical modeling techniques. Here, the premise is that CDS prices jump and those jumps cluster. Initially, a model is proposed that is driven by a diffusion and a Hawkes process to reproduce the clustering of shocks. The new element of the model is the use of hierarchical clustering to calibrate the distribution of the jumps. Partitioning the shocks identifies shifts in the volatility regime of the CDS through time, which are shown to consistently correspond to both systemic and idiosyncratic market events. A piecewise definition of a double exponential distribution for the jumps, corresponding to the identified clusters, is employed to replicate the regime switching. Subsequently, this demonstrably improves the accuracy of the calibration. The model is fitted to all CDS with more than 2000 closing prices from 2001 to 2014; a total of 1652 individual time series. For each credit, a peak-over-threshold approach is applied to the return series to separate the data into those returns that can broadly be classified as log-normal and those that can be characterized as jumps. By explicitly linking the results to market traded volumes, the results indicate a clear split of the CDS into liquid and illiquid names. A key finding is that for the illiquid CDS, it is difficult to justify the continuous component of the model. For the low liquidity names, the Hawkes process is shown to capture the price-action without a diffusion. A Markov chain is then introduced into the simulation to replicate the clustering and regime switching.