Credit Value Adjustment for Credit Default Swaps via the Structural Default Model
Education
Globally revered quant minds Dr. Alex Lipton & Dr. Artur Sepp propose a structural default model to evaluate the counterparty risk by trading in credit default swap (CDS) contracts.
Moreover, Dr. Sepp & Dr. Lipton model the joint evolution of the firm value of the entity underlying the CDS contract and the counterparty using a correlated jump-diffusion process. Unlike the reduced-form default model, where the default event is always a sudden event, in their model, the default event is triggered by a sudden drop in the value of the credit entity and subsequent deterioration of its credit quality, which is the pattern observed in practice, in particular, for financial institutions.
As a result, their model might provide a better tool to model the value of financial institutions and their creditworthiness.
Dr. Sepp & Dr. Lipton develop robust semi-analytical and numerical methods for the model calibration and solving the pricing problem, which will be presented somewhere else.
In their research they show how to apply their model to analyze the counterparty risk in credit default swaps and evaluate the counterparty charge.
Furthermore, using the market data of JP Morgan and Citigroup for illustrations, Dr. Sepp & Dr. Lipton show that in their model the counterparty charge is significant, 5%-30% compared to the present value of the default leg of the underlying CDS, and it is sensitive to both correlation and volatility parameters.
In addition, Dr. Sepp & Dr. Lipton presented a multi-dimensional extension of the Merton (1974) model, where the joint dynamics of the firm values are driven by a multi-dimensional jump-diffusion process.
By applying FFT and PIDE-based methods, they developed the forward induction procedure for their model calibration and the backward induction procedure for valuing credit-linked contracts in one and two dimensions.
Dr. Sepp & Dr. Lipton considered the jump size distribution of two types, the negative discrete and negative exponential, and showed that for the joint bivariate dynamics, the model with exponential PDF produces a noticeably lower implied Gaussian correlation than that produced by the model with constant negative jumps; although for marginal dynamics both jump specifications result in an adequate fit to the market data. Based on this observation and given a high level of the default correlation among financial institutions (above 50%), the model with constant negative jumps, albeit simple, seem to provide a more realistic description of default correlations and, thus, the counterparty risk.
Lastly, the results indicate that the counterparty risk in credit derivatives trading cannot become neglected. And in conclusion, require active management.
Read The Full Paper:
Credit Value Adjustment for Credit Default Swaps via the Structural Default Model by Alex Lipton, Artur Sepp :: SSRN
Alex Lipton
Hebrew University of Jerusalem; Massachusetts Institute of Technology (MIT), Global Head, Quantitative R&D, ADIA
Artur Sepp
Sygnum Bank Asset Management, Head Systematic Solutions and Portfolio Construction
