C14 - Semiparametric and Nonparametric Methods: GeneralReturn

Particle Filter algorithms for filtering latent states (volatility and jumps) of Stochastic-Volatility Jump-Diffusion (SVJD) models are being explained. Three versions of the SIR particle filter with adapted proposal distributions to the jump occurrences, jump sizes, and both are derived and their performance is compared in a simulation study to the un-adapted particle filter. The filter adapted to both the jump occurrences and jump sizes achieves the best performance, followed in their respective order by the filter adapted only to the jump occurrences and the filter adapted only to the jump sizes. All adapted particle filters outperformed the unadapted particle filter.

The paper proposes an application of the survival time analysis methodology to estimations of the Loss Given Default (LGD) parameter. The main advantage of the survival analysis approach compared to classical regression methods is that it allows exploiting partial recovery data. The model is also modified in order to improve performance of the appropriate goodness of fit measures. The empirical testing shows that the Cox proportional model applied to LGD modeling performs better than the linear and logistic regressions. In addition a significant improvement is achieved with the modified "pseudo" Cox LGD model

The paper provides an overview of the Exposure at Default (EAD) definition, requirements, and estimation methods as set by the Basel II regulation. A new methodology connected to the intensity of default modeling is proposed. The numerical examples show that various estimation techniques may lead to quite different results with intensity of default based model being recommended as the most faithful with respect to a precise probabilistic definition of the EAD parameter.

The Basle II parameter called Loss Given Default (LGD) aims to estimate the expected losses on not yet defaulted accounts in the case of default. Banks firstly need to collect historical recovery data, discount the recovery income and cost cash flow to the time of default, and calculate historical recovery rates and LGDs. One of the puzzling tasks is to determine an appropriate discount rate which is very vaguely characterized by the regulation. This paper proposes a market consistent methodology for the LGD discount rate determination based on estimation of the systematic, i.e. undiversifiable, recovery risk and a cost of the risk.