Loss Given Default Modelling: Comparative Analysis

In this study we investigated several most popular Loss Given Default (LGD) models (LSM, Tobit, Three-Tiered Tobit, Beta Regression, Inflated Beta Regression, Censored Gamma Regression) in order to compare their performance. We show that for a given input data set, the quality of the model calibration depends mainly on the proper choice (and availability) of explanatory variables (model factors), but not on the fitting model. Model factors were chosen based on the amplitude of their correlation with historical LGDs of the calibration data set. Numerical values of non-quantitative parameters (industry, ranking, type of collateral) were introduced as their LGD average. We show that different debt instruments depend on different sets of model factors (from three factors for Revolving Credit or for Subordinated Bonds to eight factors for Senior Secured Bonds). Calibration of LGD models using distressed business cycle periods provide better fit than data from total available time span. Calibration algorithms and details of their realization using the R statistical package are presented. We demonstrate how LGD models can be used for stress testing. The results of this study can be of use to risk managers concerned with the Basel accord compliance

Monitoring of Credit Risk through the Cycle: Risk Indicators

The new Credit Risk Indicator (CRI) based on credit rating migration matrices is introduced. We demonstrate strong correlation between CRI and a number of defaults through several business cycles. The new model for the simulation of the annual number of defaults, based on the 1st quarter CRI data, is proposed

Computer modelling and numerical simulation of the solid state diode pumped Nd:YAG laser with intracavity saturable absorber

Stimulated emission in the Nd:YAG laser with a saturable absorber Cr:YAG is modelled as a superposition of interacting optical modes which are stable in a given optical cavity. The interaction of the active laser crystal and a passive Q-switch with diode pump and optical cavity modes is modelled with account of transversal two-dimentional variation of the pump field and of all participating optical modes. Each elementary volume of an active laser crystal and the Q-switching crystal interacts with all modes (this way modes are nonlinearly linked to each other), and every optical mode interacts with the whole laser crystal. This interaction is given by rate equations. Total number in this set of equations is given by the following formula Ne=2 * kmax * jmax^2 where kmax is number of cavity modes and jmax^2 is the total number of elementary volumes representing intracavity crystals. Most of simulation experiments presented in this paper were done with Ne=2*10^5 (kmax=20 , jmax^2 =10000). Special numerical tools were used to accelerate calculations without loss of precision. Simulation experiments for two laser devices provide quantitative validation of some experimentally observed effects (domination of the fundamental mode in a Q-swithed regime, multimode operation without Q switch) and predict performance of a laser with long pump pulses (trains of laser Q-switched pulses with pule-to-pulse mode switching

Overnight Index Rate: Model, Calibration, and Simulation

In this study the extended Overnight Index Rate (OIR) model is presented. The fitting function for the probability distribution of the OIR daily returns is based on three different Gaussian distributions which provide modelling of the narrow central peak and the wide fat-tailed component. Calibration algorithm for the model is developed and investigated using the historical OIR data

Monitoring of Credit Risk through the Cycle: Risk Indicators

The new Credit Risk Indicator (CRI) based on credit rating migration matrices is introduced. We demonstrate strong correlation between CRI and a number of defaults through several business cycles. The new model for the simulation of the annual number of defaults, based on the 1st quarter CRI data, is proposed

Modelling of stochastic fat-tailed auto-correlated processes: an application to short-term rates

Many financial products sensitive to daily rate changes dictate the importance of adequate modelling of short-term rates. Their intrinsic properties are investigated based on historical market data. A new short-term rate model with the non-Gaussian random driver and auto-correlation factors is introduced. Special calibration procedures for the model are presented.Short-term rate stochastic dynamics are investigated in several numerical experiments

Loss Given Default Modelling: Comparative Analysis

In this study we investigated several most popular Loss Given Default (LGD) models (LSM, Tobit, Three-Tiered Tobit, Beta Regression, Inflated Beta Regression, Censored Gamma Regression) in order to compare their performance. We show that for a given input data set, the quality of the model calibration depends mainly on the proper choice (and availability) of explanatory variables (model factors), but not on the fitting model. Model factors were chosen based on the amplitude of their correlation with historical LGDs of the calibration data set. Numerical values of non-quantitative parameters (industry, ranking, type of collateral) were introduced as their LGD average. We show that different debt instruments depend on different sets of model factors (from three factors for Revolving Credit or for Subordinated Bonds to eight factors for Senior Secured Bonds). Calibration of LGD models using distressed business cycle periods provide better fit than data from total available time span. Calibration algorithms and details of their realization using the R statistical package are presented. We demonstrate how LGD models can be used for stress testing. The results of this study can be of use to risk managers concerned with the Basel accord compliance

Overnight Index Rate: Model, Calibration, and Simulation

In this study the extended Overnight Index Rate (OIR) model is presented. The fitting function for the probability distribution of the OIR daily returns is based on three different Gaussian distributions which provide modelling of the narrow central peak and the wide fat-tailed component. Calibration algorithm for the model is developed and investigated using the historical OIR data

Computer modelling and numerical simulation of the solid state diode pumped Nd:YAG laser with intracavity saturable absorber

Stimulated emission in the Nd:YAG laser with a saturable absorber Cr:YAG is modelled as a superposition of interacting optical modes which are stable in a given optical cavity. The interaction of the active laser crystal and a passive Q-switch with diode pump and optical cavity modes is modelled with account of transversal two-dimentional variation of the pump field and of all participating optical modes. Each elementary volume of an active laser crystal and the Q-switching crystal interacts with all modes (this way modes are nonlinearly linked to each other), and every optical mode interacts with the whole laser crystal. This interaction is given by rate equations. Total number in this set of equations is given by the following formula Ne=2 * kmax * jmax^2 where kmax is number of cavity modes and jmax^2 is the total number of elementary volumes representing intracavity crystals. Most of simulation experiments presented in this paper were done with Ne=2*10^5 (kmax=20 , jmax^2 =10000). Special numerical tools were used to accelerate calculations without loss of precision. Simulation experiments for two laser devices provide quantitative validation of some experimentally observed effects (domination of the fundamental mode in a Q-swithed regime, multimode operation without Q switch) and predict performance of a laser with long pump pulses (trains of laser Q-switched pulses with pule-to-pulse mode switching