Reduced form models

In order to solve the probability of default, reduced-form models adopt a different approach. They are mainly based on debt prices rather than equity prices. In fact, they do not take into account the fundamentals of the firm and the default event is determined as an exogenous process without considering the underlying asset movements. In addition, the models are mainly based oti X t), that is the default intensity as a function of time. In particular, these models use the decomposition of the risky rate (risk-free rate and risk premium) in order to determine the default probabilities, recovery rates and debt values. Although structural models have the advantage to foUow a reliable measure of credit risk, that is the firm value, reduced-form approach overcomes the Umitatimi in which the balance sheet is not the unique indicator of the default prediction. 

Some practitioners argue that Merton models are more appropriate than reduced form models when pricing default swaps on high-yield bonds, due to the higher correlation of high-yield bonds with the underlying equity of the issuer firm. 

Reduced form models are a form of no-arbitrage model. These models can be fitted to the current term structure of risky bonds to generate no arbitrage prices. In this way the pricing of credit derivatives using these models will be consistent with the market data on the credit risky bonds traded in the market. These models allow the default process to be separated from the asset value and are more commonly used to price credit derivatives. 

Some key features of reduced form models include the following ... 

The predecessors of the reduced-form models are full Markov chain models including those presented by Jarrow, Lando, and Turnbull, Das and Tufano and Duffie and Singleton. We consider these models in this section. 

The reduced form models described earlier models are a new generation of credit derivative pricing models, which are now increasingly being used to price total return swaps. 

Reduced Form Kamakura implements reduced form models from the Robert Jarrow family, such as the Jarrow-Chava version. These models use equity, debt, and credit derivative prices. 

Kamaknra ntilizes an ROC Accuracy Ratio to evaluate the performance of models. This ratio is designed to determine which family of models is best by determining if a model correctly identifies defaults and nondefaults in a sample of historical observations. A score of 100 would be a perfect score. According to Kamakura s analysis, the Jarrow-Chava reduced form model received a score of 92.74. This compares to scores in the 80 s for various Merton models. 

In addition, Kamakura s research has shown that reduced form models utilizing credit derivatives prices are the most effective default predictor ... 

Our results indicate that reduced form models based on credit derivatives prices and bond prices have the best performance from both a statistical and a practical point of view, said Profes-... 

In an axisymmetric flow regime all of the field variables remain constant in the circumferential direction around an axis of symmetry. Therefore the governing flow equations in axisymmetric systems can be analytically integrated with respect to this direction to reduce the model to a two-dimensional form. In order to illustrate this procedure we consider the three-dimensional continuity equation for an incompressible fluid written in a cylindrical (r, 9, 2) coordinate system as... 

Several other electron-transfer reagents have been tested with arenediazonium ions, for example, A-benzyl-l,4-dihydronicotinamide, which is a model for biochemical reductions by NAD(P)H, the reduced form of NADP+ (nicotinamide adenine cfinucleotide phosphate) (Yasui et al., 1984). 

Detailed MCD experiments carried out on the dithionite-reduced forms of the C56S and C60S mutants of C. pasteurianum ferredoxin have shown that a large fraction of the [2Fe-2S] centers have an iS = 9/2 ground state (148). These centers exhibit temperature-dependent features at ges = 10.1, 9.25, 6.00, and 3.00, corresponding to E/D = 0.16 with D = 1.1 cm (148). According to the model pre-... 

In recent years, several model complexes have been synthesized and studied to understand the properties of these complexes, for example, the influence of S- or N-ligands or NO-releasing abilities [119]. It is not always easy to determine the electronic character of the NO-ligands in nitrosyliron complexes thus, forms of NO [120], neutral NO, or NO [121] have been postulated depending on each complex. Similarly, it is difficult to determine the oxidation state of Fe therefore, these complexes are categorized in the Enemark-Feltham notation [122], where the number of rf-electrons of Fe is indicated. In studies on the nitrosylation pathway of thiolate complexes, Liaw et al. could show that the nitrosylation of complexes [Fe(SR)4] (R = Ph, Et) led to the formation of air- and light-sensitive mono-nitrosyl complexes [Fe(NO)(SR)3] in which tetrathiolate iron(+3) complexes were reduced to Fe(+2) under formation of (SR)2. Further nitrosylation by NO yields the dinitrosyl complexes [(SR)2Fe(NO)2], while nitrosylation by NO forms the neutral complex [Fe(NO)2(SR)2] and subsequently Roussin s red ester [Fe2(p-SR)2(NO)4] under reductive elimination forming (SR)2. Thus, nitrosylation of biomimetic oxidized- and reduced-form rubredoxin was mimicked [121]. Lip-pard et al. showed that dinuclear Fe-clusters are susceptible to disassembly in the presence of NO [123]. 

Since the reduced form of the model is programmed here, the parametric values cannot be easily changed. 

Using 1,4,8,11-tetraazacyclotetradecane, the structure of complex (800) (distorted trigonal planar Cu-Cu 6.739 A) was determined. Reactivity with 02 was investigated to demonstrate the formation of trans-l,2-peroxo species.585 As part of their work with copper(I) complexes with 02, the structure of a dicopper(I) complex ((801) distorted tetrahedral 7.04 A), supported by macrocyclic ligand environment, was reported by Comba and co-workers. Tolman and co-workers structurally characterized a three-coordinate copper(I)-phenoxide complex (802) (planar T-shaped) that models the reduced form of GO.587 The copper(I) analogue [Cu(L)][CF3-SO3]-0.43MeOI I (803) of a copper(II) complex (534) was also reported to demonstrate the role of ligand framework conformability in CV /Cu1 redox potentials.434 Wilson and co-workers... 

The by-product, representing a relatively reduced form of sulfur, is a reasonable model for the sulfur impurities in the synthesis gas obtained from sulfur-rich coal. This sodium sulfide test of sulfur resistance of water gas shift catalyst systems generated in basic solutions is a very severe test since the quantities of sulfur involved are much larger than those likely to be found in synthesis gas made from any sulfur-rich coals. 

The fourth state with [Fe4S4]° shown in Table 6.1 was recently described as the most reduced form possible for the Fe-protein s [Fe4S4] cluster.16 Usually, only two oxidation states for a given metal-sulfur cluster are stable. Therefore a stable [Fe4S4]° state in Fe-protein s iron-sulfur cluster (as appears likely from experimental evidence presented in reference 16) would be unique because the cluster would then have three stable oxidation states, [Fe4S4]2+/1+/0. It appears also that the all-ferrous state is only stable in the protein-bound cluster and not for model... 

Alternative kinetic models were considered for this reaction. Both of them predict rapid reduction of Cu(II) Cu(II) to Cu(I) Cu(I) by H2DTBC and subsequent formation of the Cu(II)(0 -)Cu(II) intermediate in the reaction of the reduced form with 02. The first model assumes that the rate determining formation of the intermediate is followed by a fast, acid assisted dissociation into the oxidized form of the catalyst and H202. In the other model, the rate determining step is the oxidation of H2DTBC by the intermediate. The two models predict... 

---