Giovanni Della Lunga

Liquidity and credit risk

The paper uses fuzzy measure theory to represent liquidity risk, i.e. the case in which the probability measure used to price contingent claims is not known precisely. This theory enables one to account for different values of long and short positions. Liquidity risk is introduced by representing the upper and lower bound of the price of the contingent claim computed as the upper and lower Choquet integral with respect to a subadditive function. The use of a specific class of fuzzy measures, known as g λ measures enables one to easily extend the available asset pricing models to the case of illiquid markets. As the technique is particularly useful in corporate claims evaluation, a fuzzified version of Mertons model of credit risk is presented. Sensitivity analysis shows that both the level and the range (the difference between upper and lower bounds) of credit spreads are positively related to the ‘quasi debt to firm value ratio’ and to the volatility of the firm value. This finding may be read as correlation between credit risk and liquidity risk, a result which is particularly useful in concrete risk-management applications. The model is calibrated on investment grade credit spreads, and it is shown that this approach is able to reconcile the observed credit spreads with risk premia consistent with observed default rate. Default probability ranges, rather than point estimates, seem to play a major role in the determination of credit spreads.

A new program based on stochastic Liouville equation for the analysis of superhyperfine interaction in CW-ESR spectroscopy

In the slow-motion region, ESR spectra cannot be expressed as a sum of simple Lorentzian lines. Studies of Freed and co-workers, on nitroxides in liquids gained information on the microscopic models of rotational dynamics, relying much on computer programs for simulation of ESR spectra based on the stochastic Liouville equation (SLE). However, application of Freeds method to copper system of biological interest has been for a long time precluded by lack of a full program able to simulate ESR spectra containing more than one hyperfine interaction. Direct extension of the Freeds approach in order to include superhyperfine interaction is not difficult from a theoretical point of view but the resulting algorithm is problematical because it leads to substantial increase in the dimensions of the matrix related to the spin-hamiltonian operator. In this paper preliminary results of a new program, written in C, which includes the superhyperfine interactions are presented. This preliminary version of the program does not take into account a restoring potential, so it can be used only in isotropic diffusion conditions. A comparison with an approximate method previously developed in our laboratory, based on a post-convolution approach, is discussed.

Copper Biomolecules in Solution

For copper(II) in biological systems, and even for small copper complexes in fluid solution at room temperature, the CW lineshapes are strongly influenced by molecular motion. The intermediate tumbling lineshapes for Cu(II) complexes have been analyzed using the stochastic Liouville equations. Various methods of analysing Cu(II) spectra are presented. Examples are given for complexes of peptides, phenanthroline plus glutathione, bleomycin, and β-casomorphins The methods could be extended to other paramagnetic metal ions.

Resolution enhancement of nitrogen hyperfine patterns in the EPR spectra of Cu(II) complexes: FT Analysis of Cu(II)(His-Gly)2

Fourier analysis of EPR spectra is used to achieve straightforward discrimination between an even or odd number of nitrogen nuclei bound to copper in solution. The method is tested on a copper (II) dipeptide (Cu-HistidylGlycine) complex to confirm the room temperature structural arrangement previously hypothesized by conventional techniques. Any residual uncertainty about ligand coordination around copper in solution is eliminated by the present approach. This simple straightforward method is particularly useful for extracting information from poorly resolved patterns of room temperature EPR spectra.

Complex rotational dynamics of the Cu(II)-bleomycin system in mobile and viscous media.

Metal-free bleomycin is an antitumor antibiotic. Studies on the biological activity of bleomycin indicate that the metal-free bleomycin is activated through its binding of available metal ions, such as Cu(II) and Fe(II). The Cu(II)–bleomycin [Cu(II)Blm] complex is the transport form found in blood and can be considered a “magnetopharmaceutical” compound. Its final target is cancerous tissue where it becomes localized.1,2 Living systems present a wide range of environments that can alter the dynamics of the nominally isotropically tumbling agents. Rotational correlation time, τR, is important in determining proton relaxation enhancement.3,4 A previous study in the mobilized phase showed a difference in the electron paramagnetic resonance (EPR) parameters for cupric bleomycin in the liquid as opposed to the solid state.5 Aqueous and 46% wt/vol sucrose solutions have been studied from near physiological temperature to near freezing to determine the dominant rotational correlation time in aqueous and viscous environments.