Risk management of a bond portfolio using options

In this paper, we elaborate a formula for determining the optimal strike price for a bond put option, used to hedge a position in a bond. This strike price is optimal in the sense that it minimizes, for a given budget, either Value-at-Risk or Tail Value-at-Risk. Formulas are derived for both zero-coupon and coupon bonds, which can also be understood as a portfolio of bonds. These formulas are valid for any short rate model that implies an affine term structure model and in particular that implies a lognormal distribution of future zero-coupon bond prices. As an application, we focus on the Hull-White one-factor model, which is calibrated to a set of cap prices. We illustrate our procedure by hedging a Belgian government bond, and take into account the possibility of divergence between theoretical option prices and real option prices. This paper can be seen as an extension of the work of Ahn and co-workers [Ahn, D., Boudoukh, J., Richardson, M., Whitelaw, R., 1999. Optimal risk management using options. J. Financ. 54, 359-375], who consider the same problem for an investment in a share.     

On the null-controllability of the heat equation in unbounded domains

We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting) which implies that one cannot go infinitely far away from the control region without tending to the boundary (if any), but also applies when the distance to the control region is bounded. The proof builds on heat kernel estimates. Secondly, we describe a class of null-controllable heat equations on unbounded product domains. Elementary examples include an infinite strip in the plane controlled from one boundary and an infinite rod controlled from an internal infinite rod. The proof combines earlier results on compact manifolds with a new lemma saying that the null-controllability of an abstract control system and its null-controllability cost are not changed by taking its tensor product with a system generated by a non-positive self-adjoint operator.     

Identification,synthesis and conformational study of a CN(R,S) synthon by-product: (5R, 10R)-5,10-diphenyl-1,6-diaza-3,8-dioxabicyclo[4.4.1]undecane

The title compound, containing a new heterocyclic skeleton, was identified by X-ray crystallography as the product of condensation of (R)-phenylglycinol with an excess of formaldehyde. The molecule adopts a rigid double twist-chair conformation in both solid and solution states.     

Lagrangian skeletons,periodic geodesic flows and symplectic cuttings

In this paper, we investigate symplectic manifolds endowed with a Morse–Bott function with only two critical submanifolds, one of which is Lagrangian while the other one is symplectic.     

Clustering of Eigenvalues on Translation Surfaces

We consider Riemannian surfaces in which there are many embedded Euclidean cylinders. We show that quantitative assumptions on the number of such cylinders provide estimates for the counting function of eigenvalues. These results in particular apply to translation surfaces. Communicated by Jens Marklof Submitted: 3/03/ 2005 Accepted: 18/11/2005     

Multihour engineering and traffic routing optimization in hierarchical telephone networks

Classical hierarchical routing in telephone networks is extended to a wider class called out-of-chain routing in such a way that some useful properties of hierarchical routing are retained. This new routing pattern offers more potential paths than the fixed hierarchical one and can be introduced as a dynamic routing where the fixed alternate sequences change at some predetermined instants during the day. The effect of this new routing pattern on the network performances is examined. The main topic of this paper is to present heuristic methods used to optimise such routings in large networks. We show on artificial networks that the throughput of a given network can be significantly improved by suitable routing choices. We demonstrate that the integration of routing changes within a multihour dimensioning process is possible but the lack of realistic data does not permit at this time to quantify the value of routing optimization on real networks.     

Preparation and characterization of poly(amidoamine) dendrimers functionalized with a rhenium carbonyl complex and PEG as new IR probes for carbonyl metallo immunoassay

The first poly(amidoamine) (PAMAM) dendrimers tethered with both (η⁵-cyclopentadienyl) rhenium tricarbonyl (CpRe(CO)₃) units and polyethylene glycol (PEG) chains were prepared and characterized by combining NMR spectroscopy and Fourier-transform IR spectroscopy. Grafting of CpRe(CO)₃ units was achieved by reductive amination of formyl-CpRe(CO)₃ with the peripheral amines of generation 3 and 4 PAMAMs to yield dendrimers labeled with a variable number of CpRe(CO)₃ units, ranging from 8 to 14 for PAMAM-G3 and 17-30 for PAMAM-G4. PEG chains of different lengths were then attached to some of the remaining peripheral amines, and their respective ability to improve the solubility of the metallodendrimers in aqueous buffered media was evaluated. These metallodendrimers represent new infrared probes designed to be coupled to immunological reagents for the amplification of the IR signal in carbonyl metallo immunoassay (CMIA).