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.     

Photochemical degradation of hyaluronic acid by singlet oxygen

Changes of the rheological properties of hyaluronic acid (sodium-magnesium salt) solutions after exposure to UV radiation indicate a vigorous decrease in their viscosity, but its still strong shear rate dependence. Whereas the presence of the singlet oxygen sensitizer (anthracene-1-sulphonic acid) brings about a loss of shear dependence; the studied solutions show newtonian behavior.     

内部激励源二自由度结构扬声器振动特性分析

有别于多数基于简单振子结构的扬声器,针对一类内部激励源二自由度(IE2DOF)结构的扬声器,用类比线路图法建立集总参数模型,计算分析了这种结构的频率响应,同时计算了其固有共振频率和固有反共振频率。使用叠加法分析内部激励源对频响的影响。最后实际测量和理论计算吻合,进一步支持了理论模型,揭示了IE2DOF结构扬声器的振动特性。     

Intramolecular enantiomerism as revealed from Raman optical activity spectrum

An algorithm is employed to retrieve the differential bond polarizabilities (DBP) of the C‐C bonds from the Raman optical activity spectrum of (‐)β‐pinene. (‐)β‐pinene possesses two stereo centers (chiral centers) and a local mirror reflection that interchanges the S type part and R type part in one molecular. It is demonstrated that this local mirror reflection could induce an approximate (or symmetry breaking) mirror reflection that reverses the signs of the DBP of the pair bond coordinates that are related to each other by the mirror reflection.This can be called intramolecular enantiomerism (IE). More cases of IE are discussed by the analysis of (‐)α‐pinene, (R)‐(+)‐4‐isopropyl‐1‐methylcyclohexene and (R)‐(+)‐3‐methylcyclohexanone together with previously studied limonene case. Copyright © 2015 John Wiley & Sons, Ltd.     

Commutativity of the Arens product in lattice ordered algebras

Let IE1.gif" alt=" $${\text{A}}$$ " align="middle" border="0"> be an Abelian Archimedean lattice ordered algebra. The order bidual IE2.gif" alt=" $${A'}$$ " align="middle" border="0"> furnished with the Arens product is again a lattice ordered algebra. We show that the order continuous order bidual IE3.gif" alt=" $$(A')'_n$$ " align="middle" border="0"> is Abelian. This solves an open problem and improves a result of Scheffold, who proved it for the case of normed lattice ordered algebras. The proof is based on the up-down-up approximation of positive elements in the order continuous order bidual IE4.gif" alt=" $$(A')'_n$$ " align="middle" border="0"> by elements in the canonical image IE5.gif" alt=" $${\widehat A}$$ " align="middle" border="0"> of IE6.gif" alt=" $$A$$ " align="middle" border="0"> in IE7.gif" alt=" $$(A')'_n$$ " align="middle" border="0"> Components of positive elements in IE8.gif" alt=" $${\widehat A}$$ " align="middle" border="0"> are characterized and the result is applied to the Arens product of IE9.gif" alt=" $$f$$ " align="middle" border="0"> -and almost IE10.gif" alt=" $$f$$ " align="middle" border="0"> -algebras.     

En">Characters and Composition Factor Multiplicities for the Lie Superalgebra $${\mathfrak{g}}{\mathfrak{l}}$$ ( m / n )

The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra IE2.gif" alt=" $${\mathfrak{g}}{\mathfrak{l}}$$ " align="middle" border="0"> (m/n ) were described by Serganova, leading to her solution of the character problem for IE3.gif" alt=" $${\mathfrak{g}}{\mathfrak{l}}$$ " align="middle" border="0"> (m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed.     

On the riemann zeta-function and the divisor problem II

Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of IE1.gif" alt=" $$\left| {\zeta \left( {\frac{1}{2} + it} \right)} \right|$$ " align="middle" border="0"> . If E ^*(t)=E(t)-2πΔ^*(t/2π) with IE2.gif" alt=" $$\Delta *\left( x \right) + 2\Delta \left( {2x} \right) - \frac{1}{2}\Delta \left( {4x} \right)$$ " align="middle" border="0"> , then we obtain

Pseudo-Hermiticity, $$\mathcal{P}\mathcal{T}$$ symmetry,and the metric operator

The main achievements of Pseudo-Hermitian Quantum Mechanics and its distinction from the indefinite-metric quantum theories are reviewed. The issue of the non-uniqueness of the metric operator and its consequences for defining the observables are discussed. A systematic perturbative expression for the most general metric operator is offered and its application for a toy model is outlined. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

A Class of k-Quantum Nonlinear Coherent States and Some of Their Properties

A class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powers B ^k (k 3) of the annihilation operator IE1.gif" alt=" $$B = a\frac{1}{{f(N)}}$$ " align="middle" border="0"> of f-oscillators, is obtained and its completeness is investigated. An alternative method to construct them is proposed. We introduce a new kind of higher-order squeezing and sub-Poissonian distribution. The quantum statistical properties of the k states are studied. The result shows that all of the eigenstates can be generated by a linear superposition of k Roy-type nonlinear coherent states. These states may form a complete Hilbert space, and the M-th order [M = (n + 1/2)k; n = 0,1, ...] squeezing effects exist in all of the k states when k is even. There is the sub-Poissonian distribution in all of the states.     

A Modal Logic Based on Linearly Ordered f-Spaces

A modal logic associated with the IE2.gif" alt=" $$f$$ " align="middle" border="0"> -spaces introduced by Ershov is examined. We construct a modal calculus that is complete w.r.t. the class of all strictly linearly ordered IE3.gif" alt=" $${f_0 }$$ " align="middle" border="0"> -frames, and the class of all strictly linearly ordered IE4.gif" alt=" $$f$$ " align="middle" border="0"> -frames.