The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach

This paper considers the dynamics for interest rate processes within a multi-factor Heath, Jarrow and Morton (1992) specification. Despite the flexibility of and the notable advances in theoretical research about the HJM models, the number of empirical studies is still inadequate. This paucity is principally because of the difficulties in estimating models in this class, which are not only high-dimensional, but also nonlinear and involve latent state variables. This paper treats the estimation of a fairly broad class of HJM models as a nonlinear filtering problem, and adopts the local linearization filter of Jimenez and Ozaki (2003), which is known to have some desirable statistical and numerical features, to estimate the model via the maximum likelihood method. The estimator is then applied to the interbank offered-rates of the U.S, U.K, Australian and Japanese markets. The two-factor model, with the factors being the level and the slope effect, is found to be a reasonable choice for all of the markets. However, the contribution of each factor towards overall variability of the interest rates and the financial reward each factor claims differ considerably from one market to another.term structure; Heath-Jarrow-Morton; local linearization; filtering

Domain wall space-times with a cosmological constant

We solve vacuum Einstein's field equations with the cosmological constant in space-times admitting 3-parameter group of isometries with 2-dimensional space-like orbits. The general exact solutions, which are represented in the advanced and retarded null coordinates, have two arbitrary functions due to the freedom of choosing null coordinates. In the thin-wall approximation, the Israel's junction conditions yield one constraint equation on these two functions in spherical, planar, and hyperbolic domain wall space-times with reflection symmetry. The remain freedom of choosing coordinates are completely fixed by requiring that when surface energy density $\sigma_0$ of domain walls vanishes, the metric solutions will return to some well-known solutions. It leads us to find a planar domain wall solution, which is conformally flat, in the de Sitter universe.Comment: 9 pages. no figur

The Volatility of the Instantaneous Spot Interest Rate Implied by Arbitrage Pricing - A Dynamic Bayesian Approach

This paper considers the estimation of the volatility of the instantaneous short interest rate from a new perspective. Rather than using discretely compounded market rates as a proxy for the instantaneous short rate of interest, we derive a relationship between observed LIBOR rates and certain unobserved instantaneous forward rates. We determine the stochastic dynamics for these rates under the risk- neutral measure and propose a filtering estimation algorithm for a time- discretised version of the resulting interest rate dynamics based on dynamic Bayesian updating. The method is applied to US Treasury rates of various maturities and is found to give a reasonable model fit.

Numerical methods for the TSD equation in conservation law form

The Transonic Small Disturbance (TSD) Equation is a common model equation for describing subsonic and supersonic flow close to the local speed of sound (transonic). In transonic flow there is an embedded region of locally supersonic flow inside an otherwise subsonic flow. The supersonic region is usually terminated by a shock discontinuity. The success of a numerical scheme for transonic flow prediction depends on its capability of capturing all the flow details and non-linearities including sharp shock profiles without oscillations near the shock. Most of the important phenomena in the TSD equation occur in the stream-wise direction. The nonlinearity and changes in the region of influence depend only on the stream-wise derivation. A suitable one-dimensional model equation derived from the TSD Equation is used. The one-dimensional equation is written in conservation law form. This nonlinear system of equations models the transition from supersonic to subsonic flow. In the numerical calculations the discretised problem is treated as a series of Riemann problems. We will investigate various techniques for solving these Riemann problems. It will be shown that the techniques do not allow non-physical expansion shocks to develop and that the techniques smooth out expansion shocks when these non-physical shocks are present in the initial velocity profile. A comparison will be made between the schemes based on the sharpness of the resulting shock profiles

Semi-Analytic Techniques for Solving Quasi-Normal Modes

In this chapter, we discuss an approach to obtaining black hole quasi-normal modes known as the asymptotic iteration method, which was initially developed in mathematics as a new way to solve for eigenvalues in differential equations. Furthermore, we demonstrate that the asymptotic iteration method allows one to also solve for the radial quasi-normal modes on a variety of black hole spacetimes for a variety of perturbing fields. A specific example for Dirac fields in a general dimensional Schwarzschild black hole spacetime is given, as well as for spin-3/2 field quasi-normal modes

Treatment of Head and Neck Cancers Using Radiotherapy

Radiotherapy is one of the major treatments for head and neck cancers. This chapter discusses the importance of radiotherapy in treating the common types of head and neck cancers, which can be used as a primary treatment or as a postoperative adjuvant treatment to increase the survival of head and neck cancer patients. Because head and neck cancers are likely to be closely surrounded by radiation-sensitive vital organs, the dosimetric superiority of intensity-modulated radiotherapy (IMRT) to achieve highly conformal dose to the planning target volume (PTV) and avoidance of organs at risk (OARs) helps maintain the cornerstone role of radiotherapy in treating the disease. The rationale of IMRT and the treatment planning technique are introduced. Treatment planning of radiotherapy is one of the key procedures in IMRT. The inverse planning process involves many decision-making steps, including PTV and OAR delineation, beam arrangement settings, objective function setting, etc. These important steps are all illustrated in the chapter, with a specific discussion of planning challenges relevant to head and neck cancers. Finally, the promises for further development of IMRT in terms of OARs dose sparing and PTV dose escalation are briefly discussed and reviewed

Synthesis, structure and dioxygen reactivity of a bis(µ-iodo)dicopper(I) complex supported by the [N-(3,5-di-tert-butyl-2-hydroxybenzyl)-N,N-di-(2-pyridylmethyl)]amine ligand

The air-sensitive bis(µ-iodo)dicopper(I) complex 1 supported by [N-(3,5-di-tert-butyl-2-hydroxybenzyl)-N,N-di-(2-pyridylmethyl)]amine (L) has been prepared by treating copper(I) iodide with L in anhydrous THF. Compound 1 crystallizes as a dimer in space group C2/c. Each copper(I) center has distorted tetrahedral N2I2 coordination geometry with Cu–N(pyridyl) distances 2.061(3) and 2.063(3) Å, Cu–I distances 2.6162(5) and 2.7817(5) and a CuCu distance of 2.9086(8) Å. Complex 1 is rapidly oxidized by dioxygen in CH2Cl2 with a 1 : 1 stoichiometry giving the bis(µ-iodo)peroxodicopper(II) complex [Cu(L)(µ-I)]2O2 (2). The reaction of 1 with dioxygen has been characterized by UV-vis, mass spectrometry, EPR and Cu K-edge X-ray absorption spectroscopy at low temperature (193 K) and above. The mass spectrometry and low temperature EPR measurements suggested an equilibrium between the bis(µ-iodo)peroxodicopper(II) complex 2 and its dimer, namely, the tetranuclear (peroxodicopper(II))2 complex [Cu(L)(µ-I)]4O4 (2). Complex 2 undergoes an effective oxo-transfer reaction converting PPh3 into OPPh3 under anaerobic conditions. At sufficiently high concentration of PPh3, the oxygen atom transfer from 2 to PPh3 was followed by the formation of [Cu(PPh3)3I]. The dioxygen reactivity of 1 was compared with that known for other halo(amine)copper(I) dimers

Transonic flow calculations using a dimensional splitting method

The time-dependent Transonic Small Disturbance equation, will be reformulated in Hyperbolic Conservation Law form. In Hyperbolic Conservation Law form, with dimensional splitting the equations can be discretized and treated as a series of Riemann problems. Steady subsonic and transonic flow calculations will be presented for a suitable test configuration and where possible comparisons will be made with analytic solutions

An analysis of the need for columbaria facilities in Hong Kong : a policy tools approach to public action

published_or_final_versionPolitics and Public AdministrationMasterMaster of Public Administratio

Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions.

We present an analysis of the first 10 weeks of the severe acute respiratory syndrome (SARS) epidemic in Hong Kong. The epidemic to date has been characterized by two large clusters-initiated by two separate "super-spread" events (SSEs)-and by ongoing community transmission. By fitting a stochastic model to data on 1512 cases, including these clusters, we show that the etiological agent of SARS is moderately transmissible. Excluding SSEs, we estimate that 2.7 secondary infections were generated per case on average at the start of the epidemic, with a substantial contribution from hospital transmission. Transmission rates fell during the epidemic, primarily as a result of reductions in population contact rates and improved hospital infection control, but also because of more rapid hospital attendance by symptomatic individuals. As a result, the epidemic is now in decline, although continued vigilance is necessary for this to be maintained. Restrictions on longer range population movement are shown to be a potentially useful additional control measure in some contexts. We estimate that most currently infected persons are now hospitalized, which highlights the importance of control of nosocomial transmission