A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing

Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first- and second-order optimality analysis. We prove the existence of local optimal solutions and of a Lagrange multiplier associated with the inequality constraints. Furthermore, we prove a sufficient second-order optimality condition and present some numerical results underlining the good properties of the numerical scheme.Dupire equation, parameter identification, optimal control, optimality conditions, SQP method, primal-dual active set strategy

Vegetation Dynamics at the Upper Reaches of a Tropical Montane Forest are Driven by Disturbance Over the Past 7300 Years

We assessed tropical montane cloud forest (TMCF) sensitivity to natural disturbance by drought, fire, and dieback with a 7300-year-long paleorecord. We analyzed pollen assemblages, charcoal accumulation rates, and higher plant biomarker compounds (average chain length [ACL] of n-alkanes) in sediments from Wai'ānapanapa, a small lake near the upper forest limit and the mean trade wind inversion (TWI) in Hawai‘i. The paleorecord of ACL suggests increased drought frequency and a lower TWI elevation from 2555–1323 cal yr B.P. and 606–334 cal yr B.P. Charcoal began to accumulate and a novel fire regime was initiated ca. 880 cal yr B.P., followed by a decreased fire return interval at ca. 550 cal yr B.P. Diebacks occurred at 2931, 2161, 1162, and 306 cal yr B.P., and two of these were independent of drought or fire. Pollen assemblages indicate that on average species composition changed only 2.8% per decade. These dynamics, though slight, were significantly associated with disturbance. The direction of species composition change varied with disturbance type. Drought was associated with significantly more vines and lianas; fire was associated with an increase in the tree fern Sadleria and indicators of open, disturbed landscapes at the expense of epiphytic ferns; whereas stand-scale dieback was associated with an increase in the tree fern Cibotium. Though this cloud forest was dynamic in response to past disturbance, it has recovered, suggesting a resilient TMCF with no evidence of state change in vegetation type (e.g., grassland or shrubland)

Derivation, Properties, and Simulation of a Gas-Kinetic-Based, Non-Local Traffic Model

We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average velocity contain a non-local interaction term which is very favorable for a fast and robust numerical integration, so that several thousand freeway kilometers can be simulated in real-time. The model parameters can be easily calibrated by means of empirical data. They are directly related to the quantities characterizing individual driver-vehicle behavior, and their optimal values have the expected order of magnitude. Therefore, they allow to investigate the influences of varying street and weather conditions or freeway control measures. Simulation results for realistic model parameters are in good agreement with the diverse non-linear dynamical phenomena observed in freeway traffic.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html and http://www.theo2.physik.uni-stuttgart.de/treiber.htm

Electroweak corrections to Higgs-strahlung off W/Z bosons at the Tevatron and the LHC with HAWK

The associate production of Higgs bosons with W or Z bosons, known as Higgs-strahlung, is an important search channel for Higgs bosons at the hadron colliders Tevatron and LHC for low Higgs-boson masses. We refine a previous calculation of next-to-leading-order electroweak corrections (and recalculate the QCD corrections) upon including the leptonic decay of the W/Z bosons, thereby keeping the fully differential information of the 2-lepton + Higgs final state. The gauge invariance of the W/Z-resonance treatment is ensured by the use of the complex-mass scheme. The electroweak corrections, which are at the level of -(5-10)% for total cross sections, further increase in size with increasing transverse momenta p_T in differential cross sections. For instance, for p_T,H >~ 200GeV, which is the interesting range at the LHC, the electroweak corrections to WH production reach about -14% for M_H = 120GeV. The described corrections are implemented in the HAWK Monte Carlo program, which was initially designed for the vector-boson-fusion channel, and are discussed for various distributions in the production channels pp / p \bar p -> H + l nu_l / l^-l^+ / nu_l \bar nu_l + X.Comment: 22 p

Solar Wind Neon from Genesis: Implications for the Lunar Noble Gas Record

Lunar soils have been thought to contain two solar noble gas components with distinct isotopic composition. One has been identified as implanted solar wind, the other as higher-energy solar particles. The latter was puzzling because its relative amounts were much too large compared with present-day fluxes, suggesting periodic, very high solar activity in the past. Here we show that the depth-dependent isotopic composition of neon in a metallic glass exposed on NASA's Genesis mission agrees with the expected depth profile for solar wind neon with uniform isotopic composition. Our results strongly indicate that no extra high-energy component is required and that the solar neon isotope composition of lunar samples can be explained as implantation-fractionated solar wind

Global Hopf bifurcation in the ZIP regulatory system

Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been modeled by a system of ordinary differential equations based on the uptake of zinc, expression of a transporter protein and the interaction between an activator and inhibitor. For certain parameter choices the steady state of this model becomes unstable upon variation in the external zinc concentration. Numerical results show periodic orbits emerging between two critical values of the external zinc concentration. Here we show the existence of a global Hopf bifurcation with a continuous family of stable periodic orbits between two Hopf bifurcation points. The stability of the orbits in a neighborhood of the bifurcation points is analyzed by deriving the normal form, while the stability of the orbits in the global continuation is shown by calculation of the Floquet multipliers. From a biological point of view, stable periodic orbits lead to potentially toxic zinc peaks in plant cells. Buffering is believed to be an efficient way to deal with strong transient variations in zinc supply. We extend the model by a buffer reaction and analyze the stability of the steady state in dependence of the properties of this reaction. We find that a large enough equilibrium constant of the buffering reaction stabilizes the steady state and prevents the development of oscillations. Hence, our results suggest that buffering has a key role in the dynamics of zinc homeostasis in plant cells.Comment: 22 pages, 5 figures, uses svjour3.cl

Congested Traffic States in Empirical Observations and Microscopic Simulations

We present data from several German freeways showing different kinds of congested traffic forming near road inhomogeneities, specifically lane closings, intersections, or uphill gradients. The states are localized or extended, homogeneous or oscillating. Combined states are observed as well, like the coexistence of moving localized clusters and clusters pinned at road inhomogeneities, or regions of oscillating congested traffic upstream of nearly homogeneous congested traffic. The experimental findings are consistent with a recently proposed theoretical phase diagram for traffic near on-ramps [D. Helbing, A. Hennecke, and M. Treiber, Phys. Rev. Lett. {\bf 82}, 4360 (1999)]. We simulate these situations with a novel continuous microscopic single-lane model, the ``intelligent driver model'' (IDM), using the empirical boundary conditions. All observations, including the coexistence of states, are qualitatively reproduced by describing inhomogeneities with local variations of one model parameter. We show that the results of the microscopic model can be understood by formulating the theoretical phase diagram for bottlenecks in a more general way. In particular, a local drop of the road capacity induced by parameter variations has practically the same effect as an on-ramp.Comment: Now published in Phys. Rev. E. Minor changes suggested by a referee are incorporated; full bibliographic info added. For related work see http://www.mtreiber.de/ and http://www.helbing.org

Radiative corrections to the semileptonic and hadronic Higgs-boson decays H -> W W/Z Z -> 4 fermions

The radiative corrections of the strong and electroweak interactions are calculated for the Higgs-boson decays H -> WW/ZZ -> 4f with semileptonic or hadronic four-fermion final states in next-to-leading order. This calculation is improved by higher-order corrections originating from heavy-Higgs-boson effects and photonic final-state radiation off charged leptons. The W- and Z-boson resonances are treated within the complex-mass scheme, i.e. without any resonance expansion or on-shell approximation. The calculation essentially follows our previous study of purely leptonic final states. The electroweak corrections are similar for all four-fermion final states; for integrated quantities they amount to some per cent and increase with growing Higgs-boson mass M_H, reaching 7-8% at M_H \sim 500 GeV. For distributions, the corrections are somewhat larger and, in general, distort the shapes. Among the QCD corrections, which include corrections to interference contributions of the Born diagrams, only the corrections to the squared Born diagrams turn out to be relevant. These contributions can be attributed to the gauge-boson decays, i.e. they approximately amount to \alpha_s/\pi for semileptonic final states and 2\alpha_s/\pi for hadronic final states. The discussed corrections have been implemented in the Monte Carlo event generator PROPHECY4F.Comment: 29 pages, LaTeX, 30 postscript figure

Gauge-independent MS‾\overline{MS} renormalization in the 2HDM

We present a consistent renormalization scheme for the CP-conserving Two-Higgs-Doublet Model based on $\overline{MS}$ renormalization of the mixing angles and the soft-$Z_2$-symmetry-breaking scale $M_{sb}$ in the Higgs sector. This scheme requires to treat tadpoles fully consistently in all steps of the calculation in order to provide gauge-independent $S$-matrix elements. We show how bare physical parameters have to be defined and verify the gauge independence of physical quantities by explicit calculations in a general $R_{\xi}$-gauge. The procedure is straightforward and applicable to other models with extended Higgs sectors. In contrast to the proposed scheme, the $\overline{MS}$ renormalization of the mixing angles combined with popular on-shell renormalization schemes gives rise to gauge-dependent results already at the one-loop level. We present explicit results for electroweak NLO corrections to selected processes in the appropriately renormalized Two-Higgs-Doublet Model and in particular discuss their scale dependence.Comment: 52 pages, PDFLaTeX, PDF figures, JHEP version with Eq. (5.23) correcte