Implied Volatility of Leveraged ETF Options

Abstract

This paper studies the problem of understanding implied volatilities from options written on leveraged exchanged-traded funds (LETFs), with an emphasis on the relations between LETF options with different leverage ratios. We first examine from empirical data the implied volatility skews for LETF options based on the S&P 500. In order to enhance their comparison with non-leveraged ETFs, we introduce the concept of moneyness scaling and provide a new formula that links option implied volatilities between leveraged and unleveraged ETFs. Under a multiscale stochastic volatility framework, we apply asymptotic techniques to derive an approximation for both the LETF option price and implied volatility. The approximation formula reflects the role of the leverage ratio, and thus allows us to link implied volatilities of options on an ETF and its leveraged counterparts. We apply our result to quantify matches and mismatches in the level and slope of the implied volatility skews for various LETF options using data from the underlying ETF option prices. This reveals some apparent biases in the leverage implied by the market prices of different products, long and short with leverage ratios two times and three times.     

Ra+ ion trapping: toward an atomic parity violation measurement and an optical clock

A single Ra⁺ ion stored in a Paul radio frequency ion trap has excellent potential for a precision measurement of the electroweak mixing angle at low momentum transfer and as the most stable optical clock. The effective transport and cooling of singly charged ions of the isotopes ²⁰⁹Ra to ²¹⁴Ra in a gas filled radio frequency quadrupole device is reported. The absolute frequencies of the transition 7s²S_1/2–7d²D_3/2 at wavelength 828 nm have been determined in ^212–214Ra⁺ with ≤19 MHz uncertainty using laser spectroscopy on small samples of ions trapped in a linear Paul trap at the online facility Trapped Radioactive Isotopes: µicrolaboratories for fundamental Physics (TRIµP) of the Kernfysisch Versneller Instituut.     

Creating ground state molecules with optical feshbach resonances in tight traps

We propose to create ultracold ground state molecules in an atomic Bose-Einstein condensate by adiabatic crossing of an optical Feshbach resonance. We envision a scheme where the laser intensity and possibly also frequency are linearly ramped over the resonance. Our calculations for (87)Rb show that for sufficiently tight traps it is possible to avoid spontaneous emission while retaining adiabaticity, and conversion efficiencies of up to 50% can be expected.     

Current-induced embrittlement of atomic wires

Recent experiments suggest that gold single-atom contacts and atomic chains break at applied voltages of 1 to 2 V. In order to understand why current flow affects these defect-free conductors, we have calculated the current-induced forces on atoms in a Au chain between two Au electrodes. These forces are not by themselves sufficient to rupture the chain. However, the current reduces the work to break the chain, which results in a dramatic increase in the probability of thermally activated spontaneous fracture of the chain. This current-induced embrittlement poses a fundamental limit to the current-carrying capacity of atomic wires.     

Quick synthesis of lipid-polymer hybrid nanoparticles with low polydispersity using a single-step sonication method

Lipid-polymer hybrid nanoparticle, consisting of a hydrophobic polymeric core and a lipid monolayer shell, represents a new and promising drug delivery platform that has shown controllable particle size and surface functionality, high drug loading yield, sustained drug release profile, and excellent in vitro and in vivo stability. These lipid monolayer-coated polymeric nanoparticles are typically fabricated through a modified nanoprecipitation method, which involves sample heating, vortexing, and solvent evaporation. Herein we report a new and fast method to synthesize lipid-polymer hybrid nanoparticles with controllable and nearly uniform particle size. Using a bath sonication approach, we demonstrate that the whole hybrid nanoparticle synthesis process can be completed in about 5 min compared with a few hours for previous synthesis approaches. The size and polydispersity of the resulting nanoparticles can be readily controlled by tuning the relative concentrations of individual building components. Colloidal stability tests of the synthesized hybrid nanoparticles in PBS buffer and serum show no signs of aggregation over a period of 5 days. The present method improves the production rate of the hybrid nanoparticles by near 20-fold while not compromising the physicochemical properties of the particles. This work may facilitate the bench-to-bedside translation of lipid-polymer hybrid nanoparticles as a robust drug nanocarrier by allowing for fabricating a large amount of these nanoparticles at high production rate.     

Optical sensing in microfluidic lab-on-a-chip by femtosecond-laser-written waveguides

We use direct femtosecond laser writing to integrate optical waveguides into a commercial fused silica capillary electrophoresis chip. High-quality waveguides crossing the microfluidic channels are fabricated and used to optically address, with high spatial selectivity, their content. Fluorescence from the optically excited volume is efficiently collected at a 90° angle by a high numerical aperture fiber, resulting in a highly compact and portable device. To test the platform we performed electrophoresis and detection of a 23-mer oligonucleotide plug. Our approach is quite powerful because it allows the integration of photonic functionalities, by simple post-processing, into commercial LOCs fabricated with standard techniques. Figure Femtosecond laser written waveguides can selectively excite fluorescence in a microfluidic channel of a commercial lab-on-a-chip. A compact scheme for on-chip detection by laser induced fluorescence is applied to capillary electrophoresis of a 23-mer Cy3-labeled oligonucleotide     

Nano‐Conjugate Fluorescence Probe for the Discrimination of Phosphate and Pyrophosphate

We describe a pyrophosphate (PPi) probe that is based on a fluorescent dicarboxylate‐substituted poly(para‐phenyleneethynylene) (PPE) and 10 nm cobalt–iron spinel nanoparticles (NPs) in aqueous media. The spinel NPs efficiently quench the fluorescence of the PPE at a concentration of 20–30 pmol. Addition of phosphate anions to the PPE–NP construct displaces the quenched PPE to give rise to a fluorescent response; we found that PPi and phosphate (Pi) have significantly different binding affinities for the self‐assembled materials. We can discern >40 nM PPi in the presence of 0.1 mM Pi at pH 7, which suggests that these assemblies may be useful in bio‐analytical applications. This displacement assay was used to effectively determine the ability of pyrophosphatase to hydrolyze PPi to Pi.