Accounting Noise and the Pricing of CoCos

Contingent Convertible bonds (CoCos) are debt instruments that convert into equity or are written down in times of distress. Existing pricing models assume conversion triggers based on market prices and on the assumption that markets can always observe all relevant firm information. But all Cocos issued so far have triggers based on accounting ratios and/or regulatory intervention. We incorporate that markets receive information through noisy accounting reports issued at discrete time instants, which allows us to distinguish between market and accounting values, and between automatic triggers and regulator-mandated conversions. Our second contribution is to incorporate that coupon payments are contingent too: their payment is conditional on the Maximum Distributable Amount not being exceeded. We examine the impact of CoCo design parameters, asset volatility and accounting noise on the price of a CoCo; and investigate the interaction between CoCo design features, the capital structure of the issuing bank and their implications for risk taking and investment incentives. Finally, we use our model to explain the crash in CoCo prices after Deutsche Bank's profit warning in February 2016

Snow stratigraphic heterogeneity within ground-based passive microwave radiometer footprints: implications for emission modeling

Two-dimensional measurements of snowpack properties (stratigraphic layering, density, grain size and temperature) were used as inputs to the multi-layer Helsinki University of Technology (HUT) microwave emission model at a centimeter-scale horizontal resolution, across a 4.5 m transect of ground-based passive microwave radiometer footprints near Churchill, Manitoba, Canada. Snowpack stratigraphy was complex (between six and eight layers) with only three layers extending continuously throughout the length of the transect. Distributions of one-dimensional simulations, accurately representing complex stratigraphic layering, were evaluated using measured brightness temperatures. Large biases (36 to 68 K) between simulated and measured brightness temperatures were minimized (-0.5 to 0.6 K), within measurement accuracy, through application of grain scaling factors (2.6 to 5.3) at different combinations of frequencies, polarizations and model extinction coefficients. Grain scaling factors compensated for uncertainty relating optical SSA to HUT effective grain size inputs and quantified relative differences in scattering and absorption properties of various extinction coefficients. The HUT model required accurate representation of ice lenses, particularly at horizontal polarization, and large grain scaling factors highlighted the need to consider microstructure beyond the size of individual grains. As variability of extinction coefficients was strongly influenced by the proportion of large (hoar) grains in a vertical profile, it is important to consider simulations from distributions of one-dimensional profiles rather than single profiles, especially in sub-Arctic snowpacks where stratigraphic variability can be high. Model sensitivity experiments suggested the level of error in field measurements and the new methodological framework used to apply them in a snow emission model were satisfactory. Layer amalgamation showed a three-layer representation of snowpack stratigraphy reduced the bias of a one-layer representation by about 50%

Evaluation of Operation IceBridge quick-look snow depth estimates on sea ice

We evaluate Operation IceBridge (OIB) ‘quick-look’ (QL) snow depth on sea ice retrievals using in situ measurements taken over immobile first-year ice (FYI) and multi-year ice (MYI) during March of 2014. Good agreement was found over undeformed FYI (-4.5 cm mean bias) with reduced agreement over deformed FYI (-6.6 cm mean bias). Over MYI, the mean bias was -5.7 cm but 54% of retrievals were discarded by the OIB retrieval process as compared to only 10% over FYI. Footprint scale analysis revealed a root mean square error (RMSE) of 6.2 cm over undeformed FYI with RMSE of 10.5 cm and 17.5 cm in the more complex deformed FYI and MYI environments. Correlation analysis was used to demonstrate contrasting retrieval uncertainty associated with spatial aggregation and ice surface roughness

The Theory of the Interleaving Distance on Multidimensional Persistence Modules

In 2009, Chazal et al. introduced $\epsilon$-interleavings of persistence modules. $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view towards applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $d_I$ is equal to the bottleneck distance $d_B$. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $\epsilon$-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $\epsilon$-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $d_I$ satisfies a universality property. This universality result is the central result of the paper. It says that $d_I$ satisfies a stability property generalizing one which $d_B$ is known to satisfy, and that in addition, if $d$ is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $d\leq d_I$. We also show that a variant of this universality result holds for $d_B$, over arbitrary fields. Finally, we show that $d_I$ restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in Foundations of Computational Mathematics. 36 page

Radio-frequency interference mitigating hyperspectral L-band radiometer

Radio-frequency interference (RFI) can significantly contaminate the measured radiometric signal of current spaceborne L-band passive microwave radiometers. These spaceborne radiometers operate within the protected passive remote sensing and radio-astronomy frequency allocation of 1400–1427 MHz but nonetheless are still subjected to frequent RFI intrusions. We present a unique surface-based and airborne hyperspectral 385 channel, dual polarization, L-band Fourier transform, RFI-detecting radiometer designed with a frequency range from 1400 through  ≈  1550 MHz. The extended frequency range was intended to increase the likelihood of detecting adjacent RFI-free channels to increase the signal, and therefore the thermal resolution, of the radiometer instrument. The external instrument calibration uses three targets (sky, ambient, and warm), and validation from independent stability measurements shows a mean absolute error (MAE) of 1.0 K for ambient and warm targets and 1.5 K for sky. A simple but effective RFI removal method which exploits the large number of frequency channels is also described. This method separates the desired thermal emission from RFI intrusions and was evaluated with synthetic microwave spectra generated using a Monte Carlo approach and validated with surface-based and airborne experimental measurements

Effect of snow microstructure variability on Ku-band radar snow water equivalent retrievals

Spatial variability in snowpack properties negatively impacts our capacity to make direct measurements of snow water equivalent (SWE) using satellites. A comprehensive data set of snow microstructure (94 profiles at 36 sites) and snow layer thickness (9000 vertical profiles across 9 trenches) collected over two winters at Trail Valley Creek, NWT, Canada, were applied in synthetic radiative transfer experiments. This allowed robust assessment of the impact of estimation accuracy of unknown snow microstructural characteristics on the viability of SWE retrievals. Depth hoar layer thickness varied over the shortest horizontal distances, controlled by subnivean vegetation and topography, while variability of total snowpack thickness approximated that of wind slab layers. Mean horizontal correlation lengths of layer thickness were sub-metre for all layers. Depth hoar was consistently ~30% of total depth, and with increasing total depth the proportion of wind slab increased at the expense of the decreasing surface snow layer. Distinct differences were evident between distributions of layer properties; a single median value represented density and specific surface area (SSA) of each layer well. Spatial variability in microstructure of depth hoar layers dominated SWE retrieval errors. A depth hoar SSA estimate of around 7% under the median value was needed to accurately retrieve SWE. In shallow snowpacks <0.6m, depth hoar SSA estimates of ±5-10% around the optimal retrieval SSA allowed SWE retrievals within a tolerance of ±30 mm. Where snowpacks were deeper than ~30cm, accurate values of representative SSA for depth hoar became critical as retrieval errors were exceeded if the median depth hoar SSA was applied