Prices and volumes of options: A simple theory of risk sharing when markets are incomplete

We present a simple theory of business-cycle movements of option prices and volumes. This theory relies on time-varying heterogeneity between agents in their demand for insurance against aggregate risk. Formally, we build an infinite-horizon model where agents face an aggregate risk, but also different levels of idiosyncratic risk. We manage to characterize analytically a general equilibrium in which positive quantities of derivatives are traded. This allows us to explain the informational content of derivative volumes over the business cycle. We also carry out welfare analysis with respect to the introduction of options, which appears not to be Pareto-improving.Option Pricing, Open Interest, Incomplete Markets.

Incomplete markets, liquidation risk, and the term structure of interest rates

We analyze the term structure of real interest rates in a general equilibrium model with incomplete markets and borrowing constraints. Agents are subject to both aggregate and idiosyncratic income shocks, which latter may force them into early portfolio liquidation in a bad aggregate state. We derive a closed-form equilibrium with limited agent heterogeneity (despite market incompleteness), which allows us to produce analytical expressions for bond prices and returns at any maturity. The attractiveness of bonds as liquidity makes aggregate bond demand downward-sloping, so that greater bond supply raises both the level and the slope of the yield curve. Moreover, time-variations in liquidation risk are shown to help explain the rejection of the Expectations Hypothesis.Incomplete markets; yield curve; borrowing constraints.

On deterministic error analysis in variational data assimilation

International audienceThe problem of variational data assimilation for a nonlinear evolution model is considered to identify the initial condition. The equation for the error of the optimal initial-value function through the errors of the input data is derived, based on the Hessian of the misfit functional and the second order adjoint techniques. The fundamental control functions are introduced to be used for error analysis. The sensitivity of the optimal solution to the input data (observation and model errors, background errors) is studied using the singular vectors of the specific response operators in the error equation. The relation between "quality of the model" and "quality of the prediction" via data assimilation is discussed

Quantum Algorithms for Matrix Products over Semirings

In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we obtain the following results. We construct a quantum algorithm computing the product of two n x n matrices over the (max,min) semiring with time complexity O(n^{2.473}). In comparison, the best known classical algorithm for the same problem, by Duan and Pettie, has complexity O(n^{2.687}). As an application, we obtain a O(n^{2.473})-time quantum algorithm for computing the all-pairs bottleneck paths of a graph with n vertices, while classically the best upper bound for this task is O(n^{2.687}), again by Duan and Pettie. We construct a quantum algorithm computing the L most significant bits of each entry of the distance product of two n x n matrices in time O(2^{0.64L} n^{2.46}). In comparison, prior to the present work, the best known classical algorithm for the same problem, by Vassilevska and Williams and Yuster, had complexity O(2^{L}n^{2.69}). Our techniques lead to further improvements for classical algorithms as well, reducing the classical complexity to O(2^{0.96L}n^{2.69}), which gives a sublinear dependency on 2^L. The above two algorithms are the first quantum algorithms that perform better than the $\tilde O(n^{5/2})$-time straightforward quantum algorithm based on quantum search for matrix multiplication over these semirings. We also consider the Boolean semiring, and construct a quantum algorithm computing the product of two n x n Boolean matrices that outperforms the best known classical algorithms for sparse matrices. For instance, if the input matrices have O(n^{1.686...}) non-zero entries, then our algorithm has time complexity O(n^{2.277}), while the best classical algorithm has complexity O(n^{2.373}).Comment: 19 page

Deep Galaxy survey at 6.75 micron with the ISO satellite

Deep 6.75um mid-IR ISOCAM observations were obtained of the Canada-France Redshift Survey (CFRS) 1415+52 field with the Infrared Space Observatory. The identification of the sources with optical counterparts is described in detail, and a classification scheme is devised which depends on the S/N of the detection and the inverse probability of chance coincidence. 83% of the 54 ISOCAM sources are identified with Iab<23.5 counterparts. The (I-K)ab colors, radio properties, spectrophotometric properties and frequency of nuclear activity of these counterparts differ on average from those of typical CFRS galaxies. CFRS spectra are available for 21 of the sources which have Iab <= 22.5 (including 7 stars). Most of the strongest sources are stars or AGN. Among the non--stellar counterparts with spectra, 40% are AGNs, and 53% are galaxies that display star formation activity and/or significant contributions of A stars. The ISOCAM sources also display an IR excess, even when compared with heavily-reddened local starburst galaxies. An upper limit of 30% of extragalactic ISO sources could be at z>1 of the 44 S6.75um > 150uJy sources which are non-stellar (7 "spectroscopic" and 3 "photometric" stars excluded)Comment: 13 pages, 12 figures. Accepted for publication in A

Liveness-Driven Random Program Generation

Randomly generated programs are popular for testing compilers and program analysis tools, with hundreds of bugs in real-world C compilers found by random testing. However, existing random program generators may generate large amounts of dead code (computations whose result is never used). This leaves relatively little code to exercise a target compiler's more complex optimizations. To address this shortcoming, we introduce liveness-driven random program generation. In this approach the random program is constructed bottom-up, guided by a simultaneous structural data-flow analysis to ensure that the generator never generates dead code. The algorithm is implemented as a plugin for the Frama-C framework. We evaluate it in comparison to Csmith, the standard random C program generator. Our tool generates programs that compile to more machine code with a more complex instruction mix.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

Sensitivity Analysis and Parameter Estimation for Distributed Hydrological Modeling: Potential of Variational Methods

Variational methods are widely used for the analysis and control of computationally intensive spatially distributed systems. In particular, the adjoint state method enables a very efficient calculation of the derivatives of an objective function (response function to be analysed or cost function to be optimised) with respect to model inputs. In this contribution, it is shown that the potential of variational methods for distributed catchment scale hydrology should be considered. A distributed flash flood model, coupling kinematic wave overland flow and Green Ampt infiltration, is applied to a small catchment of the Thor´e basin and used as a relatively simple (synthetic observations) but didactic application case. It is shown that forward and adjoint sensitivity analysis provide a local but extensive insight on the relation between the assigned model parameters and the simulated hydrological response. Spatially distributed parameter sensitivities can be obtained for a very modest calculation effort (6 times the computing time of a single model run) and the singular value decomposition (SVD) of the Jacobian matrix provides an interesting perspective for the analysis of the rainfall-runoff relation. For the estimation of model parameters, adjoint-based derivatives were found exceedingly efficient in driving a bound-constrained quasi-Newton algorithm. The reference parameter set is retrieved independently from the optimization initial condition when the very common dimension reduction strategy (i.e. scalar multipliers) is adopted. Furthermore, the sensitivity analysis results suggest that most of the variability in this high-dimensional parameter space can be captured with a few orthogonal directions. A parametrization based on the SVD leading singular vectors was found very promising but should be combined with another regularization strategy in order to prevent overfitting.JRC.G.9-Econometrics and applied statistic