Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling

We introduce a class of interest rate models, called the $\alpha$-CIR model, which gives a natural extension of the standard CIR model by adopting the $\alpha$-stable L{\'e}vy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign bond market such as the persistency of low interest rate together with the presence of large jumps at local extent. We emphasize on a general integral representation of the model by using random fields, with which we establish the link to the CBI processes and the affine models. Finally we analyze the jump behaviors and in particular the large jumps, and we provide numerical illustrations

Wiener Chaos and the Cox-Ingersoll-Ross model

In this we paper we recast the Cox--Ingersoll--Ross model of interest rates into the chaotic representation recently introduced by Hughston and Rafailidis. Beginning with the ``squared Gaussian representation'' of the CIR model, we find a simple expression for the fundamental random variable X. By use of techniques from the theory of infinite dimensional Gaussian integration, we derive an explicit formula for the n-th term of the Wiener chaos expansion of the CIR model, for n=0,1,2,.... We then derive a new expression for the price of a zero coupon bond which reveals a connection between Gaussian measures and Ricatti differential equations.Comment: 27 page

Bond markets where prices are driven by a general marked point process

We investigate the term structure for the case when interest rates are allowed to be driven by a general marked point process as well as by a Wiener process. Developing a theory which allows for measure-valued trading portfolios we study existence and uniqueness of a martingale measure, as well as completeness of the bond market. We also give sufficient conditions for the existence of an affine term structure. Developing the appropriate forward measures we give formulas for interest rate derivatives.Term structure of interest rates; arbitrage; bond markets; interest rates; martingales; jump processes; completeness; affine term structure

Cosmological parameter constraints for Horndeski scalar-tensor gravity

We present new cosmological parameter constraints for general Horndeski scalar-tensor theories, using CMB, redshift space distortion, matter power spectrum and BAO measurements from the Planck, SDSS/BOSS and 6dF surveys. We focus on theories with cosmological gravitational waves propagating at the speed of light, $c_{\rm GW} = c$, implementing and discussing several previously unaccounted for aspects in the constraint derivation for such theories, that qualitatively affect the resulting constraints. In order to ensure our conclusions are robust, we compare results for three different parametrisations of the free functions in Horndeski scalar-tensor theories, identifying several parametrisation-independent features of the constraints. We also consider models, where $c_{\rm GW} \neq c$ in cosmological settings (still allowed after GW170817 for frequency-dependent $c_{\rm GW}$) and show how this affects cosmological parameter constraints.Comment: 30 pages, 9 figures, 3 table

Simulating the Anisotropic Clustering of Luminous Red Galaxies with Subhalos: A Direct Confrontation with Observation and Cosmological Implications

We model the apparent clustering anisotropy of Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey using subhalos identified in cosmological $N$-body simulations. We first conduct a Markov-chain Monte Carlo analysis on the parameters characterizing subhalos hosting LRGs assuming a specific $\Lambda$CDM cosmology on which we run the simulations. We show that simple models with central and satellite subhalos can explain the observed multipole moments of the power spectrum up to hexadecapole on large scales ($k\lesssim0.3~h\mathrm{Mpc}^{-1}$). A satellite fraction of $20$ to $30$ per cent is favored weakly depending on the detail of the model. The fraction is shown to be robust when we adopt a more refined model based on the halo occupation number from the literature. We then vary cosmological parameters controlling the anisotropy in redshift-space effectively by deforming the simulation box (the Alcock-Paczynski effect) and changing the amplitude of the velocities (the redshift-space distortions). We demonstrate that we can constrain the geometry of the universe, the structure growth rate, and the parameters characterizing LRGs simultaneously. This is a step toward cosmological analysis with realistic bias description beyond empirical bias functions with nuisance parameters.Comment: 18 pages, 21 figures. HOD analysis added. Accepted for publication in MNRA