Abstract. That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of Poisson-Gaussian models of the Fed Funds rate to capture surprise effects, and show that these models offer a good statistical description of short rate behavior, and are useful in understanding many empirical phenomena. Estimators are used based on analytical derivations of the characteristic functions and moments of jump-diffusion stochastic processes for a range of jump distributions, and are extended to discrete-time models. Jump (Poisson) processes capture empirical features of the data which would not be captured by Gaussian models, and there is strong evidence that existing models would be well-enhanced by jump and ARCH-type processes. The analytical and empirical methods in the paper support many applications, such as testing for Fed intervention effects, which are shown to be an important source of surprise jumps in interest rates. The jump model is shown to mitigate the non-linearity of interest rate drifts, so prevalent in pure-diffusion models. Day-of-week effects are modelled explicitly, and the jump model provides evidence of bond market overreaction, rejecting the martingale hypothesis for interest rates. Jump models mixed with Markov switching processes predicate that conditioning on regime is important in determining short rate behavior.

Abstract. In most neural systems, neurons communicate via sequences of action potentials. Contemporary models assume that the action potentials ’ times of occurrence rather than their waveforms convey information. The mathematical tool for describing sequences of events occurring in time and/or space is the theory of point processes. Using this theory, we show that neural discharge patterns convey time-varying information intermingled with the neuron’s response characteristics. We review the basic techniques for analyzing single-neuron discharge patterns and describe what they reveal about the underlying point process model. By applying information theory and estimation theory to point processes, we describe the fundamental limits on how well information can be represented by and extracted from neural discharges. We illustrate applying these results by considering recordings from the lower auditory pathway.

We propose a reduced-form model where jumps-to-default are priced because they generate a market-wide jump in credit spreads. While this framework is consistent with a counterparty risk interpretation (e.g., Jarrow and Yu (2001)), it is most naturally interpreted as an updating of beliefs due to an unexpected event. Simple analytic solutions are obtained for the prices of risky debt regardless of the number of firms that share in the contagious response. As a special case, we show that the contagious response can be induced via a liquidity-shock, with no impact on actual default intensities. Empirically, we find that credit events of large firms generate a market wide increase in credit spreads and a significant ‘flight-to-quality ’ response in the Treasury market. A calibration argument suggests that the premium associated with jump-to-default risk for a typical investment grade firm has an upper bound of a few basis points per year, but that the risk premium for contagion-risk may be considerably larger.

Abstract not found

Nonlinear filtering is one of the classical areas of stochastic control. From the point of view of practical usefulness, it is important that the filter not be too sensitive to the assumptions made on the initial distribution, the transition function of the underlying signal process and the model for the observation. This is particularly acute if the filter is of interest over a very long or potentially infinite time interval. Then the effects of small errors in the model which is used to construct the filter might accumulate to make the output useless for large time. The problem of asymptotic sensitivity to the initial condition has been treated in several papers. We are concerned with this as well as with the sensitivity to the signal model, uniformly over the infinite time interval. It is conceivable that the effects of even small errors in the model will accumulate so that the filter will eventually be useless. The robustness is shown for three classes of problems. For the first tw...

If jumps (possibly to default) in yields of individual corporate bonds are priced, then there must be a market-wide response at the jump-event. Casual observation suggests that the jump in spreads of an individual rm can generate a change in the perception of risk inherent inthe bonds of other rms, even in the absence of direct counterparty risk. Below, we propose a general reduced-form model which captures this notion of contagion. In contrast to existing counterparty risk models (e.g., Jarrow and Yu (2001)), our framework provides simple analytic solutions for the credit spreads on risky debt even when the cross-dependence involves an arbitrarily large number of rms. Furthermore, our framework can be used to capture contagion within a `structural framework ' by generalizing the model of Du e and Lando (2001) so that the default of one rm generates revision in the beliefs about the `quality of accounting information ' of other rms. Empirically, we investigate how much of the credit spread can be attributable to the jump risk premium. While we nd that credit spread jumps of large rms do have amarket-wide impact, a calibration exercise suggests that the premium this risk

Abstract. We study the quickest detection problem of a sudden change in the arrival rate of a Poisson process from a known value to an unknown and unobservable value at an unknown and unobservable disorder time. Our objective is to design an alarm time which is adapted to the history of the arrival process and detects the disorder time as soon as possible. In previous solvable versions of the Poisson disorder problem, the arrival rate after the disorder has been assumed a known constant. In reality, however, we may at most have some prior information on the likely values of the new arrival rate before the disorder actually happens, and insufficient estimates of the new rate after the disorder happens. Consequently, we assume in this paper that the new arrival rate after the disorder is a random variable. The detection problem is shown to admit a finite-dimensional Markovian sufficient statis-tic if the new rate has a discrete distribution with finitely-many atoms. Furthermore, the detection problem is cast as a discounted optimal stopping problem with running cost for a finite-dimensional piecewise-deterministic Markov process. This optimal stopping problem is studied in detail in the special case where the new

this paper we present a tree model for defaultable bond prices which can be used for the pricing of credit derivatives. The model is based upon the two-factor Hull-White (1994) model for default-free interest rates, where one of the factors is taken to be the credit spread of the defaultable bond prices. As opposed to the tree model of Jarrow and Turnbull (1992), the dynamics of default-free interest rates and credit spreads in this model can have any desired degree of correlation, and the model can be fitted to any given term structures of default-free and defaultable bond prices, and to the term structures of the respective volatilities. Furthermore the model can accommodate several alternative models of default recovery, including the fractional recovery model of Duffie and Singleton (1994) and recovery in terms of equivalent default-free bonds (see e.g. Lando (1998)). Although based on a Gaussian setup, the approach can easily be extended to non-Gaussian processes that avoid negative interest-rates or credit spreads

Abstract—Following the discovery of a fundamental connection between information measures and estimation measures in Gaussian channels, this paper explores the counterpart of those results in Poisson channels. In the continuous-time setting, the received signal is a doubly stochastic Poisson point process whose rate is equal to the input signal plus a dark current. It is found that, regardless of the statistics of the input, the derivative of the input–output mutual information with respect to the intensity of the additive dark current can be expressed as the expected difference between the logarithm of the input and the logarithm of its noncausal conditional mean estimate. The same holds for the derivative with respect to input scaling, but with the logarithmic function replaced by � �� � �. Similar relationships hold for discrete-time versions of the channel where the outputs are Poisson random variables conditioned on the input symbols. Index Terms—Mutual information, nonlinear filtering, optimal estimation, point process, Poisson process, smoothing. I.

We consider a multiclass closed queueing network model analogous to the open network models of Rybko-Stolyar and Lu-Kumar. The closed network has two single-server stations and a fixed customer population of size n. Customers are routed in cyclic fashion through four distinct classes, two of which are served at each station, and each server uses a preemptive-resume priority discipline. The service time distribution for each customer class is exponential, and attention is focused on the critical case where all four classes have the same mean service time. Letting n approach infinity, we prove a heavy traffic limit theorem that is unconventional in three regards. First, in our heavy traffic scaling of both queue length processes and cumulative idleness processes, time is compressed by a factor of n rather than the factor of n 2 occurring in conventional theory. Second, the spatial scaling applied to some components of the queue length and idleness processes is that associated with the ...