Sequential Bayesian inference for implicit hidden Markov models and current limitations

Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to estimate the hidden Markov process given the observations and a fixed parameter value. We review some of the recent developments allowing the inclusion of parameter uncertainty as well as model uncertainty. The shortcomings of the currently available methodology are emphasised from an algorithmic complexity perspective. The statistical objects of interest for time series analysis are illustrated on a toy "Lotka-Volterra" model used in population ecology. Some open challenges are discussed regarding the scalability of the reviewed methodology to longer time series, higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages, 10 figure

The processing of non-anticipated information in financial markets: Analyzing the impact of surprises in the employment report

This paper delineates the simultaneous impact of non-anticipated information on mean and variance of the intraday return process by including appropriate variables accounting for the news flow into both the mean and the variance function. This allows us to differentiate between the consistent price reaction to surprising news and the traders’ uncertainty about the precise price impact of this information. Focussing on the US employment report, we find that headline information is almost instantaneously incorporated into T-bond futures prices. Nevertheless, large surprises, and ’bad’ news in particular, create considerable uncertainty. In contrast, if surprises in related headlines cross-validate each other, less room for differences of opinion is left, and hence volatility is decreased.high-frequency data, information processing, macroeconomic announcements, Treasury bond futures, trading process, volatility

Quality Control for Structural Credit Risk Models

Over the last four decades, a large number of structural models have been developed to estimate and price credit risk. The focus of the paper is on a neglected issue pertaining to fundamental shifts in the structural parameters governing default. We propose formal quality control procedures that allow risk managers to monitor fundamental shifts in the structural parameters of credit risk models. The procedures are sequential - hence apply in real time. The basic ingredients are the key processes used in credit risk analysis, such as most prominently the Merton distance to default process as well as financial returns. Moreover, while we propose different monitoring processes, we also show that one particular process is optimal in terms of minimal detection time of a break in the drift process and relates to the Radon-Nikodym derivative for a change of measure.

Stochastic volatility

Given the importance of return volatility on a number of practical financial management decisions, the efforts to provide good real- time estimates and forecasts of current and future volatility have been extensive. The main framework used in this context involves stochastic volatility models. In a broad sense, this model class includes GARCH, but we focus on a narrower set of specifications in which volatility follows its own random process, as is common in models originating within financial economics. The distinguishing feature of these specifications is that volatility, being inherently unobservable and subject to independent random shocks, is not measurable with respect to observable information. In what follows, we refer to these models as genuine stochastic volatility models. Much modern asset pricing theory is built on continuous- time models. The natural concept of volatility within this setting is that of genuine stochastic volatility. For example, stochastic-volatility (jump-) diffusions have provided a useful tool for a wide range of applications, including the pricing of options and other derivatives, the modeling of the term structure of risk-free interest rates, and the pricing of foreign currencies and defaultable bonds. The increased use of intraday transaction data for construction of so-called realized volatility measures provides additional impetus for considering genuine stochastic volatility models. As we demonstrate below, the realized volatility approach is closely associated with the continuous-time stochastic volatility framework of financial economics. There are some unique challenges in dealing with genuine stochastic volatility models. For example, volatility is truly latent and this feature complicates estimation and inference. Further, the presence of an additional state variable - volatility - renders the model less tractable from an analytic perspective. We examine how such challenges have been addressed through development of new estimation methods and imposition of model restrictions allowing for closed-form solutions while remaining consistent with the dominant empirical features of the data.Stochastic analysis