Drew D. Creal

A Survey of Sequential Monte Carlo Methods for Economics and Finance

This article serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation-based algorithms used to compute the high-dimensional and/or complex integrals that arise regularly in applied work. These methods are becoming increasingly popular in economics and finance; from dynamic stochastic general equilibrium models in macro-economics to option pricing. The objective of this article is to explain the basics of the methodology, provide references to the literature, and cover some of the theoretical results that justify the methods in practice.

A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations

We propose a new class of observation-driven time-varying parameter models for dynamic volatilities and correlations to handle time series from heavy-tailed distributions. The model adopts generalized autoregressive score dynamics to obtain a time-varying covariance matrix of the multivariate Student t distribution. The key novelty of our proposed model concerns the weighting of lagged squared innovations for the estimation of future correlations and volatilities. When we account for heavy tails of distributions, we obtain estimates that are more robust to large innovations. We provide an empirical illustration for a panel of daily equity returns.

Observation Driven Mixed-Measurement Dynamic Factor Models with an Application to Credit Risk

We propose an observation-driven dynamic factor model for mixed-measurement and mixed-frequency panel data. Time series observations may come from a range of families of distributions, be observed at different frequencies, have missing observations, and exhibit common dynamics and cross-sectional dependence due to shared dynamic latent factors. A feature of our model is that the likelihood function is known in closed form. This enables parameter estimation using standard maximum likelihood methods. We adopt the new framework for signal extraction and forecasting of macro, credit, and loss given default risk conditions for U.S. Moodys-rated firms from January 1982 to March 2010.

A General Framework for Observation Driven Time-Varying Parameter Models

We propose a new class of observation driven time series models referred to as Generalized Autoregressive Score (GAS) models. The driving mechanism of the GAS model is the scaled score of the likelihood function. This approach provides a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, the autoregressive conditional duration, the autoregressive conditional intensity, and the single source of error models. In addition, the GAS specification provides a wide range of new observation driven models. Examples include non-linear regression models with time-varying parameters, observation driven analogues of unobserved components time series models, multivariate point process models with time-varying parameters and pooling restrictions, new models for time-varying copula functions, and models for time-varying higher order moments. We study the properties of GAS models and provide several non-trivial examples of their application.

High Dimensional Dynamic Stochastic Copula Models

We build a class of copula models that captures time-varying dependence across large panels of financial assets. Our models nest Gaussian, Student’s t, grouped Student’s t, and generalized hyperbolic copulas with time-varying correlations matrices, as special cases. We introduce time-variation into the densities by writing them as factor models with stochastic loadings. The proposed copula models have flexible dynamics and heavy tails yet remain tractable in high dimensions due to their factor structure. Our Bayesian estimation approach leverages a recent advance in sequential Monte Carlo methods known as particle Gibbs sampling which can draw large blocks of latent variables efficiently and in parallel. We use this framework to model an unbalanced, 200-dimensional panel consisting of credit default swaps and equities for 100 US corporations. Our analysis shows that the grouped Student’s t stochastic copula is preferred over seven competing models.

Analysis of filtering and smoothing algorithms for Lévy-driven stochastic volatility models

Filtering and smoothing algorithms that estimate the integrated variance in Levy-driven stochastic volatility models are analyzed. Particle filters are algorithms designed for nonlinear, non-Gaussian models while the Kalman filter remains the best linear predictor if the model is linear but non-Gaussian. Monte Carlo experiments are performed to compare these algorithms across different specifications of the model including different marginal distributions and degrees of persistence for the instantaneous variance. The use of realized variance as an observed variable in the state space model is also evaluated. Finally, the particle filters ability to identify the timing and size of jumps is assessed relative to popular nonparametric estimators.

Market-Based Credit Ratings

We present a methodology for rating in real-time the creditworthiness of public companies in the U.S. from the prices of traded assets. Our approach uses asset pricing data to impute a term structure of risk neutral survival functions or default probabilities. Firms are then clustered into ratings categories based on their survival functions using a functional clustering algorithm. This allows all public firms whose assets are traded to be directly rated by market participants. For firms whose assets are not traded, we show how they can be indirectly rated by matching them to firms that are traded based on observable characteristics. We also show how the resulting ratings can be used to construct loss distributions for portfolios of bonds. Finally, we compare our ratings to Standard & Poors and find that, over the period 2005 to 2011, our ratings lead theirs for firms that ultimately default.

The Multinational Advantage

Using a confidential dataset, we evaluate whether the degree of foreign operations affects U.S. multinational corporation (MNC) value by comparing actual value to imputed value for these firms. We control for differences in discount rates and expected growth rates across countries and industries through time with benchmark firms matched on these dimensions. This isolates the value effects of organizing otherwise independent activities within a multinational network. Our analyses offer robust evidence of a MNC value premium relative to a benchmark portfolio of independent firms operating in the same country-industry footprint as the MNC.

Testing for Parameter Instability in Competing Modeling Frameworks

We develop a new parameter stability test against the alternative of observation driven generalized autoregressive score dynamics. The new test generalizes the ARCH-LM test of Engle (1982) to settings beyond time-varying volatility and exploits any autocorrelation in the likelihood scores under the alternative. We compare the tests performance with that of alternative tests developed for competing time-varying parameter frameworks, such as structural breaks and observation driven parameter dynamics. The new test has higher and more stable power against alternatives with frequent regime switches or with non-local parameter driven time-variation. For parameter driven time variation close to the null or for infrequent structural changes, the test of Muller and Petalas (2010) performs best overall. We apply all tests empirically to a panel of losses given default over the period 1982--2010 and find significant evidence of parameter variation in the underlying beta distribution.

Bond Risk Premia in Consumption-Based Models

Workhorse Gaussian affine term structure models (ATSMs) attribute time-varying bond risk premia entirely to changing prices of risk, while structural models with recursive preferences credit it completely to stochastic volatility. We reconcile these competing channels by introducing a novel form of external habit into an otherwise standard model with recursive preferences. The new model has an ATSM representation with analytical bond prices making it empirically tractable. We find that time variation in bond term premia is predominantly driven by the price of risk, especially, the price of expected inflation risk that co-moves with expected inflation itself.