54,659 research outputs found
Combining long memory and level shifts in modeling and forecasting the volatility of asset returns
We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons
Combining long memory and level shifts in modeling and forecasting the volatility of asset returns
We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean- and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in high-frequency measures of volatility whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes, and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons
A Collaborative Kalman Filter for Time-Evolving Dyadic Processes
We present the collaborative Kalman filter (CKF), a dynamic model for
collaborative filtering and related factorization models. Using the matrix
factorization approach to collaborative filtering, the CKF accounts for time
evolution by modeling each low-dimensional latent embedding as a
multidimensional Brownian motion. Each observation is a random variable whose
distribution is parameterized by the dot product of the relevant Brownian
motions at that moment in time. This is naturally interpreted as a Kalman
filter with multiple interacting state space vectors. We also present a method
for learning a dynamically evolving drift parameter for each location by
modeling it as a geometric Brownian motion. We handle posterior intractability
via a mean-field variational approximation, which also preserves tractability
for downstream calculations in a manner similar to the Kalman filter. We
evaluate the model on several large datasets, providing quantitative evaluation
on the 10 million Movielens and 100 million Netflix datasets and qualitative
evaluation on a set of 39 million stock returns divided across roughly 6,500
companies from the years 1962-2014.Comment: Appeared at 2014 IEEE International Conference on Data Mining (ICDM
A flexible approach to parametric inference in nonlinear time series models
Many structural break and regime-switching models have been used with macroeconomic and ā¦nancial data. In this paper, we develop an extremely flexible parametric model which can accommodate virtually any of these speciā¦cations and does so in a simple way which allows for straightforward Bayesian inference. The basic idea underlying our model is that it adds two simple concepts to a standard state space framework. These ideas are ordering and distance. By ordering the data in various ways, we can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the state equation variances to depend on the distance between observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). We show how our model will (approximately) nest virtually every popular model in the regime-switching and structural break literatures. Bayesian econometric methods for inference in this model are developed. Because we stay within a state space framework, these methods are relatively straightforward, drawing on the existing literature. We use artiā¦cial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth
USLV: Unspanned Stochastic Local Volatility Model
We propose a new framework for modeling stochastic local volatility, with
potential applications to modeling derivatives on interest rates, commodities,
credit, equity, FX etc., as well as hybrid derivatives. Our model extends the
linearity-generating unspanned volatility term structure model by Carr et al.
(2011) by adding a local volatility layer to it. We outline efficient numerical
schemes for pricing derivatives in this framework for a particular four-factor
specification (two "curve" factors plus two "volatility" factors). We show that
the dynamics of such a system can be approximated by a Markov chain on a
two-dimensional space (Z_t,Y_t), where coordinates Z_t and Y_t are given by
direct (Kroneker) products of values of pairs of curve and volatility factors,
respectively. The resulting Markov chain dynamics on such partly "folded" state
space enables fast pricing by the standard backward induction. Using a
nonparametric specification of the Markov chain generator, one can accurately
match arbitrary sets of vanilla option quotes with different strikes and
maturities. Furthermore, we consider an alternative formulation of the model in
terms of an implied time change process. The latter is specified
nonparametrically, again enabling accurate calibration to arbitrary sets of
vanilla option quotes.Comment: Sections 3.2 and 3.3 are re-written, 3 figures adde
A flexible approach to parametric inference in nonlinear and time varying time series models
Many structural break and regime-switching models have been used with macroeconomic and ā¦nancial data. In this paper, we develop an extremely flexible parametric model which can accommodate virtually any of these speciā¦cations and does so in a simple way which allows for straightforward Bayesian inference. The basic idea underlying our model is that it adds two simple concepts to a standard state space framework. These ideas are ordering and distance. By ordering the data in various ways, we can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the state equation variances to depend on the distance between observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). We show how our model will (approximately) nest virtually every popular model in the regime-switching and structural break literatures. Bayesian econometric methods for inference in this model are developed. Because we stay within a state space framework, these methods are relatively straightforward, drawing on the existing literature. We use artiā¦cial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth
Ambiguous volatility and asset pricing in continuous time
This paper formulates a model of utility for a continuous time framework that
captures the decision-maker's concern with ambiguity about both volatility and
drift. Corresponding extensions of some basic results in asset pricing theory
are presented. First, we derive arbitrage-free pricing rules based on hedging
arguments. Ambiguous volatility implies market incompleteness that rules out
perfect hedging. Consequently, hedging arguments determine prices only up to
intervals. However, sharper predictions can be obtained by assuming preference
maximization and equilibrium. Thus we apply the model of utility to a
representative agent endowment economy to study equilibrium asset returns. A
version of the C-CAPM is derived and the effects of ambiguous volatility are
described
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