HMM filtering and parameter estimation of an electricity spot price model

In this paper we develop a model for electricity spot price dynamics. The spot price is assumed to follow an exponential Ornstein-Uhlenbeck (OU) process with an added compound Poisson process, therefore the model allows for mean-reversion and possible jumps. A sinusoidal factor is also introduced to capture the seasonality component of prices. The mean-reverting level, speed of adjustment and volatility of the OU process as well as the mean and variance of the normally distributed jump sizes of the compound Poisson process are all modulated by a hidden Markov chain in discrete time. The parameters are able to switch between different economic regimes representing various levels of supply and demand. Through the application of reference probability technique, adaptive filters are derived, which in turn, provide optimal estimates for the state of the Markov chain and related quantities of the observation process. The EM algorithm is applied to find optimal estimates of the model parameters in terms of the recursive filters. Since the parameters are updated everytime a new information is available, the model is self-calibrating. We implement the model on a deseasonalized series of daily spot electricity prices from the Nordic exchange Nord Pool. On the basis of one-step ahead forecasts, we found that the model is able to capture the stylised features of Nord Pool spot prices

Filtering and forecasting commodity futures prices under an HMM framework

We propose a model for the evolution of arbitrage-free futures prices under a regime-switching framework. The estimation of model parameters is carried out using the hidden Markov filtering algorithms. Comprehensive numerical experiments on real financial market data are provided to illustrate the effectiveness of our algorithm. In particular, the model is calibrated with data from heating oil futures and its forecasting performance as well as statistical validity is investigated. The proposed model is parsimonious, self-calibrating and can be very useful in predicting futures prices. © 2013 Elsevier B.V

A partially linearized sigma point filter for latent state estimation in nonlinear time series models

A new technique for the latent state estimation of a wide class of nonlinear time series models is proposed. In particular, we develop a partially linearized sigma point filter in which random samples of possible state values are generated at the prediction step using an exact moment matching algorithm and then a linear programming-based procedure is used in the update step of the state estimation. The effectiveness of the new ¯ltering procedure is assessed via a simulation example that deals with a highly nonlinear, multivariate time series representing an interest rate process

Filtering of an HMM-based multivariate Ornstein-Uhlenbeck model with application to forecasting market liquidity

Non UBCUnreviewedAuthor affiliation: University of Western Ontario (Canada)Facult

A unified approach to explicit bond price solutions under a time-dependent affine term structure modelling framework

The richness and simplicity in the econometric specification of interest rate dynamics are the main motivations why affine term structure models (ATSMs) continue to be popular nowadays. Analytic solutions for bond prices are also available for some cases of these models. With explicit bond price formulae, the estimation of parameters using market data can, in principle, be carried out. In addition, with the appropriate choice of functional forms for the drift and volatility components, certain desirable features of interest rate behaviours (e.g., mean reversion, positive rates, etc.) can be captured. The desirable properties of the family of ATSMs also include the capacity to specify the distribution of the rates, their suitability for Monte Carlo simulation, and the fact that interest rate derivatives are computable from the bond prices and interest rate dynamics in a straightforward manner. It is therefore not surprising that the characterization of ATSMs has been the subject of many previous investigations in interest rate theory

An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions

We propose a new method to calibrate the Vasicek and Cox--Ingersoll--Ross interest rate models from bond prices. We define an appropriate generating function and derive recursive relations between the derivatives of the generating function and the bond prices. The parameters of the Vasicek and CIR models are then obtained by solving a system of linearly independent equations arising from the recursive relations. We include numerical results that show the method\u27s accuracy when bond prices generated from the exact formulas are used

A time-varying Markov chain model of term structure

This paper provides the term structure characterization of a Markov interest rate model when the Markov chain is time dependent.Markov chain Term structure modeling Fundamental transition matrix

A computing platform for pairs-trading online implementation via a blended Kalman-HMM filtering approach

Abstract This paper addresses the problem of designing an efficient platform for pairs-trading implementation in real time. Capturing the stylised features of a spread process, i.e., the evolution of the differential between the returns from a pair of stocks, exhibiting a heavy-tailed mean-reverting process is also dealt with. Likewise, the optimal recovery of time-varying parameters in a return-spread model is tackled. It is important to solve such issues in an integrated manner to carry out the execution of trading strategies in a dynamic market environment. The Kalman and hidden Markov model (HMM) multi-regime dynamic filtering approaches are fused together to provide a powerful method for pairs-trading actualisation. Practitioners’ considerations are taken into account in the way the new filtering method is automated. The synthesis of the HMM’s expectation–maximisation algorithm and Kalman filtering procedure gives rise to a set of self-updating optimal parameter estimates. The method put forward in this paper is a hybridisation of signal-processing algorithms. It highlights the critical role and beneficial utility of data fusion methods. Its appropriateness and novelty support the advancements of accurate predictive analytics involving big financial data sets. The algorithm’s performance is tested on historical return spread between Coca-Cola and Pepsi Inc.’s equities. Through a back-testing trade, a hypothetical trader might earn a non-zero profit under the assumption of no transaction costs and bid-ask spreads. The method’s success is illustrated by a trading simulation. The findings from this work show that there is high potential to gain when the transaction fees are low, and an investor is able to benefit from the proposed interplay of the two filtering methods