Tore Selland Kleppe

Simulated maximum likelihood estimation of continuous time stochastic volatility models

In this chapter we develop and implement a method for maximum simulated likelihood estimation of the continuous time stochastic volatility model with the constant elasticity of volatility. The approach does not require observations on option prices, nor volatility. To integrate out latent volatility from the joint density of return and volatility, a modified efficient importance sampling technique is used after the continuous time model is approximated using the Euler–Maruyama scheme. The Monte Carlo studies show that the method works well and the empirical applications illustrate usefulness of the method. Empirical results provide strong evidence against the Heston model.

Fitting general stochastic volatility models using Laplace accelerated sequential importance sampling

A methodology for fitting general stochastic volatility (SV) models that are naturally cast in terms of a positive volatility process is developed. Two well known methods for evaluating the likelihood function, sequential importance sampling and Laplace importance sampling, are combined. The statistical properties of the resulting estimator are investigated by simulation for an ensemble of SV models. It is found that the performance is good compared to the efficient importance sampling (EIS) algorithm. Finally, the computational framework, building on automatic differentiation (AD), is outlined. The use of AD makes it easy to implement other SV models with non-Gaussian latent volatility processes.

Efficient importance sampling in mixture frameworks

A flexible importance sampling procedure for the likelihood evaluation of dynamic latent variable models involving mixtures of distributions leading to possibly heavy tailed or multi-modal target densities is provided. The procedure is based upon the efficient importance sampling (EIS) approach and exploits the mixture structure of the model via data augmentation when constructing importance sampling distributions as mixtures of distributions. The proposed mixture EIS procedure is illustrated with ML estimation of a Student-t state space model for realized volatilities. MC simulations are used to characterize the sampling distribution of the ML estimator based upon the mixture EIS approach.

Efficient High-Dimensional Importance Sampling in Mixture Frameworks

This paper provides high-dimensional and flexible importance sampling procedures for the likelihood evaluation of dynamic latent variable models involving finite or infinite mixtures leading to possibly heavy tailed and/or multi-modal target densities. Our approach is based upon the efficient importance sampling (EIS) approach of Richard and Zhang (2007) and exploits the mixture structure of the model when constructing importance sampling distributions as mixture of distributions. The proposed mixture EIS procedures are illustrated with ML estimation of a student-t state space model for realized volatilities and a stochastic volatility model with leverage effects and jumps for asset returns.

On the application of improved symplectic integrators in Hamiltonian Monte Carlo

ABSTRACT We explore the construction of new symplectic numerical integration schemes to be used in Hamiltonian Monte Carlo and study their efficiency. Integration schemes from Blanes et al., and a new scheme are considered as candidates to the commonly used leapfrog method. All integration schemes are tested within the framework of the No-U-Turn sampler (NUTS), both for a logistic regression model and a student t-model. The results show that the leapfrog method is inferior to all the new methods both in terms of asymptotic expected acceptance probability for a model problem and the efficient sample size per computing time for the realistic models.

The Gibbs Sampler with Particle Efficient Importance Sampling for State-Space Models

We consider Particle Gibbs (PG) as a tool for Bayesian analysis of non-linear non-Gaussian state-space models. PG is a Monte Carlo (MC) approximation of the standard Gibbs procedure which uses sequential MC (SMC) importance sampling inside the Gibbs procedure to update the latent and potentially high-dimensional state trajectories. We propose to combine PG with a generic and easily implementable SMC approach known as Particle Efficient Importance Sampling (PEIS). By using SMC importance sampling densities which are closely globally adapted to the targeted density of the states, PEIS can substantially improve the mixing and the efficiency of the PG draws from the posterior of the states and the parameters relative to existing PG implementations. The efficiency gains achieved by PEIS are illustrated in PG applications to a stochastic volatility model for asset returns and a Gaussian nonlinear local level model for interest rates.

Price Dynamics in Biological Production Processes Exposed to Environmental Shocks

This paper demonstrates a mechanism by which environmental shocks in biological production processes can lead to extreme price movements and thus be a contributing factor to short‐term food price volatility. In biological production processes, environmental shocks can lead to a stock‐out when the harvest transitions to a new stock (year class) with a different marginal value. The result in the market is a temporary price spike, or bubble, bounded by the marginal value of the new stock. We highlight this phenomenon in a cohort, or year class, biological production setting. Each year class in the model is a finite “non‐renewable” capital stock, and capital theory is used to solve for the stochastic dynamic competitive equilibrium. The model is parameterized to be representative of the Norwegian salmon aquaculture industry. Results suggest that the model can replicate much of the observed patterns in price, harvest, and capital stock dynamics, including the infrequent occurrence of extremely high prices in the market.

Bandwidth selection in pre-smoothed particle filters

For the purpose of maximum likelihood estimation of static parameters, we apply a kernel smoother to the particles in the standard SIR filter for non-linear state space models with additive Gaussian observation noise. This reduces the Monte Carlo error in the estimates of both the posterior density of the states and the marginal density of the observation at each time point. We correct for variance inflation in the smoother, which together with the use of Gaussian kernels, results in a Gaussian (Kalman) update when the amount of smoothing turns to infinity. We propose and study of a criterion for choosing the optimal bandwidth h in the kernel smoother. Finally, we illustrate our approach using examples from econometrics. Our filter is shown to be highly suited for dynamic models with high signal-to-noise ratio, for which the SIR filter has problems.

Trade with Endogenous Transportation Costs: The Value of LNG Exports

This paper investigates the economic value of trade when prices of transportation services are endogenous to cross-market price spreads. This is relevant for liquefied natural gas (LNG) exports. LNG transportation capacity is limited in the short-run, and long lead-times are involved in extending the transportation infrastructure. We establish empirically that LNG transportation costs have been endogenous to regional gas prices spreads. As such, transportation service providers have been able to capture part of the price spread. We proceed to develop a method to value LNG exports under conditions of endogenous transportation costs and market integration. We use this method to quantify the effect of endogenous transportation costs on the value of LNG exports from the US to Japan. Our analysis shows that when transportation costs are correctly treated as endogenous, the LNG export benefit can drop by as much as 20-50% relative to the case of exogenous cost.

Modified Cholesky Riemann Manifold Hamiltonian Monte Carlo: exploiting sparsity for fast sampling of high-dimensional targets

Riemann manifold Hamiltonian Monte Carlo (RMHMC) has the potential to produce high-quality Markov chain Monte Carlo output even for very challenging target distributions. To this end, a symmetric positive definite scaling matrix for RMHMC is proposed. The scaling matrix is obtained by applying a modified Cholesky factorization to the potentially indefinite negative Hessian of the target log-density. The methodology is able to exploit the sparsity of the Hessian, stemming from conditional independence modeling assumptions, and thus admit fast implementation of RMHMC even for high-dimensional target distributions. Moreover, the methodology can exploit log-concave conditional target densities, often encountered in Bayesian hierarchical models, for faster sampling and more straightforward tuning. The proposed methodology is compared to alternatives for some challenging targets and is illustrated by applying a state-space model to real data.