"Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student's t-Distribution Models"

Bayesian analysis of a stochastic volatility model with a generalized hyperbolic (GH) skew Student's t-error distribution is described where we first consider an asymmetric heavy-tailed error and leverage effects. An efficient Markov chain Monte Carlo estimation method is described that exploits a normal variance-mean mixture representation of the error distribution with an inverse gamma distribution as the mixing distribution. The proposed method is illustrated using simulated data, daily S&P500 and TOPIX stock returns. The models for stock returns are compared based on the marginal likelihood in the empirical study. There is strong evidence in the stock returns high leverage and an asymmetric heavy-tailed distribution. Furthermore, a prior sensitivity analysis is conducted whether the results obtained are robust with respect to the choice of the priors.

Stochastic Volatility Model with Leverage and Asymmetrically Heavy-tailed Error Using GH Skew Student's t-distribution

Bayesian analysis of a stochastic volatility model with a generalized hyperbolic (GH) skew Student's t-error distribution is described where we first consider an asymmetric heavy-tailness as well as leverage effects. An efficient Markov chain Monte Carlo estimation method is described exploiting a normal variance-mean mixture representation of the error distribution with an inverse gamma distribution as a mixing distribution. The proposed method is illustrated using simulated data, daily TOPIX and S&P500 stock returns. The model comparison for stock returns is conducted based on the marginal likelihood in the empirical study. The strong evidence of the leverage and asymmetric heavy-tailness is found in the stock returns. Further, the prior sensitivity analysis is conducted to investigate whether obtained results are robust with respect to the choice of the priors.generalized hyperbolic skew Student's t-distribution, Markov chain Monte Carlo, Mixing distribution, State space model, Stochastic volatility, Stock returns

"Leverage, heavy-tails and correlated jumps in stochastic volatility models"

This paper proposes the efficient and fast Markov chain Monte Carlo estimation methods for the stochastic volatility model with leverage effects, heavy-tailed errors and jump components, and for the stochastic volatility model with correlated jumps. We illustrate our method using simulated data and analyze daily stock returns data on S&P500 index and TOPIX. Model comparisons are conducted based on the marginal likelihood for various SV models including the superposition model.

"Stochastic Volatility with Leverage: Fast Likelihood Inference"

Kim, Shephard, and Chib (1998) provided a Bayesian analysis of stochastic volatility models based on a fast and reliable Markov chain Monte Carlo (MCMC) algorithm. Their method ruled out the leverage effect, which is known to be important in applications. Despite this, their basic method has been extensively used in the financial economics literature and more recently in macroeconometrics. In this paper we show how the basic approach can be extended in a novel way to stochastic volatility models with leverage without altering the essence of the original approach. Several illustrative examples are provided.

SLD Fisher information for kinetic uncertainty relations

We investigate a symmetric logarithmic derivative (SLD) Fisher information for kinetic uncertainty relations (KURs) of open quantum systems described by the GKSL quantum master equation with and without the detailed balance condition. In a quantum kinetic uncertainty relation derived by Vu and Saito [Phys. Rev. Lett. 128, 140602 (2022)], the Fisher information of probability of quantum trajectory with a time-rescaling parameter plays an essential role. This Fisher information is upper bounded by the SLD Fisher information. For a finite time and arbitrary initial state, we derive a concise expression of the SLD Fisher information, which is a double time integral and can be calculated by solving coupled first-order differential equations. We also derive a simple lower bound of the Fisher information of quantum trajectory. We point out that the SLD Fisher information also appears in the speed limit based on the Mandelstam-Tamm relation by Hasegawa [arXiv:2203.12421v4]. When the jump operators connect eigenstates of the system Hamiltonian, we show that the Bures angle in the interaction picture is upper bounded by the square root of the dynamical activity at short times, which contrasts with the classical counterpart.Comment: 12 pages, 3 figure

Stochastic volatility with leverage: fast likelihood inference

Kim, Shephard and Chib (1998) provided a Bayesian analysis of stochastic volatility models based on a very fast and reliable Markov chain Monte Carlo (MCMC) algorithm. Their method ruled out the leverage effect, which limited its scope for applications. Despite this, their basic method has been extensively used in financial economics literature and more recently in macroeconometrics. In this paper we show how to overcome the limitation of this analysis so that the essence of the Kim, Shephard and Chib (1998) can be used to deal with the leverage effect, greatly extending the applicability of this method. Several illustrative examples are provided.Leverage effect, Markov chain Monte Carlo, Mixture sampler, Stochastic volatility, Stock returns.

Generalized Extreme Value Distribution with Time-Dependence Using the AR and MA Models in State Space Form

A new state space approach is proposed to model the time- dependence in an extreme value process. The generalized extreme value distribution is extended to incorporate the time-dependence using a state space representation where the state variables either follow an autoregressive (AR) process or a moving average (MA) process with innovations arising from a Gumbel distribution. Using a Bayesian approach, an efficient algorithm is proposed to implement Markov chain Monte Carlo method where we exploit a very accurate approximation of the Gumbel distribution by a ten-component mixture of normal distributions. The methodology is illustrated using extreme returns of daily stock data. The model is fitted to a monthly series of minimum returns and the empirical results support strong evidence for time-dependence among the observed minimum returns.Extreme values, Generalized extreme value distribution, Markov chain Monte Carlo, Mixture sampler, State space model, Stock returns

Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student?s t-Distribution

Bayesian analysis of a stochastic volatility model with a generalized hyperbolic (GH) skew Student?s t-error distribution is described where we first consider an asymmetric heavy-tailed error and leverage effects. An efficient Markov chain Monte Carlo estimation method is described that exploits a normal variance-mean mixture representation of the error distribution with an inverse gamma distribution as the mixing distribution. The proposed method is illustrated using simulated data, daily S&P500 and TOPIX stock returns. The models for stock returns are compared based on the marginal likelihood in the empirical study. There is strong evidence in the stock returns high leverage and an asymmetric heavy-tailed distribution. Furthermore, a prior sensitivity analysis is conducted whether the results obtained are robust with respect to the choice of the priors.