Model Volatilitas ARCH(1) dengan Returns Error Berdistribusi non-central Student-t Studi Kasus: Kurs Beli JPY dan EUR terhadap IDR

Studi ini mengaplikasikan model volatilitas Autoregressive Conditional Heteroscedasticity (ARCH) lag 1 untuk returns kurs beli Japanese Yen (JPY) dan Euro (EUR) terhadap Indonesian Rupiah (IDR) dari Januari 2009 sampai Desember 2014. Distribusi non-central Student-t (NCT) dipilih untuk mengakomodasi flexible skewness dan heavy-tailedness pada returns error. Algoritma Markov Chain Monte Carlo (MCMC) yang efisien dikonstruksi untuk memperbarui nilai-nilai parameter dalam model yang tidak bisa dibangkitkan secara langsung dari distribusi posterior. Berdasarkan 95% interval highest posterior density (HPD), hasil menunjukkan penolakan terhadap distribusi NCT untuk semua data yang diamati. Meskipun begitu, Bayes factor mengindikasikan bukti sangat kuat dalam mendukung penggunaan distribusi NCT daripada distribusi normal dan Student-t. Kata Kunci : kurs beli, MCMC, model ARCH, non-central Student-t, volatilitas return

Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic Volatility Models

Bayesian inference for stochastic volatility models using MCMC methods highly depends on actual parameter values in terms of sampling efficiency. While draws from the posterior utilizing the standard centered parameterization break down when the volatility of volatility parameter in the latent state equation is small, non-centered versions of the model show deficiencies for highly persistent latent variable series. The novel approach of ancillarity-sufficiency interweaving has recently been shown to aid in overcoming these issues for a broad class of multilevel models. In this paper, we demonstrate how such an interweaving strategy can be applied to stochastic volatility models in order to greatly improve sampling efficiency for all parameters and throughout the entire parameter range. Moreover, this method of "combining best of different worlds" allows for inference for parameter constellations that have previously been infeasible to estimate without the need to select a particular parameterization beforehand.Series: Research Report Series / Department of Statistics and Mathematic

Econometric analysis of volatile art markets

A new heteroskedastic hedonic regression model is suggested which takes into account time-varying volatility and is applied to a blue chips art market. A nonparametric local likelihood estimator is proposed, and this is more precise than the often used dummy variables method. The empirical analysis reveals that errors are considerably non-Gaussian, and that a student distribution with time-varying scale and degrees of freedom does well in explaining deviations of prices from their expectation. The art price index is a smooth function of time and has a variability that is comparable to the volatility of stock indices.Volatility, art markets, hedonic regression, semiparametric estimation

The time-varying asymmetry of exchange rate returns : a stochastic volatility - stochastic skewness model

While the time-varying volatility of financial returns has been extensively modelled, most existing stochastic volatility models either assume a constant degree of return shock asymmetry or impose symmetric model innovations. However, accounting for time-varying asymmetry as a measure of crash risk is important for both investors and policy makers. This paper extends a standard stochastic volatility model to allow for time-varying skewness of the return innovations. We estimate the model by extensions of traditional Markov Chain Monte Carlo (MCMC) methods for stochastic volatility models. When applying this model to the returns of four major exchange rates, skewness is found to vary substantially over time. In addition, stochastic skewness can help to improve forecasts of risk measures. Finally, the results support a potential link between carry trading and crash risk

Exploring option pricing and hedging via volatility asymmetry

This paper evaluates the application of two well-known asymmetric stochastic volatility (ASV) models to option price forecasting and dynamic delta hedging. They are specied in discrete time in contrast to the classical stochastic volatility (SV) models used in option pricing. There is some related literature, but little is known about the empirical implications of volatility asymmetry on option pricing. The objectives of this paper are to estimate ASV option pricing models using a Bayesian approach unknown in this type of literature, and to investigate the e ect of volatility asymmetry on option pricing for di erent size equity sectors and periods of volatility. Using the S&P MidCap 400 and S&P 500 European call option quotes, results show that volatility asymmetry benets the accuracy of option price forecasting and hedging cost e ectiveness in the large-cap equity sector. However, asymmetric SV models do not improve the option price forecasting and dynamic hedging in the mid-cap equity sector.The second author acknowledges nancial support from Spanish Ministry of Economy and Competitiveness, research projects ECO2015-70331-C2-2-R and ECO2015-65701-P, and FCT grant UID/GES/00315/2013

Score driven asymmetric stochastic volatility models

In this paper we propose a new class of asymmetric stochastic volatility (SV) models, which specifies the volatility as a function of the score of the distribution of returns conditional on volatilities based on the Generalized Autoregressive Score (GAS) model. Different specifications of the log-volatility are obtained by assuming different return error distributions. In particular, we consider three of the most popular distributions, namely, the Normal, Student-t and Generalized Error Distribution and derive the statistical properties of each of the corresponding score driven SV models. We show that some of the parameters cannot be property identified by the moments usually considered as to describe the stylized facts of financial returns, namely, excess kurtosis, autocorrelations of squares and cross-correlations between returns and future squared returns. The parameters of some restricted score driven SV models can be estimated adequately using a MCMC procedure. Finally, the new proposed models are fitted to financial returns and evaluated in terms of their in-sample and out-of-sample performanceFinancial support from the Spanish Ministry of Education and Science, research project ECO2012-32401, is acknowledged. The third author is also grateful for project MTM2010-1732

AN APPLICATION OF THE ECF METHOD AND NUMERICAL INTEGRATION IN ESTIMATION OF THE STOCHASTIC VOLATILITY MODELS

In this paper, the Empirical Characteristic Function (ECF) method is described in parameter estimations of the stochastic volatility (SV) models,  as well as the original thresholds modification (and a generalization) of these models, named the Split-SV model. The estimation procedure is based on minimization of the objective function which represents the double integral with respect to the some weight function $g:\mathbb R^2\rightarrow\mathbb R$. Some typical, exponential classes of the weight functions $g(u_1,u_2)$ are considered, as well as the different types of cubature formulas. Estimation procedures are realized by the original authors' codes written in statistical programming language ``R'', and the performances of the ECF method are examined, by statistical and numerical aspects. The numerical simulation of the obtained estimates is given, also. Finally, the standard SV model, and the Split-SV model as its alternative, are applied for fitting  the empirical data: the daily returns of the exchange rates of GBP and USD per euro, and the efficiency of their fitting is compared

An empirical application of stochastic volatility models to Latin-American stock returns using GH skew student's t-distribution

This paper represents empirical studies of stochastic volatility (SV) models for daily stocks returns data of a set of Latin American countries (Argentina, Brazil, Chile, Mexico and Peru) for the sample period 1996:01-2013:12. We estimate SV models incorporating both leverage effects and skewed heavy-tailed disturbances taking into account the GH Skew Student’s t-distribution using the Bayesian estimation method proposed by Nakajima and Omori (2012). A model comparison between the competing SV models with symmetric Student´s t-disturbances is provided using the log marginal likelihoods in the empirical study. A prior sensitivity analysis is also provided. The results suggest that there are leverage effects in all indices considered but there is not enough evidence for Peru, and skewed heavy-tailed disturbances is confirmed only for Argentina, symmetric heavy-tailed disturbances for Mexico, Brazil and Chile, and symmetric Normal disturbances for Peru. Furthermore, we find that the GH Skew Student s t-disturbance distribution in the SV model is successful in describing the distribution of the daily stock return data for Peru, Argentina and Brazil over the traditional symmetric Student´s t-disturbance distribution.Tesi