An empirical application of stochastic volatility models

Mahieu, Ronald; Schotman, Peter C.

doi:10.1002/(sici)1099-1255(199807/08)13:4<333::aid-jae479>3.0.co;2-i

Cited by 76 publications

(59 citation statements)

References 31 publications

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“…In this paper, we use the MCMC method of Kim et al (1998) for estimating the parameters (l, s v ) and filtering the unobserved volatility {V t } T t=1 . 7 Given the estimates of (l, s v ) and {V t } T t=1 , we construct multi-step forecasts of the conditional volatility by the recursion , where (see also Mahieu and Schotman, 1998).…”

Section: Stochastic Volatility Modelsmentioning

confidence: 99%

Forecasting volatility

Gospodinov

and

Jiang

2006

Journal of Forecasting

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In this paper, we investigate the time series properties of S&P 100 volatility and the forecasting performance of different volatility models. We consider several nonparametric and parametric volatility measures, such as implied, realized and model-based volatility, and show that these volatility processes exhibit an extremely slow mean-reverting behavior and possible long memory. For this reason, we explicitly model the near-unit root behavior of volatility and construct median unbiased forecasts by approximating the finite-sample forecast distribution using bootstrap methods. Furthermore, we produce prediction intervals for the next-period implied volatility that provide important information about the uncertainty surrounding the point forecasts. Finally, we apply intercept corrections to forecasts from misspecified models which dramatically improve the accuracy of the volatility forecasts.

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Section: Stochastic Volatility Modelsmentioning

confidence: 99%

Forecasting volatility

Gospodinov

and

Jiang

2006

Journal of Forecasting

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“…It is also an important model because of its significance in financial applications where it has been used to understand timevarying volatility in high frequency asset returns. Kim, Shephard, and Chib (1998) developed an approach for fitting and comparing the SV model that has been extensively employed (for example, Mahieu and Schotman (1998), Primiceri (2005) and Stroud, Muller, and Polson (2003)). …”

Section: Introductionmentioning

confidence: 99%

Stochastic volatility with leverage: Fast and efficient likelihood inference

Omori

Chib

Shephard

et al. 2007

Journal of Econometrics

390

374

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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.

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“…Hull and White [1] assume constant interest rate and stochastic volatility. The Hull and White formula is used by Mahieu and Schotman [2] in a discrete time univariate stochastic volatility model. Merton [3], Turnbull and Milne [4] consider the cases with constant asset return volatility but stochastic interest rates.…”

Section: A Pajormentioning

confidence: 99%

Bayesian Forecasting of the Discounted Payoff of Options on WIG20 Index in Discrete-Time SV Models

Pajor

2008

Acta Phys. Pol. A

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In this paper the bivariate stochastic volatility models (with stochastic volatility and stochastic interest rate) and the univariate fat-tailed and correlated stochastic volatility model (with stochastic volatility and constant interest rate) are used in the Bayesian forecasting of the payoff of European call options. The basic instrument is the WIG20 index. The predictive distribution of the discounted payoff is induced by the predictive distribution of the growth rate of the WIG20 index and the WIBOR1m interest rate. The Bayesian inference about the volatilities and the predictive distribution of the discounted payoff function is based on the joint posterior distribution of the latent variables, the parameters, and the predictive distribution of future observations, which we simulate via Markov chain Monte Carlo methods (the Metropolis-Hastings algorithm is used within the Gibbs sampler). The results show that allowing interest rate to be stochastic does not significantly improve forecasting performance of the discounted payoff. The predictive distributions of the discounted payoff are characterised by huge dispersion and thick tails, thus uncertainty about the future value of the payoff was ex-ante very big.

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An empirical application of stochastic volatility models

Cited by 76 publications

References 31 publications

Forecasting volatility

Forecasting volatility

Stochastic volatility with leverage: Fast and efficient likelihood inference

Bayesian Forecasting of the Discounted Payoff of Options on WIG20 Index in Discrete-Time SV Models

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