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Ardia, David

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Ardia, David
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https://libra.unine.ch/handle/123456789/832

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  • Publication
    Accès libre
    A Note on Jointly Backtesting Models for Multiple Assets and Horizons
    (2016-5)
    Ardia, David 
    ;
    Guerrouaz, Anas
    ;
    Hoogerheide, Lennart
    We propose a simulation-based methodology, which allows us to test the performance of multi-level and/or multi-horizon value-at-risk forecasts.
  • Publication
    Accès libre
    Return and risk of pairs trading using a simulation-based Bayesian procedure for predicting stable ratios of stock prices
    (2016)
    Ardia, David 
    ;
    Gatarek, Lukasz T.
    ;
    Hoogerheide, Lennart
    ;
    Van Dijk, Herman
    We investigate the direct connection between the uncertainty related to estimated stable ratios of stock prices and risk and return of two pairs trading strategies: a conditional statistical arbitrage method and an implicit arbitrage one. A simulation-based Bayesian procedure is introduced for predicting stable stock price ratios, defined in a cointegration model. Using this class of models and the proposed inferential technique, we are able to connect estimation and model uncertainty with risk and return of stock trading. In terms of methodology, we show the effect that using an encompassing prior, which is shown to be equivalent to a Jeffreys’ prior, has under an orthogonal normalization for the selection of pairs of cointegrated stock prices and further, its effect for the estimation and prediction of the spread between cointegrated stock prices. We distinguish between models with a normal and Student t distribution since the latter typically provides a better description of daily changes of prices on financial markets. As an empirical application, stocks are used that are ingredients of the Dow Jones Composite Average index. The results show that normalization has little effect on the selection of pairs of cointegrated stocks on the basis of Bayes factors. However, the results stress the importance of the orthogonal normalization for the estimation and prediction of the spread—the deviation from the equilibrium relationship—which leads to better results in terms of profit per capital engagement and risk than using a standard linear normalization.
  • Publication
    Accès libre
    Worldwide equity risk prediction
    (2014)
    Ardia, David 
    ;
    Hoogerheide, Lennart
    Various GARCH models are applied to daily returns of more than 1200 constituents of major stock indices worldwide. The value-at-risk forecast performance is investigated for different markets and industries, considering the test for correct conditional coverage using the false discovery rate (FDR) methodology. For most of the markets and industries we find the same two conclusions. First, an asymmetric GARCH specification is essential when forecasting the 95% value-at-risk. Second, for both the 95% and 99% value-at-risk it is crucial that the innovations’ distribution is fat-tailed (e.g., Student-t or – even better – a non-parametric kernel density estimate).
  • Publication
    Accès libre
    Cross-sectional distribution of GARCH coefficients across S&P 500 constituents
    (2013)
    Ardia, David 
    ;
    Hoogerheide, Lennart
    We investigate the time-variation of the cross-sectional distribution of asymmetric GARCH model parameters over the S&P 500 constituents for the period 2000-2012. We find the following results. First, the unconditional variances in the GARCH model obviously show major time-variation, with a high level after the dot-com bubble and the highest peak in the latest financial crisis. Second, in these more volatile periods it is especially the persistence of deviations of volatility from its unconditional mean that increases. Particularly in the latest financial crisis, the estimated models tend to Integrated GARCH models, which can cope with an abrupt regime-shift from low to high volatility levels. Third, the leverage effect tends to be somewhat higher in periods with higher volatility. Our findings are mostly robust across sectors, except for the technology sector, which exhibits a substantially higher volatility after the dot-com bubble. Further, the financial sector shows the highest volatility during the latest financial crisis. Finally, in an analysis of different market capitalizations, we find that small cap stocks have a higher volatility than large cap stocks where the discrepancy between small and large cap stocks increased during the latest financial crisis. Small cap stocks also have a larger conditional kurtosis and a higher leverage effect than mid cap and large cap stocks.
  • Publication
    Accès libre
    Density prediction of stock index returns using GARCH models: Frequentist or Bayesian estimation?
    (2012)
    Hoogerheide, Lennart
    ;
    Ardia, David 
    ;
    Corré, Nienke
    Using GARCH models for density prediction of stock index returns, a comparison is provided between frequentist and Bayesian estimation. No significant difference is found between qualities of whole density forecasts, whereas the Bayesian approach exhibits significantly better left-tail forecast accuracy.
  • Publication
    Accès libre
    A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihoods
    (2012)
    Ardia, David 
    ;
    Basturk, Nalan
    ;
    Hoogerheide, Lennart
    ;
    Van Dijk, Herman
    Strategic choices for efficient and accurate evaluation of marginal likelihoods by means of Monte Carlo simulation methods are studied for the case of highly non-elliptical posterior distributions. A comparative analysis is presented of possible advantages and limitations of different simulation techniques; of possible choices of candidate distributions and choices of target or warped target distributions; and finally of numerical standard errors. The importance of a robust and flexible estimation strategy is demonstrated where the complete posterior distribution is explored. Given an appropriately yet quickly tuned adaptive candidate, straightforward importance sampling provides a computationally efficient estimator of the marginal likelihood (and a reliable and easily computed corresponding numerical standard error) in the cases investigated, which include a non-linear regression model and a mixture GARCH model. Warping the posterior density can lead to a further gain in efficiency, but it is more important that the posterior kernel be appropriately wrapped by the candidate distribution than that it is warped.
  • Publication
    Accès libre
    Efficient Bayesian estimation and combination of GARCH-type models
    (London: Klaus Bocker, 2010)
    Ardia, David 
    ;
    Hoogerheide, Lennart
    This chapter proposes an up-to-date review of estimation strategies available for the Bayesian inference of GARCH-type models. The emphasis is put on a novel efficient procedure named AdMitIS. The methodology automatically constructs a mixture of Student-t distributions as an approximation to the posterior density of the model parameters. This density is then used in importance sampling for model estimation, model selection and model combination. The procedure is fully automatic which avoids difficult and time consuming tuning of MCMC strategies. The AdMitIS methodology is illustrated with an empirical application to S&P index log-returns where non-nested GARCH-type models are estimated and combined to predict the distribution of next-day ahead log-returns.
  • Publication
    Accès libre
    Bayesian estimation of the GARCH(1,1) model with Student-t innovations in R
    (2010)
    Ardia, David 
    ;
    Hoogerheide, Lennart
    This paper presents the R package bayesGARCH which provides functions for the Bayesian estimation of the parsimonious but effective GARCH(1,1) model with Student-t innovations. The estimation procedure is fully automatic and thus avoids the time-consuming and difficult task of tuning a sampling algorithm. The usage of the package is shown in an empirical application to exchange rate log-returns.
  • Publication
    Accès libre
    Adaptive mixture of Student-t distributions as a flexible distribution for efficient simulation: The R package AdMit
    (2009)
    Ardia, David 
    ;
    Hoogerheide, Lennart
    ;
    Van Dijk, Herman
    This paper presents the R package AdMit which provides flexible functions to approximate a certain target distribution and to efficiently generate a sample of random draws from it, given only a kernel of the target density function. The core algorithm consists of the function AdMit which fits an adaptive mixture of Student-t distributions to the density of interest. Then, importance sampling or the independence chain Metropolis-Hastings algorithm is used to obtain quantities of interest for the target density, using the fitted mixture as the importance or candidate density. The estimation procedure is fully automatic and thus avoids the time-consuming and difficult task of tuning a sampling algorithm. The relevance of the package is shown in two examples. The first aims at illustrating in detail the use of the functions provided by the package in a bivariate bimodal distribution. The second shows the relevance of the adaptive mixture procedure through the Bayesian estimation of a mixture of ARCH model fitted to foreign exchange log-returns data. The methodology is compared to standard cases of importance sampling and the Metropolis-Hastings algorithm using a naive candidate and with the Griddy-Gibbs approach.