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Jeudi 25 Février :
16H15 : Genaro SUCCARAT (bi Norwegian Business School)
"Models of Financial Return with Time-Varying Zero Probability"

17H30 : Jihyun KIM (Toulouse School of Economics)
"Mean Reversion and Stationarity : A New Perspective from the Asymptotics of Diffusion Models"

16H15 : Genaro SUCARRAT (bi Norwegian Business School)


The probability of an observed financial return being equal to zero is not necessarily zero. This can be due to price discreteness or rounding error, liquidity issues (e.g. low trading volume), market closures, data issues (e.g. data imputation due to missing values), characteristics specific to the market, and so on. Moreover, the zero probability may change and depend on market conditions. In standard models of return volatility, however, e.g. ARCH, SV and continuous time models, the zero probability is zero, constant or both. We propose a new class of models that allows for a time-varying zero probability, and which can be combined with standard models of return volatility: They are nested and obtained as special cases when the zero probability is constant and equal to zero. Another attraction is that the return properties of the new class (e.g. volatility, skewness, kurtosis, Value-at-Risk, Expected Shortfall) are obtained as functions of the underlying volatility model. The new class allows for autoregressive conditional dynamics in both the zero probability and volatility specifications, and for additional covariates. Simulations show parameter and risk estimates are biased if zeros are not appropriately handled, and an application illustrates that risk-estimates can be substantially biased in practice if the time-varying zero probability is not accommodated.

17H30 : Jihyun KIM (Toulouse School of Economics)


This paper analyzes the mean reversion and unit root properties of general diffusion models and their discrete samples. In particular, we find that the Dickey-Fuller unit root test applied to discrete samples from a diffusion model becomes a test of no mean reversion rather than a unit root, or more generally, nonstationarity in the underlying diffusion. The unit root test has a well defined limit distribution if and only if the underlying diffusion has no mean reversion, and diverges to minus infinity in probability if and only if the underlying diffusion has mean reversion. It is shown, on the other hand, that diffusions are mean-reverting as long as their drift terms play the dominant role, and therefore, nonstationary diffusions may well have mean reversion.

JEL Classifcation: C12, C22, C58

Keywords and phrases: mean reversion, stationarity and nonstationarity, diffusion model, unit root test, stationarity test.