58 research outputs found
Multivariate backtests and copulas for risk evaluation
Risk evaluation is a forecast, and its validity must be backtested.
Probability distribution forecasts are used in this work and allow for more
powerful validations compared to point forecasts. Our aim is to use bivariate
copulas in order to characterize the in-sample copulas and to validate
out-of-sample a bivariate forecast. For both set-ups, probability integral
transforms (PIT) and Rosenblatt transforms are used to map the problem into an
independent copula. For this simple copula, statistical tests can be applied to
validate the choice of the in-sample copula or the validity of the bivariate
forecast. The salient results are that a Student copula describes well the
dependencies between financial time series (regardless of the correlation), and
that the bivariate forecasts provided by a risk methodology based on historical
innovations performs correctly out-of-sample. A prerequisite is to remove the
heteroskedasticity in order to have stationary time series, in this work a
long-memory ARCH volatility model is used.Comment: 26 pages, 14 figure
Heterogeneous volatility cascade in financial markets
Using high frequency data, we have studied empirically the change of
volatility, also called volatility derivative, for various time horizons. In
particular, the correlation between the volatility derivative and the
volatility realized in the next time period is a measure of the response
function of the market participants. This correlation shows explicitly the
heterogeneous structure of the market according to the characteristic time
horizons of the differents agents. It reveals a volatility cascade from long to
short time horizons, with a structure different from the one observed in
turbulence. Moreover, we have developed a new ARCH-type model which
incorporates the different groups of agents, with their characteristic memory.
This model reproduces well the empirical response function, and allows us to
quantify the importance of each group.Comment: 10 pages, 2 figures, To be published in Physica
Consistent high-precision volatility from high-frequency data
Estimates of daily volatility are investigated. Realized volatility can be computed from returns observed over time intervals of different sizes. For simple statistical reasons, volatility estimators based on high-frequency returns have been proposed, but such estimators are found to be strongly biased as compared to volatilities of daily returns. This bias originates from microstructure effects in the price formation. For foreign exchange, the relevant microstructure effect is the incoherent price formation, which leads to a strong negative first-order auto- correlation for tick-by-tick returns and to the volatility bias. On the basis of a simple theoretical model for foreign exchange data, the incoherent term can be filtered away from the tick-by-tick price series. With filtered prices, the daily volatility can be estimated using the information contained in high-frequency data, providing a high-precision measure of volatility at any time interval.volatility, high-frequency data, foreign exchange,
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