Estimating the distribution of volatility of realized stock returns and exchange rate changes

Realized stock return volatility is modelled with a distribution based on the Laplace distribution. The moment properties of suggested volatility distribution, η(σλ), are derived. The properties of distribution correspond to the empirical regularities found in the finance literature. ML-estimator for λ is also provided. The advantage of Laplace approach lies in estimating λ from returns distribution f(xλ) directly instead of volatility distribution based on bias sensitive standard deviation estimates. The goodness-to-fit tests with 5 day standard deviations of daily HEX closing price returns in period 3.1.1983–4.3.2003, daily S&P500 closing stock index returns in period 1.3.1950–27.3.2003 and daily USD/Euro exchange rate changes in period 28.12.1978–28.2.2003 support the suggested volatility distribution model.