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(σ|λ), 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(x|λ) 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.