I'm reading about volatility. I've charted the histogram of EURUSD and I am wondering if this looks plausible? What I've charted are the 1-hour percent change returns (not log returns). I've removed 0 returns because it completely destroys the plot (you get an impulse centred on 0) and I've standardised the returns by doing
ret = (ret-mean)/std
I've added a N(0,1) density and the 5% conf intervals (at 0.025 and 0.975). The skewness is -0.12248942201701185 - pretty much symmetric. The histogram for USDCHF has newgative skew of -13 but still looks pretty much symmetric.
Legend: $\mu$ is mean, $\sigma$ is std, $\kappa$ is skew, $\gamma$ is kurtosis.